5-dimensionality-reduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reducción de dimensionalidad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn.decomposition # Módulo donde encontramos el análisis de componentes principales\n",
    "import sklearn.manifold # Módulo donde encontramos el método t-Distributed Stochastic Neighbor Embedding\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta tarea de aprendizaje no supervisado nos permite disminuir la cantidad de variables de un conjunto de datos intentando no perder información del espacio original"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importamos un conjunto de puntos organizados sobre una linea de inclinación de 30°"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Análisis de componentes principales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.143944</td>\n",
       "      <td>-0.083106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.644160</td>\n",
       "      <td>0.371906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.466565</td>\n",
       "      <td>0.269372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.054760</td>\n",
       "      <td>0.031616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.309486</td>\n",
       "      <td>-0.178682</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0 -0.143944 -0.083106\n",
       "1  0.644160  0.371906\n",
       "2  0.466565  0.269372\n",
       "3  0.054760  0.031616\n",
       "4 -0.309486 -0.178682"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line = pd.read_csv(\"data/line.csv\")\n",
    "line.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD4CAYAAADxeG0DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAQO0lEQVR4nO3dfYhc13nH8d+zq1VZOYa1sYrRWtt1XbPNi18EixWjP9omDlJDXmQ1jqOkIZAQ/dNATMLWUSWIC3XtdonbggPptjGhZKsktqWxi2M2MnExLbaw7JG0VuRN3UCsHYV4Q7KNsQZrtX76x+5od0czO29n5t4z9/sBIc2d0Z2Hi/TT0XPPOdfcXQCAePUkXQAAoDUEOQBEjiAHgMgR5AAQOYIcACK3IYkvveaaa3x4eDiJrwaAaL300ku/cvfN5ccTCfLh4WEdP348ia8GgGiZ2c8rHae1AgCRI8gBIHIEOQBEjiAHgMgR5AAQOYIcACJHkANA5AhyAIgcQQ4AkSPIASByBDkARI4gB4DIEeQAEDmCHAAiR5ADQOQIcgCIHEEOAJFrOcjNbKuZPWtmZ8zstJl9OURhAID6hHjU20VJX3X3l83sSkkvmdlRd/9JgHMDAGpoeUTu7r9w95eXf/2mpDOSBls9LwCgPkF75GY2LGmbpGMV3ttnZsfN7Pjc3FzIrwWATAsW5Gb2LkmPS7rH3X9b/r67T7j7qLuPbt68OdTXAkDmBQlyM+vTUohPuvvhEOcEANQnxKwVk/RtSWfc/aHWSwIANCLEiHyHpM9K+oCZnVj+8eEA5wUA1KHl6Yfu/l+SLEAtAIAmsLITACJHkANA5AhyAIgcQQ4AkSPIASByBDkARI4gB4DIEeQAEDmCHAAiR5ADQOQIcgCIHEEOAJEjyAEgcgQ5AESOIAeAyBHkABA5ghwAIkeQA0DkCHIAiBxBDgCRI8gBIHIEOQBEjiAHgMgR5AAQuQ1JFwAAMcvlCxqfmtG5+aK2DPRrbOeIdm8b7GgNBDkANCmXL2j/4WkVFxYlSYX5ovYfnpakjoY5rRUAaNL41MylEC8pLixqfGqmo3UQ5ADQpHPzxYaOtwtBDgBN2jLQ39DxdiHIAWCVXL6gHQ/+WNd/7SntePDHyuULVT87tnNE/X29a4719/VqbOdIu8tcg5udALCs0ZuXpWPMWgGAlFjv5mW1cN69bbDjwV2OIAeQKevN+07LzctG0SMHkBml1klhvijXSuuk1AdPy83LRgUJcjN7xMzeMLNXQpwPANqh1rzvtNy8bFSo1sp3JD0s6d8CnQ8AGlZruXyt1klabl42KkiQu/tzZjYc4lwA0Ix6ZpxsGehXoUKYr26dpOHmZaPokQPoCvUsl4+1dVJLx2atmNk+SfskaWhoqFNfC6CL5PIFHTgyrbcuLAW2SfrM+4f0N7tvqmvGSaytk1o6FuTuPiFpQpJGR0e9U98LIH4Hc9OafOF1lQeHS/ruC69Lqq9tIsXZOqmF1gqA1MrlCxo5+LS+WyHEVzt07GzXtk3qEWr64SFJz0saMbNZM/tCiPMCyK5cvqCxx07q7Yvv1Pzsort2bxvUA3tu0uBAv0zS4EC/HthzU9eNvisJNWtlb4jzAEDJ+NSMFhbr68L2mknqzrZJPWitAEilRpbF792+tY2VpB97rQDouHqec1nt5uVqq2etZBlBDqCj6t0qdmzniMYeO1mxvbLjhqs1+cXbO1NwBGitAOioep9zuXvboMY/cYuu2tR36dhAf5/+8e5bCfEyjMgBBFNPy6SRrWKzevOyUQQ5gJbl8gWNPXpCC6tmChbmixp79KSktS2TehfuoH60VgA07WBuWr+//ynd8/21IV6y8I7rvidPrzmW5YU77cKIHEBDDuamdejYWS16fXO854sLa153634nSSLIAdTUaHjXQu87LIIcQEXlOw02a/WsE7QHQQ5gjUo3LpvVY9LXP/re1k+EdRHkACQttU9KW8KGcMXGXt1/ZzY2rUoaQQ5kVGnOd61l8PXqNdPe7Vszv1w+CQQ5kEHVHtTQKMI7HQhyIANWr7gc2NSn35xfqP2bqmCjqvQhyIEuVmnk3UqI/zkBnkoEOdBFQve9SwjwdCPIgS4QcspgCS2UeBDkQORy+YK+8v0TCpHh3LyME0EORORDD/2n/ueNt9Yc6zE1HOJ9vaYrNm7Q/xUX2OukCxDkQCS2339Uv3zzwmXH32lwDiELdboPQQ6kVOiVlvS8uxdBDqRM6ACn7939CHIgBUKHd49Jn97O6DsrCHIgISHnfPf1msY/cQt974wiyIEE5PIF7T88fdnT5Juxqa9Hf7vnZkI8wwhyoAMO5qY1eex1BXrAjqSlBzZ8/aPvJcBBkAPtlMsX9JePndSFxTAJ/jsbevR3f8boG2sR5EBg7Vguz14nWA9BDgQQetaJJO244WpNfvH2oOdEdyLIgSaFGHn3mmnR/dLPgyyXRxMIcqABuXxB9z15WvPF5vf0Lukx6RufZMogWkeQA3UIGeCStLHX9PfM+0YgBDmwjoO5af37sdcb3piqmoH+Pt33MaYMIiyCHCjzmX95Xv/9v78Oek5uXKKdggS5me2S9E+SeiX9q7s/GOK8QCeEeqJ8JUwbRCe0HORm1ivpm5I+JGlW0otm9qS7/6TVcwPtFnraICNvJCHEiPw2Sa+5+88kycy+J+njkghypFLo1ZbcuETSQgT5oKSzq17PStpe/iEz2ydpnyQNDQ0F+FqgPqFnnJSwzzfSIkSQW4Vjlw113H1C0oQkjY6OtqMdCawResYJT9hBWoUI8llJW1e9vk7SuQDnBZqytEXsKRUDbnbCTUukWYggf1HSjWZ2vaSCpE9J+nSA8wINqfSE+Wb1SHro7lvpeyMKLQe5u180sy9JmtLS9MNH3P10y5UBdQj5lB2JvjfiFGQeubv/UNIPQ5wLqIWdBoG1WNmJaGy//6h++eaFYOfjCTvoFgQ5UqsdS+UlRt/oPgQ5UiV8z1v6xie5aYnuRpAjFXL5gu59/JTevhhuyuCNv3uFjn7lj4OdD0grghyJyuULOnBkWm9dWAxyPtomyCKCHB3VruXyEot2kF0EOTqiXVvFEt4AQY42Cn3jkp43UBlBjuBy+YL+6vApnQ+01wlPlgfWR5AjqFy+oLFHT2ohwJaDtE2A+hDkaNrq1kmvmRbdL/3cLB5ODDSOIEfDKu3zXQrvZkKcfb6B1hDkqEvojar6eqTxu1hxCYRAkKOmkHuecOMSCI8gxxqlvve5+aK2DPTrT/5wc1MhbiaVuizsMgi0F0GOS8oX7RTmi5psop3S39erB/bcRHADHUKQZ1wuX9Bf/8dp/eZ85SXz9d66tOXP0joBOo8gz6DQKy6Z7w0kiyDPkGZXXJZG2+UIcCAdCPIuFmKL2NIc72dfnbt0A5TWCZAuBHmXCdk2YaEOEAeCvIuEXLTDlEEgHgR5l8jlC0FCnL1OgPgQ5BE6mJvWoWNnL21StXf7Vj376lzT5+OmJRA3gjwiS1vEntDqSSeL7k2PxGmfAN2BII/Eyj7frZ2H0TfQfQjyFCrf72Rs54jGp2ZqPqyhr8cqfoaRN9DdCPKUyeUL2n94WsWFpbnfhfnimtfV9Jpp/K5b1jyhngAHsoEgT4HVI/CeCk/YKS4s1nzyzt7tW7V72yChDWQQQZ6w8hF4tbBedK/aOtlxw9X0vYEMI8g7pFLfe/e2QY1PzdRsm0gruwrSOgFQjiDvgGp9b0k6V8dS+v6+3kvBT2gDKNeTdAFZUGnUXVxY1PjUjLYM9Ff8Pb1mMi2NxHlIA4D1MCIPqFr7pNqo+9x8Uf9w962XzUrhCTsAGtFSkJvZXZLuk/RuSbe5+/EQRcVovfbJloH+irsRbhnovxTWlf4BAIB6tDoif0XSHkn/HKCWqJSPvt96+2LV9snYzpGKo+6xnSOSRO8bQEtaCnJ3PyNJZhammgjk8oU1M0ckrbv397n5IqNuAG1Fj7wB5e2TepRuZjLqBtAuNYPczJ6RdG2Ftw64+xP1fpGZ7ZO0T5KGhobqLjBN6p3zXbK6fQIA7VIzyN39jhBf5O4TkiYkaXR0dP3dn1Kq1pzvqzb1adPGDbRPAHQUrZUGVJt9Ii2NvlllCSAJLS0IMrM7zWxW0u2SnjKzqTBlpdPYzhH19/VedvyqTX3M+waQmFZnrRyRdCRQLanH7BMAaURrpUHMPgGQNuy1AgCRI8gBIHJRt1aqbVIFAFkSbZCvt0kVYQ4gS6Jtray3xzcAZEm0Qb7eHt8AkCXRBnm1J+tUOw4A3SraIK+0ypJNqgBkUbQ3O1llCQBLog1yiVWWACBF3FoBACwhyAEgcgQ5AESOIAeAyBHkABA5ghwAIkeQA0DkCHIAiBxBDgCRI8gBIHIEOQBEjiAHgMgR5AAQOYIcACJHkANA5AhyAIgcQQ4AkSPIASByBDkARI4gB4DIEeQAEDmCHAAiR5ADQOQIcgCIXEtBbmbjZvaqmZ0ysyNmNhCqMABAfVodkR+V9D53v1nSTyXtb70kAEAjWgpyd/+Ru19cfvmCpOtaLwkA0IiQPfLPS3q62ptmts/MjpvZ8bm5uYBfCwDZtqHWB8zsGUnXVnjrgLs/sfyZA5IuSpqsdh53n5A0IUmjo6PeVLUAgMvUDHJ3v2O9983sc5I+IumD7k5AA0CH1Qzy9ZjZLkn3Svojdz8fpiQAQCNa7ZE/LOlKSUfN7ISZfStATQCABrQ0Inf3PwhVCACgOazsBIDIEeQAEDmCHAAiR5ADQOQIcgCIHEEOAJEjyAEgcgQ5AESOIAeAyBHkABA5ghwAIkeQA0DkCHIAiBxBDgCRI8gBIHIEOQBEzpJ4zKaZzUn6ece/eK1rJP0q4RrSgmuxgmuxgmuxIi3X4vfcfXP5wUSCPA3M7Li7jyZdRxpwLVZwLVZwLVak/VrQWgGAyBHkABC5LAf5RNIFpAjXYgXXYgXXYkWqr0Vme+QA0C2yPCIHgK5AkANA5DId5GY2bmavmtkpMztiZgNJ15QUM7vLzE6b2TtmltppVu1kZrvMbMbMXjOzryVdT1LM7BEze8PMXkm6lqSZ2VYze9bMziz//fhy0jVVkukgl3RU0vvc/WZJP5W0P+F6kvSKpD2Snku6kCSYWa+kb0r6U0nvkbTXzN6TbFWJ+Y6kXUkXkRIXJX3V3d8t6f2S/iKNfy4yHeTu/iN3v7j88gVJ1yVZT5Lc/Yy7zyRdR4Juk/Sau//M3S9I+p6kjydcUyLc/TlJv066jjRw91+4+8vLv35T0hlJg8lWdblMB3mZz0t6OukikJhBSWdXvZ5VCv/CIjlmNixpm6RjyVZyuQ1JF9BuZvaMpGsrvHXA3Z9Y/swBLf0XarKTtXVaPdciw6zCMebmQpJkZu+S9Like9z9t0nXU67rg9zd71jvfTP7nKSPSPqgd/mk+lrXIuNmJW1d9fo6SecSqgUpYmZ9WgrxSXc/nHQ9lWS6tWJmuyTdK+lj7n4+6XqQqBcl3Whm15vZRkmfkvRkwjUhYWZmkr4t6Yy7P5R0PdVkOsglPSzpSklHzeyEmX0r6YKSYmZ3mtmspNslPWVmU0nX1EnLN72/JGlKSze0fuDup5OtKhlmdkjS85JGzGzWzL6QdE0J2iHps5I+sJwRJ8zsw0kXVY4l+gAQuayPyAEgegQ5AESOIAeAyBHkABA5ghwAIkeQA0DkCHIAiNz/A39BXaZo1tO3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(line.x,line.y)\n",
    "plt.ylim([-2.5,2.5])\n",
    "plt.xlim([-2.5,2.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ajustamos análisis de componentes principales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line = sklearn.decomposition.PCA() # Instanciamos PCA\n",
    "pca_line.fit(line) # Ajustamos el análisis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Al tener nuestro método ajustado podemos obtener los componentes (vectores propios) de nuestro análisis. Se puede observar que el valor absoluto del primer componente es el mayor, debido a que la mayor parte de nuestro conjunto de datos original se encuenta proyectado sobre el el primer componente principal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.8660254, -0.5      ],\n",
       "       [-0.5      ,  0.8660254]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line.components_ # Componentes de nuesto PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Al visualizar los componentes sobre nuestro espacio original se puede observar que el primer componente principal se sitúa precisamente sobe nuestra linea de puntos. El segundo componente principal es despreciable debido a que su varianza explicada es mínima."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD4CAYAAADxeG0DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3daXBdZX7n8e9z7r5osyRL3mQbL2DAxoAwOzQ2NGZps3cauntCJRPmxWQmqUqqMqmuqeqXU0lVaibTSXUzSQ+TNCG90KwGY2NozGbAGG9g8IKQN9lar5a7n3ueeSFLXnDj7VpXR/p9qiisew/n/n3L/tXD//yfc4y1FhER8S+n0gWIiMj5UZCLiPicglxExOcU5CIiPqcgFxHxuWAlPrShocHOmTOnEh8tIuJbH3/8cbe1tvHk1ysS5HPmzGHTpk2V+GgREd8yxrSf6nW1VkREfE5BLiLicwpyERGfU5CLiPicglxExOcU5CIiPqcgFxHxOQW5iIjPKchFRHxOQS4i4nMKchERn1OQi4j4nIJcRMTnFOQiIj6nIBcR8TkFuYiIzynIRUR87ryD3BgzyxjzpjFmpzHmU2PMn5WjMBEROTPleNSbC/yFtXazMaYK+NgYs85a+1kZzi0iIqdx3itya22HtXbz0V8PAjuBGed7XhEROTNl7ZEbY+YAVwIfnOK9J4wxm4wxm7q6usr5sSIik1rZgtwYkwSeBf7cWjtw8vvW2ietta3W2tbGxsZyfayIyKRXliA3xoQYDvGnrbW/Lcc5RUTkzJRjasUA/wzstNb+3fmXJCIiZ6McK/IbgR8Cy40xW47+c3cZzisiImfgvMcPrbXvAKYMtYiIyDnQzk4REZ9TkIuI+JyCXETE5xTkIiI+pyAXEfE5BbmIiM8pyEVEfE5BLiLicwpyERGfU5CLiPicglxExOcU5CIiPqcgFxHxOQW5iIjPKchFRHxOQS4i4nMKchERn1OQi4j4nIJcRMTnFOQiIj6nIBcR8TkFuYiIzynIRUR8TkEuIuJzwUoXICLiZ6lMgbbuNAPZItWxEHMbEtTGw2Nag1bkIiLnKJUp8Mm+PgquR108TMH1+GRfH6lMYUzrUJCLiJyjtu408XCQeDiIMWb0123d6TGtQ0EuInKOBrJFYqHACa/FQgEGssUxrUNBLiJyjqpjIbLF0gmvZYslqmOhMa1DFztFRI5zNhcv5zYk+GRfHzC8Es8WS2QKLhc3141lyVqRi4iMONuLl7XxMFe21BEOOvRlCoSDDle21I351IpW5CIiRx1/8RIY/Xdbd5orW04dzsNhPrbBfTIFuYhMKt/UOhnIFqk7aTUdCwXoG+NxwrOl1oqITBqna52Ml4uXZ6ssQW6M+bkxptMYs6Mc5xMRuRBON/c9tyFBpuCSKbhYa0d/PbchUeHKv1m5VuRPASvLdC4RkXMysuJ+64vOU16kPN3c93i5eHm2ytIjt9ZuMMbMKce5RETOxUiIx8NB6uJhssUSn+zrOyGIR1onIxcx4eutk/Fw8fJsqUcuIhPCmWyX92vr5HTGbGrFGPME8ARAS0vLWH2siEwgqUyB9/f28FFbL/miy/ymKpYvamJ2feKMJk5GWidt3Wn6MgWqYyEubh7/rZPTGbMgt9Y+CTwJ0Nraasfqc0XE/9p70ryx8wjv7+2mJ11gfmOS+mSEPUcG6RzI8b1rZ59R2wT82To5Hc2Ri8i4lcoUeP2zw7y05RC5okum6BENOuzrzZCIhqhLRMkVi2zc28OdlzePi+3ylVCu8cNngPeBi40xB4wxf1yO84rI5JXKFHhndxfrPztCMhIkFArSly6Sdz0CjmF/b4ZQwGCMoWsw59uJk3Io19TKo+U4j4jIiLbuNKlMEddaGhJhXA9i4QDZoiUW9vAKLsWSxVpLY1UUmJhtkzOhqRURGZcGskWKJY+6eIRcsURVbHisMOcWSWWLhB1DXzpHKOBw3bz6SpdbUeqRi8iYO5NbxVbHQoQCDi31cXYcSBELQ3NNBLdUYjDvUh0LnzC1MpkpyEVkTJ3Jxh0Ynvk+2JdhKF/kshk1fNmVJpUpcElzNY9eN5vFM2sr+LsYXxTkIjKmzvRWsbXxMDctaGTbgRS7O4dYPLOa+VOrWDKzdlJcwDwbCnIRKZszaZmcza1ia+Nhblk4lVsWTr2gdfudglxEzlsqU2DdZ4dZvfUQQ3mXhqowi5prOdCX4eYFjSeE+Zlu3JEzpyAXkXPW3pNm/c7DvP9lD191pomFg9QlgqTSRT7e10Om6FITC52woh4vz7mcSBTkInJW2nvSbNzbw64jg3zVm2ZKPETB9SiUwM251MbDJKNBiiWPzsE8ezoHTwjyiXq/k0pSkIvIaY2E9+7OQb7qHmLRtBoGswVCGL7syuB5EA0ZPAs9Q3lm1ccpliyD2SIW87XzTdaNOxeKglxETmnkToPrdx7mi45BZtTGwLEEjcOuziGy+RIz6qJkXY8jAzkiwQDZQoms6+GWPFzPEgsbFkxNVvq3MuEpyEXkBCMXLp//5AAHUzkA6uNh+nNFOgbyXD69mlDAoWcwR64YpiEZpiedJxAAsASA3qE8iWiQa+fWs0Tz3hecglxEgOH2yW82HWD954c50p8j4Bjq4iH6MkWsZ5kxJUHIMRzoy7GoOUkiEiRTKGGsZV5jnHAwwM6OQWpjYVrqY9y8YCrXz6tX73sMKMhFJqmRme/dRwbZtj/F1oMpUukCYAkGDIM5FwOEnACuZ+lP56lLhOgdKtCXLtBUFaGpJsZnHQPMSMZZ2FTFny5fOOm3y1eCglxkEmrvSbPus8N0D+bZ2zVEKl1gMFcEA0M5j2Q0SCRoybse4Whg+MJlwaU+EaalPo5rLVWxEDPr4jzcOkvhXWEKcpFJ4Pgdl8bA1v39VEUC9KbzRIJBBgtZvBIEAw6hgCVXLBELB+jPFCiWPGpiYXIlj4zrsXx+I/csmabwHkcU5CIT2Mgj0rYfSNFYFeOq2bV0DebZ35tm8cxaBvMetbEgyXCQTM7FGkMi4tCXdklEHBKRIB4Wx8B3ljTzSGuLAnwcUpCLTCDH97237k+x68ggkWCA2fVxrPV464tOGqqi1CcidKSyVEcD5IoezTVRuocKeJ5HIhSgOgYFt0RNPMSdl03jEbVPxjUFucgEMDIyuHZHB+mCR65YAmsJhRzybom9nYNcOqOWZCTIof4clzQlaeseYlZdgu0HUxgLFzXEKFrLwd4sLVPiXD+/gXuXTFeA+4CCXMTnUpkCa3Z0sPbTw8TCAXrTRTJ5l/68y5wpMTAQDDrs781w2fRq+rIurucxuz5JXTzEUCHJgZ4MM6YMT55cN69e4e0zCnIRH3lvTxf/9kE7X3alCTiGK2bVclFjgvaeDOGAQ00szP7eHFWxEOlCie6hIlOrIzjGMJArks4VmRIPM7MuTnUshLUwv6nqlLebFf9QkIv4xNodHfzNmp2kix7W8wgHA7y1q5v9PWlcYGoijFuyREMOpZKlKhqkL1NkuhMhHnLwPOhKF7jzsmnaqDPBKMhFxqn2njS/3rSPd3d3MZAv0ZnKEQwaEpEQgVAAzwLWciCVY1pNlJzrYU2J+mSY9u401sD06jDRUJBUrsjNC6ZqbHCCUpCLjDPtPWl+8X4br2w7TCqbJxYOEgsFyBQ9HBfAUBMPE3KgVCqRLZSoi4fpyxZpTEYZokhVNETeLbFoeg2LZ9aq7z3BKchFxoGR1feGXV0c6s+TLxbBGgKOoeBaXM8l6IBnh8cCC65HLBQgX7IkwkEWz6qh6Hr0pPNEbIA7L29ixaJmhfckoSAXqZCRme+t+/tYve0QHf15rLWUSiUKrqXkWeJhh2DQUHRLhIOGbMFSdC35oksJS7Hocdm0BNNrYtx00iPVZPJQkItUQCpT4JN9fXgebGrvo3soT9Ax5F2LZyEUcHA9j1zRozoYwODgOIZk1FLCw1rA87h0RhUPtc7khnkNCvFJTEEuMgZGnm25p3OISChAQyLMJc019GUK5IslrIVYyKFYsjjGYAIGxx0O7IJbwgJBx1AbCzOvKcnimXUsmVnDkpm1CnBRkItcSKlMgdc/O8Kzmw+QL5aYXhOlLuGw8cseskWPRCRIXTxMKBDA9RgeHfQCDOUKJEIO1kCpBIGAYV5TkkeunsXtlzYrvOUECnKRMhvZLv/6p0fY35dhKD/8JPn6ZIRUzsViSEaDtHdnmNMQp2VKnH29Gdp7MiTDAWpiQQquizGGeVOT3LqwkXuvmKELl/J7KchFyqC9J82/vv8Vr+88Qmd/jpK11MXD1MSDpAsu6XyRRDhIMhoi53pURxz6MkUCjkM8EmTZnHqCDnQOFih6HssXNfGHN8xlsR6TJmdAQS5yjkZW3q9s7+DTQwMMZos4xlLyoORBT7pAznWJh0Pkii4d/VkWxcPk3BJZ1zC7Ic60mijJaJBEOMjF0+YwvTam7fJy1hTkImchlSmw7UCKD9p6+fCrHo6k8hhjyeaLlDxLyQwfFwkaXM9SKHrEQ+AYw1DeJVt0cUsejoFLp1Vz5+Xqd8v5U5CLnIGRAH9tewefHxmiL11gIFskHHQoepaiZzEGsFCyYB0D1uIBrmepi4XxgFS2SF08zN2Lp3P7pU0KcSkLBbnINxgZG9x+oJ/BXJGOgTzGgmc9XM9iiy4m4GAMWA+MA8aDkucBEApAOOAQCDjcuqCeWxZO1ciglJ2CXOQk2w+k+OVH+9m8r4/+dJ6GqiiXz6hm95Eh+rMFaqIhYuEgg/kSYMBCNBhksORCCUIOBIAiEAuFuH5+Pf/h+jm6cCkXTFmC3BizEvhfDP/5/Sdr7f8ox3lFxkJ7T5rV2zr4sK2HzsEsvUNFIgGHTFcbhz9ay+bPP6Bt+XeZtuweosEAg4US9YkwsZDDUL6EwdJcHSWQMWRyLuGAQ30ywm2XTOWH18/R2KBccOcd5MaYAPAPwB3AAeAjY8yL1trPzvfcIhdae0+av1+/iy3tKXLFEqm+Hnq2vcngjjfIHNo9elx/Xw9NxhAMQNa1uKXh8cKgKZIulLDGcOeiJr63bLZW3jLmyrEiXwbssdZ+CWCM+XfgPkBBLuPSyG7L333RxY6DKXqG0rjt2+jbspbOHe9hPReAQDTB1KXLabn2Lkr184gHHay1VEcNoSAY6zC9LsaDV83ShUupqHIE+Qxg/3E/HwCuPfkgY8wTwBMALS0tZfhYkTMzMnGy7UA/X3WnaescoDPtEh86yOdvvED31vWU0qnhg41D/KKrqVmygplLbiUQCRMLOnhYkrEgsWCA5uooNfEwLVPius+3jAvlCHJzitfs116w9kngSYDW1tavvS9SbiMTJ2/s7GRfbwbX9ShkBjiy5Q36tq4jffBY6yRcP4uGq+5g7rUr6bNx8i4EI0GqYgEGsy71yQg3zmvUE3ZkXCpHkB8AZh3380zgUBnOK3JOUpkC7+3tZt2Ow3Rn8uzp6Ce1+yOOfLyW/l0bsaXh1kkwmqB+yW1ULV5BqHkBALHaBPlMnmDAI+AESERCfPvSaTzcOksBLuNWOYL8I2CBMWYucBD4HvBYGc4rclbe29PFMx/sY0/XEK5rmVI8zMY1z9GxeR3Fob7hg4xDYt7V1C65nUXXLyccitCbKVAseZQ8S75Qor4qyqPLZnHf0pnqe4svnHeQW2tdY8yfAq8xPH74c2vtp+ddmcgZGHnKzsYvu1m9tQOTH6Bv65vseOtl0gd3jR4XbZxF41XfpnbxcqLV9aSyLiUbJBQ0NCSjeHhcObNOz7cUXyrLHLm19hXglXKcS+R0Rp5vuX7nEboG8lRFAnTu/IDeLes4suPd0dZJIJqg9vJvMfOalUSmLwQzfDOrUNChLmFwjj6R5+qWWv5gWYvGBsW3tLNTfGPtjg5+8sYednUOUHCh1PMV+c/epGfbG7jHtU6aLr2WBTfdi5ndSrpkqI4Eh7fTW4YnUAzcdkkT376sSdvlZUJQkMu4tf1Aild3HOZIf5Z0wWXr/j4G+vro3fom/dvXUzi8Z/TYcP0spiy9nYtvvIuqhmaaqqJ0D2aJ5D1m1sUoeh7xcJD5TVXcdXmzVt8yoSjIZVwZ6Xm/v7eHtTs6qI2FaEgGeGPtGg5vWsPQrg9HN+w4kQSJRbcwY9lKYjMWks6VKEQiTIkFGcoXyLkeP7xhNquWztCqWyY0BbmMC8O7LQ/z2o7D5Esl9vVmoXcfuzev5asP1pLp7xk+8OjUSfLyFcTmXwfBMKFogHg4RHU0TMAxZF2PmVPi/NcVM7lhfmNlf2MiY0BBLhWVyhR4f28Pq7cdYmfHAEmb5tDmN/l0w0tkj7vXSbRhFtWLV1C7ZAXxukbSeRd3+E6xlEolPBtkYVMV/2XFQrVNZNJRkMuYGtku/2FbL7uODJJKF3BLLod3bOTL91+h89P3Tpg6mXHVCi6/7T5qWy5h874+HAzV0QCuV6KYt0QcmDUlwR2XNmvTjkxaCnIZE+09aV7edoj3dneTyhXBWtzudna/+woHP1pL4bipk4ZLrmXGNXcSnHsNsViMac1JgsZhTkMCY6AvXWRKIsr9Sxv5j7dcpPCWSU9BLhfMyIXLrfv7ePPzTnrTRUrpfvZ8sJaOTa8xdNyGnVhjC9Ov+TYLbriHQNUUPM9iHMgVPNIFjymJIP/93svU8xY5BQW5lN3IvU7e3tWJtYa9HX0c/OwDvnzv662T6VetYNayu4jNvJhswaO6LkrOLRHAUJsIc9vVTVwxq1ZPlhf5BgpyKatUpsDbu7v4sK2X9OGveO/V37J9w8sUBo+1TuouXkbT1d+m8fKbiEciBAMO8ZADcQfXsyTDQW6c38g9V0xX20TkDCjI5ZyNtE4OpbIM5VyS0SAdR7pYv/q3vPXyb+jYe+zZIvGpLcy5/m6mXnkHkeopdA3lcYIhqmIhIkGHkgdXzanj2rlTtNtS5CwpyOWsHf9k+epYiEQQDu34gHde/Q1b3n2DklsEIJas5pIb72TOdXfTn5yF4wRoroqSd0tkCiWqI0Gaq2NcNbuW5YuatPoWOUcKcjkj7T1pXt56kPf29tDRn6UuFmZKvoMN619i5zuryQ70AmAchwVX38wVy1dx2XXLCYYjdKRyVBeKZPMujgPVsRCPXDOLOy5t1spbpAwU5HJa2w+k+Nnv9tDek2Eg1Uvn1jf58MNXT3jCzpQZc7nnwUdZdMvdVE1ppL0ny6yGJF1DeYIBw/SaGEtb6ljQVKULlyJlpiCXE4z0vQeyRapjIaYkwvzqwza2bXyTfRtfZd+Wt489YSeWpKX1dq5b+SBVsxZx68JGQgGHuniYeDgAQGN1lBvmN6jvLXIBKchlVHtPmnWfHabkwZR4iF07P+M3//4L3lnz/An3Oqm/5FpmLltJ1YJlNNZVk6yKEgoYsgWXqfVJHAcevGqWgltkjCjIJ7njnzC/dX8vVSZP99Y3eeeVZ2n7fPvocdXNs1lw473Mvn4lKRun5FmSkSDxcICggUumVdNUE2NKMqzWicgYU5BPQsePDbZ1DZHL59n+wQbeXv0s7VvexjvaOolXVXPFrXdz5Yr7MY3z6EhlSUaDkHU5ks4TDDhcP6+ee6+YoYkTkQpSkE8ix++4DAcD9O7fzUdrn2fHhtWk+49OnRiHuUtv5OZ7Huauu+/lcNojGQ3SmIzw0VfdfN4xiAfcv3Qmj+gmVSLjgoJ8Ahu5RexHbb305wpYC+n+Pg5tXs8n61/g4J5jz8iun3ERV91xPy3XfJtoTQPTaqLkPIdk1HDHpU30pgvUxqfx0NUtap2IjDMK8glmpG2y+8ggG9t6ONSbpT4R4Kst77LljRfp2H7s4cSRRBUt19xO6+0PMP/SpUTCAfLFEoO5InnXw7Vwx6XNzK5PaOUtMo4pyCeQ9p40L245yMFUhr2dQ3R8uZvOza9xYNO60Q07GIcZi6/njvv+gItab6WtN4+1kIgEqE9GaO/J0Fwb4/qL6jUyKOITCvIJIpUp8OKWg+zd38G2t15hyxsv0Lfvi9H3a6fPYeaylcy9biXhqgYuu6geC0yvDeB5HoloCMeBO/RkeRHfUZD7UHtPmo17e+gazNFYFeXqlmpefuVVfvZ//pndmzaM3uskGEvStPQ2Ftz4Ha5sbeWr7jSOgaaaMK7n0ZsuMGtKnFVLNXUi4mcKch9JZQqs++wwL209RDwYIDy4n+c2vMyH615kKDW8Ycc4DhddeRMLb76X+PxrODzkEY+HKHmWmliIWDjInIYEUxJh7bgUmSAU5D4xcp/vlz/aRdvG19j99mqOtO0cfX/qrHncdPeDzL52JXUNzXQP5cgWSpRMjqDjkMoUWTa3TjPfIhOQgnwcOvl+JzNrwjz97Is8/a//wua3Xx/dsBNJVHHJDSv51r0PM33BYhZNr2b3kSGKrkcsNDyBctXsOr518VStvEUmMAX5OJPKFPhkXx/xcJDufbv52S+fZs3zv6avpxsY3rAzZ+mNLF1+PwuuuZUCARKRELPrE9y8oJGaWIg9nYM0VEdYMDWpABeZBBTk48DxK/Bd7YfY+tZq3njp1+zcvnX0mBlz5nPTPQ+x+OZ72ZePEg8H8BwoFEpEgh7XzaunNh7mloVTuWXh1Ar+bkRkrCnIKyyVKfDR3k62bnyLNc/9kt+tWzM6dVJVU8Ndqx5m1SOPUtNyCRY40JelxvXY2zPEkYE8s+riPHrtbPW9RSYxBfkYObnvPbchwf69X/A3f/9TVj/3a/p6uoDhqZPF193K7au+y2OPPEQkGiVTcAkHHeY2JNh2IMWezkEun1Gr1omIAAryMXF835vcIL/4t1/z0m+eYfdn20aPuWjBxax65DG+dfeD9Ng4xZJHOBIhU3DJFFwubq5T60RETklBPgZ2daT4+O3XWfPcL3nr9TW4xaOtk+oaVq56iJUPfo/W1mswxgCQHMjRPZSnL1OgOhYaDXERkVNRkJfRye2TzOE2fvvLp/m//+9fRqdOHMfhptvuYNXDj3LFTStYNr+ZT/b1kS2WiIUCZIslHAfuvFwPJhaRM3NeQW6MeQT4MbAIWGat3VSOovxopH1SGOrnzVee5/lfPc0Xnx5rncyZv5D7v/t97n3gu0xtnjba966Nh7mypY627rRW4CJyTs53Rb4DeBD4WRlq8ZXjV9+xIKxf9xprn/8V77zx2tdaJ//pT/4I0ziPRCRELBQ4oe8NHA1zBbeInJvzCnJr7U5gtLc7GYw843LLvhTpw1+y9Y0XWPvis6NTJyOtk/seeYxbb19JxnO49eKpo8GvVbeIlJt65GchlSnwu617+O1vfsXbq5/lqy92jL43fc58br7nIf7k8ceZ2jwNgEzBpTriAFp1i8iFc9ogN8a8DjSf4q0fWWtfONMPMsY8ATwB0NLScsYFjgfFYpE1a9bwP//xSTasP9Y6SVTVcP0d32H5qu9y8/XXsnlfH8kpDVhryRZLJ7RPREQulNMGubX29nJ8kLX2SeBJgNbWVluOc15o27dv56mnnuIXv/gFnZ2dwHDr5MobbuPmux/mhuV3EgpHGMgVCQUDLG2pIxx01D4RkTGl1spJuru7eeaZZ3jqqafYvHnz6OuLFi3ijvv/gDu+8xBTGpv54vAgnhMgV3QJOoZMweXKFgW3iIy98x0/fAD430AjsNoYs8Vae2dZKhtDI62Tp556ipdeeoni0dZJbW0tjz76KI8//jjXXHMN/dkin+zrI+AYFjYlaetJ0zuUZ2lLnbbKi0jFnO/UynPAc2WqZcz9vtbJXXfdxeOPP86qVauIRqOjxx8/850rlrhseg1zGxIKcBGpqEnXWvmm1snjjz/OD37wA6ZPn/57/3tNn4jIeDMpgvxMWyeTaR5eRCaOCR3kZ9s6ERHxI18H+anu8e1mBs6rdSIi4je+DfLj7/GdDBnWv/YKL/76GTb+bu0JrZPHHnuMxx9/nNbWVrVORGRC8k2Qr1u3jg0bNvDjH/+YQCBAW3eaQ227WPvcL3n5uV/R233sXidqnYjIZOKLIH/llVe47777cF2XBx54gHfffZef/PSf2HXyE3YefpSbVj7AQ7csqWC1IiJja9wH+TvvvMPDDz+M67osWLCA6667brR1UlVdw933P8J9jzzGZVdcSbZYIhx0KlyxiMjYGtdBvm7dOr7zne+Qz+cB2L1792jr5JFHf8D0JTdSW5UcfbKOblIlIpPRuA7y73//+6MhPqK+vp4nnniC+++/X/f4FhFhnAf5X/7lX/Lzn/+cUChEf38/HR0ddHV10dbWBmiXpYgIgLF27O8o29raajdtOvvHe3qex9DQENXV1RegKhGR8c0Y87G1tvXk1311ZdBxHIW4iMhJfBXkIiLydQpyERGfU5CLiPicglxExOcU5CIiPqcgFxHxOQW5iIjPKchFRHxOQS4i4nMKchERn1OQi4j4nIJcRMTnFOQiIj6nIBcR8TkFuYiIzynIRUR8TkEuIuJzCnIREZ9TkIuI+JyCXETE5xTkIiI+pyAXEfG58wpyY8zfGmM+N8ZsM8Y8Z4ypLVdhIiJyZs53Rb4OuNxauwTYBfz1+ZckIiJn47yC3Fq71lrrHv1xIzDz/EsSEZGzUc4e+R8Br/6+N40xTxhjNhljNnV1dZXxY0VEJrfg6Q4wxrwONJ/irR9Za184esyPABd4+vedx1r7JPAkQGtrqz2nakVE5GtOG+TW2tu/6X1jzB8C9wIrrLUKaBGRMXbaIP8mxpiVwF8Bt1prM+UpSUREzsb59sh/AlQB64wxW4wxPy1DTSIichbOa0VurZ1frkJEROTcaGeniIjPKchFRHxOQS4i4nMKchERn1OQi4j4nIJcRMTnFOQiIj6nIBcR8TkFuYiIzynIRUR8TkEuIuJzCnIREZ9TkIuI+JyCXETE5xTkIiI+pyAXEfE5U4nHbBpjuoD2Mf/gEzUA3RWuYbzQd3GMvotj9F0cM16+i9nW2saTX6xIkI8HxphN1trWStcxHui7OEbfxTH6Lo4Z79+FWisiIj6nIBcR8bnJHORPVrqAcUTfxTH6Lo7Rd3HMuP4uJm2PXERkopjMK3IRkQlBQS4i4nOTOsiNMX9rjPncGLPNGPOcMaa20jVVijHmEWPMp8YYzxgzbi3O/ukAAAIQSURBVMesLiRjzEpjzBfGmD3GmP9W6XoqxRjzc2NMpzFmR6VrqTRjzCxjzJvGmJ1H/378WaVrOpVJHeTAOuBya+0SYBfw1xWup5J2AA8CGypdSCUYYwLAPwB3AZcCjxpjLq1sVRXzFLCy0kWMEy7wF9baRcB1wH8ej38uJnWQW2vXWmvdoz9uBGZWsp5KstbutNZ+Uek6KmgZsMda+6W1tgD8O3BfhWuqCGvtBqC30nWMB9baDmvt5qO/HgR2AjMqW9XXTeogP8kfAa9WugipmBnA/uN+PsA4/AsrlWOMmQNcCXxQ2Uq+LljpAi40Y8zrQPMp3vqRtfaFo8f8iOH/hXp6LGsba2fyXUxi5hSvaTZXADDGJIFngT+31g5Uup6TTfggt9be/k3vG2P+ELgXWGEn+FD96b6LSe4AMOu4n2cChypUi4wjxpgQwyH+tLX2t5Wu51QmdWvFGLMS+CtglbU2U+l6pKI+AhYYY+YaY8LA94AXK1yTVJgxxgD/DOy01v5dpev5fSZ1kAM/AaqAdcaYLcaYn1a6oEoxxjxgjDkAXA+sNsa8VumaxtLRi95/CrzG8AWtX1lrP61sVZVhjHkGeB+42BhzwBjzx5WuqYJuBH4ILD+aEVuMMXdXuqiTaYu+iIjPTfYVuYiI7ynIRUR8TkEuIuJzCnIREZ9TkIuI+JyCXETE5xTkIiI+9/8B+OTt52JoZBAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(line.x,line.y, alpha=0.2)\n",
    "plt.ylim([-2.5,2.5])\n",
    "plt.xlim([-2.5,2.5])\n",
    "for length, vector in zip(pca_line.explained_variance_, pca_line.components_):\n",
    "    ax=plt.gca()\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', pca_line.mean_ + v, pca_line.mean_, arrowprops=arrowprops)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora importamos exactamente la misma linea anterior, pero a esta se le agregó ruido."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.159395</td>\n",
       "      <td>-0.056345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.673869</td>\n",
       "      <td>0.320449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.484614</td>\n",
       "      <td>0.238111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.120637</td>\n",
       "      <td>-0.082488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.228911</td>\n",
       "      <td>-0.318242</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0 -0.159395 -0.056345\n",
       "1  0.673869  0.320449\n",
       "2  0.484614  0.238111\n",
       "3  0.120637 -0.082488\n",
       "4 -0.228911 -0.318242"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line_noised = pd.read_csv(\"data/line_noised.csv\")\n",
    "line_noised.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora contamos con nuestra nube de puntos, pero hay que notar que tiene exactamente la misma inclinación que el caso anterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(line_noised.x,line_noised.y)\n",
    "plt.ylim([-2.5,2.5])\n",
    "plt.xlim([-2.5,2.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ajustamos PCA sobre nuestra nube de puntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line_noised = sklearn.decomposition.PCA(n_components=2)\n",
    "pca_line_noised.fit(line_noised)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observamos que los vectores propios son iguales a los anteriores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.85937911, -0.51133898],\n",
       "       [-0.51133898,  0.85937911]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line_noised.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Además el 88% de la varianza de nuestro ocnjunto de datos está explicada por el primer componente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.88459308, 0.0342513 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line_noised.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los vectores propios son exactamente los mismos que en el caso anterior, pero ahora el segundo componente sí nos explica varianza."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(line_noised.x,line_noised.y, alpha=0.2)\n",
    "plt.ylim([-2.5,2.5])\n",
    "plt.xlim([-2.5,2.5])\n",
    "for length, vector in zip(pca_line_noised.explained_variance_, pca_line_noised.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    ax=plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', pca_line_noised.mean_ + v, pca_line_noised.mean_, arrowprops=arrowprops)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.85937911, -0.51133898],\n",
       "       [-0.51133898,  0.85937911]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line_noised.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Así extraemos el primer componente principal desde PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.85937911, -0.51133898]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_line_noised.components_[0].reshape(1,-1) # Debemos hacer reshape del componente para que siga teniendo la forma de una fila"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proyectamos nuestro conjunto de datos sobre el primer componente a través de un producto punto."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "line_noised_reduced = np.dot( \n",
    "    line_noised.values, \n",
    "    pca_line_noised.components_[0].reshape(1,-1).T # Debemos trasponer nuestro componente principal para realizar el producto punto\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ahora nuestro conjunto de datos reducidos tiene sólo una columna."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.16579193],\n",
       "       [-0.74296694],\n",
       "       [-0.53822228],\n",
       "       [-0.06149407],\n",
       "       [ 0.35945078],\n",
       "       [ 1.12917482],\n",
       "       [ 0.26836244],\n",
       "       [ 0.36697232],\n",
       "       [ 0.54100028],\n",
       "       [-1.37937048],\n",
       "       [ 0.53854007],\n",
       "       [ 0.88952878],\n",
       "       [ 0.91589936],\n",
       "       [-0.21927819],\n",
       "       [ 1.500758  ],\n",
       "       [-0.59893964],\n",
       "       [ 1.27609483],\n",
       "       [-1.79808335],\n",
       "       [ 0.06594636],\n",
       "       [ 0.40518292],\n",
       "       [-2.25247149],\n",
       "       [ 1.07526223],\n",
       "       [ 1.9214896 ],\n",
       "       [-0.40317477],\n",
       "       [-1.38661375],\n",
       "       [-0.71657911],\n",
       "       [-0.29879262],\n",
       "       [-0.85756776],\n",
       "       [-0.05946076],\n",
       "       [ 0.46699175],\n",
       "       [ 0.26860771],\n",
       "       [ 0.61602583],\n",
       "       [ 0.36123448],\n",
       "       [-0.71861418],\n",
       "       [-0.48978715],\n",
       "       [-0.82226191],\n",
       "       [ 0.69738065],\n",
       "       [-0.27301133],\n",
       "       [ 1.14002492],\n",
       "       [-0.15840394],\n",
       "       [-1.28572116],\n",
       "       [-1.20780254],\n",
       "       [-0.28763807],\n",
       "       [ 0.96046066],\n",
       "       [-0.29185852],\n",
       "       [-0.64418896],\n",
       "       [ 0.15998887],\n",
       "       [-0.2629046 ],\n",
       "       [-1.15858139],\n",
       "       [-0.63389853],\n",
       "       [-2.46987082],\n",
       "       [ 0.01129608],\n",
       "       [-0.62735498],\n",
       "       [ 0.22273343],\n",
       "       [-0.12980106],\n",
       "       [ 1.08959926],\n",
       "       [ 0.35432006],\n",
       "       [-0.65634786],\n",
       "       [-0.24536826],\n",
       "       [ 0.40998674],\n",
       "       [-1.14792123],\n",
       "       [ 1.18928168],\n",
       "       [ 0.47366093],\n",
       "       [ 0.66935699],\n",
       "       [-0.38585002],\n",
       "       [ 0.11785904],\n",
       "       [-0.36632614],\n",
       "       [-0.7219623 ],\n",
       "       [-1.58494056],\n",
       "       [-0.33047009],\n",
       "       [ 0.33910052],\n",
       "       [-0.33972037],\n",
       "       [-0.8927292 ],\n",
       "       [ 0.57124872],\n",
       "       [ 0.48032568],\n",
       "       [-0.01238975],\n",
       "       [-0.33854526],\n",
       "       [ 1.36733354],\n",
       "       [-0.04192026],\n",
       "       [-0.03976649],\n",
       "       [ 0.62620688],\n",
       "       [ 0.39126109],\n",
       "       [-0.10732841],\n",
       "       [-1.04264607],\n",
       "       [ 0.03174948],\n",
       "       [-0.69894127],\n",
       "       [ 0.27239101],\n",
       "       [-1.33018592],\n",
       "       [-1.12603449],\n",
       "       [-1.07296921],\n",
       "       [-1.28339348],\n",
       "       [-0.83426316],\n",
       "       [ 2.04447345],\n",
       "       [-0.76061551],\n",
       "       [ 0.02033971],\n",
       "       [-1.79096424],\n",
       "       [ 0.26007205],\n",
       "       [-0.04323   ],\n",
       "       [ 1.47372029],\n",
       "       [ 2.00134233],\n",
       "       [-0.33709061],\n",
       "       [ 0.52405195],\n",
       "       [-0.30249418],\n",
       "       [ 1.22827565],\n",
       "       [ 0.73908348],\n",
       "       [-0.0975092 ],\n",
       "       [-1.41725043],\n",
       "       [-1.83762447],\n",
       "       [-2.10834721],\n",
       "       [-0.16631611],\n",
       "       [-1.11967179],\n",
       "       [ 0.97642179],\n",
       "       [-1.38654576],\n",
       "       [-1.77040696],\n",
       "       [-1.74768072],\n",
       "       [-0.62024419],\n",
       "       [ 0.56324162],\n",
       "       [-1.20500128],\n",
       "       [ 0.39439136],\n",
       "       [ 0.15310422],\n",
       "       [ 0.33760575],\n",
       "       [ 0.06190716],\n",
       "       [ 0.39808211],\n",
       "       [ 0.01369552],\n",
       "       [-0.89182514],\n",
       "       [ 1.79187235],\n",
       "       [ 0.71349436],\n",
       "       [ 0.20120834],\n",
       "       [-1.82955751],\n",
       "       [-1.23804673],\n",
       "       [ 0.01682846],\n",
       "       [-1.18435483],\n",
       "       [-0.55633332],\n",
       "       [ 0.09571908],\n",
       "       [-0.54616928],\n",
       "       [-0.23466529],\n",
       "       [-0.56050499],\n",
       "       [ 0.91528061],\n",
       "       [ 0.48926714],\n",
       "       [ 1.35263622],\n",
       "       [ 0.40380682],\n",
       "       [-1.16475249],\n",
       "       [ 0.01061101],\n",
       "       [-0.17376271],\n",
       "       [-0.64843749],\n",
       "       [ 0.11941294],\n",
       "       [-0.92097282],\n",
       "       [ 0.77687317],\n",
       "       [-1.23733719],\n",
       "       [-0.43210524],\n",
       "       [-0.72047943],\n",
       "       [-0.66562324],\n",
       "       [ 1.31789604],\n",
       "       [-0.53129375],\n",
       "       [ 1.28330709],\n",
       "       [-1.01693648],\n",
       "       [ 1.35297902],\n",
       "       [-1.11762951],\n",
       "       [-0.6241883 ],\n",
       "       [-1.13148366],\n",
       "       [ 1.49359078],\n",
       "       [-0.59620611],\n",
       "       [-0.29578184],\n",
       "       [ 2.54986947],\n",
       "       [ 0.15059937],\n",
       "       [ 1.67803786],\n",
       "       [-1.34054534],\n",
       "       [ 1.30350606],\n",
       "       [ 0.39880256],\n",
       "       [ 0.76957985],\n",
       "       [-1.96544593],\n",
       "       [ 1.60857814],\n",
       "       [ 0.65334639],\n",
       "       [ 0.98550492],\n",
       "       [-0.72734267],\n",
       "       [-0.40254842],\n",
       "       [ 0.6909346 ],\n",
       "       [-0.20129417],\n",
       "       [ 0.06549919],\n",
       "       [-1.40754403],\n",
       "       [-1.07171186],\n",
       "       [-0.18459898],\n",
       "       [ 0.97526236],\n",
       "       [-0.23725108],\n",
       "       [ 0.58733406],\n",
       "       [ 0.64885519],\n",
       "       [ 0.84909467],\n",
       "       [ 1.47438683],\n",
       "       [ 0.94777022],\n",
       "       [-0.84087928],\n",
       "       [-0.91455492],\n",
       "       [-0.96578439],\n",
       "       [-1.82343198],\n",
       "       [ 0.16326036],\n",
       "       [ 0.20019368],\n",
       "       [ 0.31531794],\n",
       "       [ 0.34135831],\n",
       "       [ 1.21821197],\n",
       "       [-0.27917901],\n",
       "       [-0.55491555]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line_noised_reduced"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para recrear el conjunto de datos original desde el reducido debemos realizar el producto punto de nuestro conjunto de datos reducido con el primer componente principal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "line_noised_original = np.dot(line_noised_reduced, pca_line_noised.components_[0].reshape(1,-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora tenemos nuestro conjunto de datos original recreado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.14247812, -0.08477588],\n",
       "       [ 0.63849026,  0.37990795],\n",
       "       [ 0.46253698,  0.27521403],\n",
       "       [ 0.05284672,  0.03144431],\n",
       "       [-0.30890449, -0.18380119],\n",
       "       [-0.97038925, -0.57739109],\n",
       "       [-0.23062508, -0.13722418],\n",
       "       [-0.31536835, -0.18764725],\n",
       "       [-0.46492434, -0.27663453],\n",
       "       [ 1.18540217,  0.70532589],\n",
       "       [-0.46281008, -0.27537653],\n",
       "       [-0.76444245, -0.45485074],\n",
       "       [-0.78710477, -0.46833504],\n",
       "       [ 0.1884431 ,  0.11212549],\n",
       "       [-1.28972007, -0.76739606],\n",
       "       [ 0.51471622,  0.30626118],\n",
       "       [-1.09664923, -0.65251702],\n",
       "       [ 1.54523527,  0.9194301 ],\n",
       "       [-0.05667292, -0.03372094],\n",
       "       [-0.34820573, -0.20718582],\n",
       "       [ 1.93572694,  1.15177646],\n",
       "       [-0.9240579 , -0.54982349],\n",
       "       [-1.65128802, -0.98253253],\n",
       "       [ 0.34647998,  0.20615898],\n",
       "       [ 1.19162689,  0.70902965],\n",
       "       [ 0.61581311,  0.36641483],\n",
       "       [ 0.25677614,  0.15278431],\n",
       "       [ 0.73697582,  0.43850782],\n",
       "       [ 0.05109934,  0.0304046 ],\n",
       "       [-0.40132295, -0.23879108],\n",
       "       [-0.23083585, -0.13734959],\n",
       "       [-0.52939973, -0.31499802],\n",
       "       [-0.31043737, -0.18471327],\n",
       "       [ 0.61756201,  0.36745544],\n",
       "       [ 0.42091284,  0.25044726],\n",
       "       [ 0.70663471,  0.42045456],\n",
       "       [-0.59931436, -0.35659791],\n",
       "       [ 0.23462024,  0.13960134],\n",
       "       [-0.9797136 , -0.58293918],\n",
       "       [ 0.13612904,  0.08099811],\n",
       "       [ 1.1049219 ,  0.65743934],\n",
       "       [ 1.03796027,  0.61759651],\n",
       "       [ 0.24719015,  0.14708056],\n",
       "       [-0.82539983, -0.49112097],\n",
       "       [ 0.25081711,  0.14923863],\n",
       "       [ 0.55360253,  0.32939892],\n",
       "       [-0.13749109, -0.08180855],\n",
       "       [ 0.22593472,  0.13443337],\n",
       "       [ 0.99566064,  0.59242782],\n",
       "       [ 0.54475915,  0.32413702],\n",
       "       [ 2.12255538,  1.26294122],\n",
       "       [-0.00970762, -0.00577613],\n",
       "       [ 0.53913576,  0.32079105],\n",
       "       [-0.19141246, -0.11389228],\n",
       "       [ 0.11154832,  0.06637234],\n",
       "       [-0.93637884, -0.55715457],\n",
       "       [-0.30449526, -0.18117766],\n",
       "       [ 0.56405164,  0.33561624],\n",
       "       [ 0.21086435,  0.12546635],\n",
       "       [-0.35233404, -0.2096422 ],\n",
       "       [ 0.98649952,  0.58697686],\n",
       "       [-1.02204383, -0.60812607],\n",
       "       [-0.40705431, -0.2422013 ],\n",
       "       [-0.57523142, -0.34226832],\n",
       "       [ 0.33159144,  0.19730015],\n",
       "       [-0.1012856 , -0.06026592],\n",
       "       [ 0.31481303,  0.18731683],\n",
       "       [ 0.62043931,  0.36916746],\n",
       "       [ 1.3620648 ,  0.81044188],\n",
       "       [ 0.28399909,  0.16898224],\n",
       "       [-0.2914159 , -0.17339531],\n",
       "       [ 0.29194859,  0.17371227],\n",
       "       [ 0.76719283,  0.45648724],\n",
       "       [-0.49091922, -0.29210174],\n",
       "       [-0.41278186, -0.24560924],\n",
       "       [ 0.01064749,  0.00633536],\n",
       "       [ 0.29093872,  0.17311139],\n",
       "       [-1.17505788, -0.69917093],\n",
       "       [ 0.0360254 ,  0.02143546],\n",
       "       [ 0.03417449,  0.02033416],\n",
       "       [-0.53814911, -0.32020398],\n",
       "       [-0.33624161, -0.20006704],\n",
       "       [ 0.09223579,  0.0548812 ],\n",
       "       [ 0.89602825,  0.53314557],\n",
       "       [-0.02728484, -0.01623475],\n",
       "       [ 0.60065553,  0.35739591],\n",
       "       [-0.23408714, -0.13928414],\n",
       "       [ 1.14313399,  0.6801759 ],\n",
       "       [ 0.96769051,  0.57578532],\n",
       "       [ 0.92208732,  0.54865098],\n",
       "       [ 1.10292154,  0.65624911],\n",
       "       [ 0.71694833,  0.42659127],\n",
       "       [-1.75697777, -1.04541896],\n",
       "       [ 0.65365708,  0.38893235],\n",
       "       [-0.01747952, -0.01040049],\n",
       "       [ 1.53911726,  0.91578982],\n",
       "       [-0.22350049, -0.13298498],\n",
       "       [ 0.03715096,  0.02210519],\n",
       "       [-1.26648443, -0.75357062],\n",
       "       [-1.71991179, -1.02336434],\n",
       "       [ 0.28968863,  0.17236757],\n",
       "       [-0.4503593 , -0.26796819],\n",
       "       [ 0.25995718,  0.15467706],\n",
       "       [-1.05555444, -0.62806521],\n",
       "       [-0.6351529 , -0.37792219],\n",
       "       [ 0.08379737,  0.04986025],\n",
       "       [ 1.21795541,  0.72469538],\n",
       "       [ 1.57921608,  0.93964901],\n",
       "       [ 1.81186955,  1.0780801 ],\n",
       "       [ 0.14292859,  0.08504391],\n",
       "       [ 0.96222255,  0.57253183],\n",
       "       [-0.83911649, -0.49928252],\n",
       "       [ 1.19156846,  0.70899489],\n",
       "       [ 1.52145075,  0.90527808],\n",
       "       [ 1.5019203 ,  0.89365727],\n",
       "       [ 0.5330249 ,  0.31715503],\n",
       "       [-0.48403808, -0.28800739],\n",
       "       [ 1.03555292,  0.61616412],\n",
       "       [-0.33893169, -0.20166767],\n",
       "       [-0.13157457, -0.07828816],\n",
       "       [-0.29013133, -0.17263098],\n",
       "       [-0.05320172, -0.03165555],\n",
       "       [-0.34210345, -0.2035549 ],\n",
       "       [-0.01176964, -0.00700305],\n",
       "       [ 0.7664159 ,  0.45602495],\n",
       "       [-1.53989766, -0.91625417],\n",
       "       [-0.61316215, -0.36483748],\n",
       "       [-0.17291425, -0.10288567],\n",
       "       [ 1.5722835 ,  0.93552406],\n",
       "       [ 1.0639515 ,  0.63306155],\n",
       "       [-0.01446202, -0.00860505],\n",
       "       [ 1.0178098 ,  0.60560679],\n",
       "       [ 0.47810123,  0.28447491],\n",
       "       [-0.08225898, -0.0489449 ],\n",
       "       [ 0.46936647,  0.27927764],\n",
       "       [ 0.20166644,  0.11999351],\n",
       "       [ 0.48168628,  0.28660805],\n",
       "       [-0.78657304, -0.46801865],\n",
       "       [-0.42046596, -0.25018136],\n",
       "       [-1.16242731, -0.69165562],\n",
       "       [-0.34702314, -0.20648216],\n",
       "       [ 1.00096396,  0.59558334],\n",
       "       [-0.00911888, -0.00542582],\n",
       "       [ 0.14932804,  0.08885164],\n",
       "       [ 0.55725363,  0.33157136],\n",
       "       [-0.10262099, -0.06106049],\n",
       "       [ 0.7914648 ,  0.4709293 ],\n",
       "       [-0.66762857, -0.39724553],\n",
       "       [ 1.06334173,  0.63269873],\n",
       "       [ 0.37134222,  0.22095225],\n",
       "       [ 0.61916497,  0.36840922],\n",
       "       [ 0.57202271,  0.34035911],\n",
       "       [-1.13257233, -0.67389161],\n",
       "       [ 0.45658275,  0.2716712 ],\n",
       "       [-1.1028473 , -0.65620493],\n",
       "       [ 0.87393396,  0.51999926],\n",
       "       [-1.16272191, -0.69183091],\n",
       "       [ 0.96046746,  0.57148753],\n",
       "       [ 0.53641439,  0.31917181],\n",
       "       [ 0.97237342,  0.57857169],\n",
       "       [-1.28356072, -0.76373118],\n",
       "       [ 0.51236707,  0.30486342],\n",
       "       [ 0.25418874,  0.15124478],\n",
       "       [-2.19130455, -1.30384764],\n",
       "       [-0.12942195, -0.07700733],\n",
       "       [-1.44207068, -0.85804616],\n",
       "       [ 1.15203666,  0.68547308],\n",
       "       [-1.12020587, -0.66653345],\n",
       "       [-0.34272259, -0.20392329],\n",
       "       [-0.66136085, -0.39351617],\n",
       "       [ 1.68906317,  1.00500911],\n",
       "       [-1.38237845, -0.8225287 ],\n",
       "       [-0.56147224, -0.33408147],\n",
       "       [-0.84692234, -0.50392707],\n",
       "       [ 0.6250631 ,  0.37191866],\n",
       "       [ 0.3459417 ,  0.2058387 ],\n",
       "       [-0.59377476, -0.35330179],\n",
       "       [ 0.172988  ,  0.10292955],\n",
       "       [-0.05628864, -0.03349229],\n",
       "       [ 1.20961393,  0.71973212],\n",
       "       [ 0.92100678,  0.54800804],\n",
       "       [ 0.1586405 ,  0.09439265],\n",
       "       [-0.8381201 , -0.49868966],\n",
       "       [ 0.20388862,  0.12131572],\n",
       "       [-0.50474262, -0.3003268 ],\n",
       "       [-0.5576126 , -0.33178495],\n",
       "       [-0.72969422, -0.4341752 ],\n",
       "       [-1.26705724, -0.75391145],\n",
       "       [-0.81449392, -0.48463185],\n",
       "       [ 0.72263408,  0.42997435],\n",
       "       [ 0.78594939,  0.46764758],\n",
       "       [ 0.82997493,  0.4938432 ],\n",
       "       [ 1.56701935,  0.93239184],\n",
       "       [-0.14030254, -0.08348138],\n",
       "       [-0.17204227, -0.10236683],\n",
       "       [-0.27097765, -0.16123435],\n",
       "       [-0.2933562 , -0.17454981],\n",
       "       [-1.04690592, -0.62291926],\n",
       "       [ 0.23992061,  0.14275511],\n",
       "       [ 0.47688283,  0.28374995]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line_noised_original"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos observar que el conjunto de datos recreado es sólo una linea, porque perdemos la varianza que explica el segundo componente principal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(line_noised_original[:,0],line_noised_original[:,1])\n",
    "plt.ylim([-2.5,2.5])\n",
    "plt.xlim([-2.5,2.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST es un conjunto de datos de imágenes de números manuscritos. Cada fila del conjunto de datos contiene los 64 pixeles de cada imagen junto con el número al cual pertenece."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pixel_0_0</th>\n",
       "      <th>pixel_0_1</th>\n",
       "      <th>pixel_0_2</th>\n",
       "      <th>pixel_0_3</th>\n",
       "      <th>pixel_0_4</th>\n",
       "      <th>pixel_0_5</th>\n",
       "      <th>pixel_0_6</th>\n",
       "      <th>pixel_0_7</th>\n",
       "      <th>pixel_1_0</th>\n",
       "      <th>pixel_1_1</th>\n",
       "      <th>...</th>\n",
       "      <th>pixel_6_7</th>\n",
       "      <th>pixel_7_0</th>\n",
       "      <th>pixel_7_1</th>\n",
       "      <th>pixel_7_2</th>\n",
       "      <th>pixel_7_3</th>\n",
       "      <th>pixel_7_4</th>\n",
       "      <th>pixel_7_5</th>\n",
       "      <th>pixel_7_6</th>\n",
       "      <th>pixel_7_7</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 65 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   pixel_0_0  pixel_0_1  pixel_0_2  pixel_0_3  pixel_0_4  pixel_0_5  \\\n",
       "0        0.0        0.0        5.0       13.0        9.0        1.0   \n",
       "1        0.0        0.0        0.0       12.0       13.0        5.0   \n",
       "2        0.0        0.0        0.0        4.0       15.0       12.0   \n",
       "3        0.0        0.0        7.0       15.0       13.0        1.0   \n",
       "4        0.0        0.0        0.0        1.0       11.0        0.0   \n",
       "\n",
       "   pixel_0_6  pixel_0_7  pixel_1_0  pixel_1_1  ...  pixel_6_7  pixel_7_0  \\\n",
       "0        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "1        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "2        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "3        0.0        0.0        0.0        8.0  ...        0.0        0.0   \n",
       "4        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "\n",
       "   pixel_7_1  pixel_7_2  pixel_7_3  pixel_7_4  pixel_7_5  pixel_7_6  \\\n",
       "0        0.0        6.0       13.0       10.0        0.0        0.0   \n",
       "1        0.0        0.0       11.0       16.0       10.0        0.0   \n",
       "2        0.0        0.0        3.0       11.0       16.0        9.0   \n",
       "3        0.0        7.0       13.0       13.0        9.0        0.0   \n",
       "4        0.0        0.0        2.0       16.0        4.0        0.0   \n",
       "\n",
       "   pixel_7_7  label  \n",
       "0        0.0      0  \n",
       "1        0.0      1  \n",
       "2        0.0      2  \n",
       "3        0.0      3  \n",
       "4        0.0      4  \n",
       "\n",
       "[5 rows x 65 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist = pd.read_csv(\"data/mnist.csv\")\n",
    "mnist.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El conjunto de datos contiene 1797 imágenes y 65 atributos (pixeles + etiqueta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 65)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Así se ve el conjunto de datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x648 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs = plt.subplots(8,8,figsize=(9, 9),subplot_kw={'xticks':[], 'yticks':[]})\n",
    "\n",
    "for i,ax in enumerate(axs.flat):\n",
    "    ax.imshow(\n",
    "        mnist.iloc[i,:-1].values.reshape(8,-1),\n",
    "        cmap=\"gray\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ajustemos un PCA sobre el conjunto de datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA()"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mnist = sklearn.decomposition.PCA()\n",
    "pca_mnist.fit(mnist.iloc[:,:-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtenemos una matriz con 64 componentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 64)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mnist.components_.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Así se ve el primer componente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.77484909e-19, -1.73094651e-02, -2.23428835e-01, -1.35913304e-01,\n",
       "       -3.30323092e-02, -9.66340844e-02, -8.32943805e-03,  2.26900082e-03,\n",
       "       -3.20516495e-04, -1.19308905e-01, -2.44451676e-01,  1.48512745e-01,\n",
       "       -4.67319410e-02, -2.17740744e-01, -1.48136776e-02,  4.47779518e-03,\n",
       "       -4.94136398e-05, -7.95419375e-02,  8.33951454e-02,  2.15915342e-01,\n",
       "       -1.72126801e-01, -1.63712098e-01,  2.86444452e-02,  4.23251803e-03,\n",
       "        9.85488574e-05,  6.42319144e-02,  2.54093316e-01, -3.56771026e-02,\n",
       "       -2.09462569e-01, -4.31311420e-02,  5.13118688e-02,  2.13422732e-04,\n",
       "       -0.00000000e+00,  1.59950883e-01,  3.68690774e-01,  1.64406827e-01,\n",
       "        8.52007908e-02,  3.72982855e-02,  2.15866980e-02, -0.00000000e+00,\n",
       "        1.28865585e-03,  1.06945287e-01,  3.03067457e-01,  2.47813041e-01,\n",
       "        2.09637296e-01,  1.22325219e-02, -3.69458497e-02,  1.61485028e-03,\n",
       "        6.93023548e-04, -8.35144239e-03, -5.58598986e-02,  9.30534169e-02,\n",
       "        1.07387720e-01, -1.37734565e-01, -6.32879466e-02,  9.61671077e-04,\n",
       "        9.55079131e-06, -1.40786840e-02, -2.35675488e-01, -1.41225588e-01,\n",
       "       -9.15964553e-03, -8.94184677e-02, -3.65977111e-02, -1.14684954e-02])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mnist.components_[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x648 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs = plt.subplots(8,8,figsize=(9, 9),subplot_kw={'xticks':[], 'yticks':[]})\n",
    "\n",
    "for i,ax in enumerate(axs.flat):\n",
    "    ax.imshow(\n",
    "        pca_mnist.components_[i].reshape(8,-1),\n",
    "        cmap=\"gray\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Acá podemos ver cuánta varianza explica cada uno de los 64 componentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.48905936e-01, 1.36187712e-01, 1.17945938e-01, 8.40997942e-02,\n",
       "       5.78241466e-02, 4.91691032e-02, 4.31598701e-02, 3.66137258e-02,\n",
       "       3.35324810e-02, 3.07880621e-02, 2.37234084e-02, 2.27269657e-02,\n",
       "       1.82186331e-02, 1.77385494e-02, 1.46710109e-02, 1.40971560e-02,\n",
       "       1.31858920e-02, 1.24813782e-02, 1.01771796e-02, 9.05617439e-03,\n",
       "       8.89538461e-03, 7.97123157e-03, 7.67493255e-03, 7.22903569e-03,\n",
       "       6.95888851e-03, 5.96081458e-03, 5.75614688e-03, 5.15157582e-03,\n",
       "       4.89539777e-03, 4.28887968e-03, 3.73606048e-03, 3.53274223e-03,\n",
       "       3.36683986e-03, 3.28029851e-03, 3.08320884e-03, 2.93778629e-03,\n",
       "       2.56588609e-03, 2.27742397e-03, 2.22277922e-03, 2.11430393e-03,\n",
       "       1.89909062e-03, 1.58652907e-03, 1.51159934e-03, 1.40578764e-03,\n",
       "       1.16622290e-03, 1.07492521e-03, 9.64053065e-04, 7.74630271e-04,\n",
       "       5.57211553e-04, 4.04330693e-04, 2.09916327e-04, 8.24797098e-05,\n",
       "       5.25149980e-05, 5.05243719e-05, 3.29961363e-05, 1.24365445e-05,\n",
       "       7.04827911e-06, 3.01432139e-06, 1.06230800e-06, 5.50074587e-07,\n",
       "       3.42905702e-07, 9.50687638e-34, 9.50687638e-34, 9.36179501e-34])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mnist.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizamos la suma acumulada de las varianzas explicadas por cada componente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1480dc18a48>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAcxElEQVR4nO3deXRc5Z3m8e9P+y7L1mLZsi3vtoLxEmFIDAQIYQw4GNJZcDqdxMOESQe6e6aZyZBJh54mCX0m6TNJukMWugPOQqAJCYkbnLjpxEBYbLwbb7JlyYtsy5Jsa19KVfXOHyobWQirbJd8q249n3PqVN1bV9JzRfnR5b2bOecQEZHEl+J1ABERiQ0VuoiIT6jQRUR8QoUuIuITKnQREZ9I8+oHFxcXu8rKSq9+vIhIQtq8eXOLc65kuPc8K/TKyko2bdrk1Y8XEUlIZnbo3d7TkIuIiE+o0EVEfEKFLiLiEyp0ERGfUKGLiPjEiIVuZo+bWZOZ7XyX983M/tHMas1sh5ktin1MEREZSTRb6KuAped5/1ZgZuRxL/D9S48lIiIXasTj0J1zr5hZ5XkWWQ78xA1ch3e9mY0xs3Ln3PEYZRSROOCcoy8YpicQojcYGnjuDxMIhQkEI49QiEDQ0R8KEwyHCYYcwfDAwzlHKOwIOwiHHWHncIBz4HAMvpL3mct6n5nnznl97ntn3o9iBS71VxAzH5xbxvxJY2L+fWNxYtFE4Mig6YbIvHcUupndy8BWPJMnT47BjxaRkQSCYdp6+s8+2nv76ewN0tkXpCPyuqMvSFdfkK6+0KDXQXr6Q3T1hegOBOkOhLxelUtm5nWCAaUFWXFb6MP9iob9U+icewx4DKC6ujp+/lyKJIi+YIiWzgAtHX2c6g7Q2h3gVFc/p7sCnO4O0NrdT2tPgNNd/bR2B2jt6R+xiM0gLyON3Mw0cjNTycsceD02N4fcjFRyMtPIzUglOyON7PRUstNTyEpPJTsjlcy0FDLTUslISyE9NSXybKSnppCWEnlONVJTjFQzUsxISTFSDFLMMAPDzhbt2efB887mtEGv354nb4tFoTcAkwZNVwDHYvB9RZJGb3+IpvY+jrf1cKKjj6b2Xk6093KivY8T7b00d/bR0tFHe29w2K9PMRiTk8GYnHSKcjIoL8xibnkBY3LSGZOdTmFOOoXZ6RRkp1OQlU5BVhp5WWnkZ6WTk55KSoqK0Q9iUeirgfvN7GngaqBN4+cib+vtD3G0tYdjrT0cb+ulsa038txDY3sfjW09nO7uf8fXZaWnUFaQRWl+JnPHF1AyM5PivAyK8zIpzstkbF4GRTkZjM3JID8rTaUsIxe6mT0F3AAUm1kD8LdAOoBz7gfAGuA2oBboBlaOVliReOSco7mjj4Mnuzl4sotDJ7s4dLKbhtM9NJzuoaWz7x1fMy43g/GFWUwozGLR5DGUF2ZRVpDF+MIsyguzKMnPoiArTUMKckGiOcplxQjvO+C+mCUSiVPtvf3UNXdR39JJfXMXB1q6qG/u4uDJrnPGqVNTjIqibCqKsvngnFImRl5PGJPNhMJsSgsyyUpP9XBNxK88u3yuSDxyztHU0UdtUyf7T3RwoLmLA82d1DZ10tTx9pZ2aooxqSibyuJcFk8dy7SSXKaMy6VyXA4TxmSTnqqTsOXyU6FLUjpT3PtOdFDT2MG+Ex3sbxoo7o5BOx7zs9KYUZrH9bNKmF6Sx/SSXKaX5jGpKIeMNJW2xBcVuvhedyBITWMHexs72Hu8nT2NAyXe1vP2jsjivAxmlOZx54KJzCjNY2ZpHjNK8yjJz9Q4tiQMFbr4Sm9/iN3H29lxpJUdR9vY0dDGgebOsycJ5makMqe8gNuvLGd2WT6zyvKZVZbHuLxMb4OLxIAKXRLaqa4Amw6eYtOh02w8eIqdR9voDw20d3FeJvMrCll2ZTlV5QXMLS9g4phsHd4nvqVCl4TS1NHLhrpTrK87yYb6U9Q2dQKQkZrC/EmF3HPtNBZMGsP8SYWML8jScIkkFRW6xLX23n5erz3JH/c388aBk9S1dAGQl5lGdWURH1k0kasqxzJvYqEOBZSkp0KXuBIOO9462sbL+5p5ZV8zW4+0Ego78jLTuHrqWO5ePIlrpo2jqryANB0aKHIOFbp47nRXgFf2N/NyTTMv72vmZFcAgHkTC/n8B6Zx/cwSFk0p0rHdIiNQoYsnmjp6WbuzkRfeOs6b9acIOyjKSef6WSXcMLuE62aWUKwjT0QuiApdLpuWzj5+u7ORF3YcO1vi00tyue/GGdw4p5T5FWNI1REoIhdNhS6jqr23n7U7G1m9/RivHzhJKOyYXpLL/TfN5PZ55cwqy9ORKCIxokKXmAsEw6yraeK5LUf5Q00TgWCYiqJs/uv10/jw/AnMGZ+vEhcZBSp0iQnnHDsa2vjVlgZWbz/G6e5+ivMy+eTiydyxYAILJ41RiYuMMhW6XJLmjj6e29rAM5saqG3qJCMthVuqyviTRRVcN7NYhxaKXEYqdLlgwVCYdTXNPLPpCOv2NhEMOxZNHsMjd83j9ivLKcxO9zqiSFJSoUvUWjr7eGrDYX624RAn2vsozsvknmun8rHqCmaU5nsdTyTpqdBlRDsaWln1+kGe336cQCjM9bNK+Oryydw4p1Qn+4jEERW6DKs/FGbtrkYef7WeLYdbyc1IZcXiSXz6/ZVML8nzOp6IDEOFLuc43RXgqY2H+ekbhzje1suUcTk8tKyKj1VXkJ+lsXGReKZCFwCOt/Xwg5cO8K+bjtDbH2bJjHF87c4ruHF2qa4fLpIgVOhJ7sipbr7/8gGe3dRA2DnuWjiRe66bypzxBV5HE5ELpEJPUsfbevjWi/v41ZajpJjx8asq+PwHplNRlON1NBG5SCr0JBMIhvnRq/X80x/2Ewo7PnXNFD7/gemML8zyOpqIXCIVehJ5dX8LD63eSV1zF7dUlfGVZVVMGqstchG/UKEngRPtvTz8b7t54a3jTBmXwxMrr+LG2aVexxKRGFOh+1g47HjyzcN847d7CYTCPPChWXzu+mm696aIT6nQfWrfiQ6+9Ku32HzoNEtmjOPrd86jsjjX61giMopU6D4TCIb57rpavv9SLbmZafzDx+bzJ4sm6tK1IklAhe4ju4+188AvtrPneDt3LpjAV5ZVMU735RRJGip0HwiGwvzg5QN85/f7KczO4J8/Xc2Hqsq8jiUil5kKPcHVNnXywDPb2N7QxrIry/nq8isoys3wOpaIeECFnqCcc/x0/SG+/sIecjJS+e4nF7LsyglexxIRD6nQE1BTRy9ffHYHL9U084FZJXzzo1dSWqAzPUWSnQo9wby4+wT/65c76OoL8nd3vIdPv2+KjmAREUCFnjCCoTBfe2EPq14/SFV5Ad+5ewEzy3TbNxF5mwo9AXT09vMXT23lpZpmVi6p5MFb55CZprM9ReRcKvQ4d7S1h3tWbWR/UyeP3DWPT1492etIIhKnorrDr5ktNbMaM6s1sweHeX+yma0zs61mtsPMbot91OSz/Ugry7/7GkdP97Bq5VUqcxE5rxEL3cxSgUeBW4EqYIWZVQ1Z7G+AZ5xzC4G7ge/FOmiy+d3ORj7x2Btkpafwqy+8n+tmlngdSUTiXDRb6IuBWudcnXMuADwNLB+yjAPO3LOsEDgWu4jJ54nX6vnzJzczZ3wBz31hiXZ+ikhUohlDnwgcGTTdAFw9ZJn/A/y7mf0FkAvcPNw3MrN7gXsBJk/W8MFQ4bDj62v28KNX6/lP7ynj259YSHaGdn6KSHSi2UIf7iBnN2R6BbDKOVcB3Ab81Mze8b2dc48556qdc9UlJRpCGKy3P8R9P9/Cj16t57Pvr+R7f/pelbmIXJBottAbgEmDpit455DKPcBSAOfcG2aWBRQDTbEI6Xdt3f385x9vZMvh03xlWRX3XDvV60gikoCi2ULfCMw0s6lmlsHATs/VQ5Y5DHwQwMzmAllAcyyD+lVPIMTKVW/yVkMb3/vkIpW5iFy0EQvdORcE7gfWAnsYOJpll5k9bGZ3RBZ7APicmW0HngI+65wbOiwjQ/SHwnzhyc1sO9LKP65YwK3zyr2OJCIJLKoTi5xza4A1Q+Y9NOj1bmBJbKP5Wzjs+OKzO1hX08wjd81j6RUqcxG5NFGdWCSx5Zzjay/s4bmtR/kft8zSCUMiEhMqdA98/+UDPP5aPSuXVHLfjTO8jiMiPqFCv8ye3dzAN35Xw/IFE/jK7VW69K2IxIwK/TJ6dX8LD/5yB9fOKOabH51PSorKXERiR4V+mew53s7nf7aZGaV5fO9Ti8hI069eRGJLrXIZHG/rYeUTG8nLTOOJlVdRkJXudSQR8SEV+ihr7+1n5RMb6eoL8sTKqygvzPY6koj4lG5wMYpCYcd9T26htqmTVSsXM7e8YOQvEhG5SCr0UfTEa/X8cX8Lf/+ReVw7s9jrOCLicxpyGSW1TZ18Y20NN88t4+6rJo38BSIil0iFPgqCoTAP/GI7ORmpPPKRK3SsuYhcFhpyGQU/fKWO7Uda+acVCynNz/I6jogkCW2hx9jexna+/R/7uH1eOR+eP8HrOCKSRFToMdQfCvPAM9spzE7nq3de4XUcEUkyGnKJoUfX1bLrWDs/+NR7GZub4XUcEUky2kKPkdqmDh5dV8vyBRNYesV4r+OISBJSoceAc44vP7eTnIw0vrKsyus4IpKkVOgx8OzmBjbUn+LBW+dQnJfpdRwRSVIq9Et0qivAI2v2UD2liE9U6wQiEfGOCv0S/f2aPXT0Bvn6XfN0fXMR8ZQK/RJsqDvJLzY38F+um8bs8flexxGRJKdCv0iBYJgv/3onE8dk85cf1H1BRcR7Og79Iv3zH+uoberk8c9Wk5OhX6OIeE9b6BfhRHsvj66r5ZaqMm6aU+Z1HBERQIV+Uf5hbQ39oTBfvn2u11FERM5SoV+gnUfbeHZLAyuXTGXKuFyv44iInKVCvwDOOR5+fjdjczK4/ybtCBWR+KJCvwBrdzXyZv0p/vuHZlGQle51HBGRc6jQo9QXDPHImr3MLsvXLeVEJC6p0KO06rWDHD7Vzd8sm0taqn5tIhJ/1ExRaOns47t/qOWmOaVcN7PE6zgiIsNSoUfhe+sO0N0f4n/fpsMURSR+qdBH0NLZx8/fPMRdCycyozTP6zgiIu9KhT6Cx1+tpy8Y5s9vmO51FBGR81Khn0dbdz8/eeMQt80rZ3qJts5FJL6p0M/jx28cpLMvyP036iQiEYl/KvR30dUX5PHX6rl5bilzywu8jiMiMqKoCt3MlppZjZnVmtmD77LMx81st5ntMrOfxzbm5ffkhkO0dvdzn7bORSRBjHghbzNLBR4FPgQ0ABvNbLVzbvegZWYCXwKWOOdOm1npaAW+HHr7Qzz2Sj3Xzihm4eQir+OIiEQlmi30xUCtc67OORcAngaWD1nmc8CjzrnTAM65ptjGvLye2XSEls4+bZ2LSEKJptAnAkcGTTdE5g02C5hlZq+Z2XozWzrcNzKze81sk5ltam5uvrjEoywQDPPDl+uonlLENdPGeh1HRCRq0RT6cLeyd0Om04CZwA3ACuBfzGzMO77Iucecc9XOueqSkvg8hf75Hcc42trDfTfNwGy4VRcRiU/RFHoDMPjyghXAsWGW+Y1zrt85Vw/UMFDwCefHrx9kekkuN8yKzz84IiLvJppC3wjMNLOpZpYB3A2sHrLMr4EbAcysmIEhmLpYBr0cth1pZXtDG595f6W2zkUk4YxY6M65IHA/sBbYAzzjnNtlZg+b2R2RxdYCJ81sN7AO+J/OuZOjFXq0/OT1g+RlpvGRRRVeRxERuWAjHrYI4JxbA6wZMu+hQa8d8NeRR0Jq6ezj+R3HWbF4EnmZUf1aRETiis4UjXj6zcMEQmH+7H2VXkcREbkoKnQgGArzs/WHuW5msS6RKyIJS4UOvLj7BI3tvXxaW+ciksBU6MCq1w9SUZTNTXMS+ooFIpLkkr7Q9za2s6H+FH92zRRSU3SooogkrqQv9J+8cYjMtBQ+Xj1p5IVFROJYUhd6e28/z205yvIFEyjKzfA6jojIJUnqQv/tW8fp6Q/xyauneB1FROSSJXWhP7f1KNOKc5lfUeh1FBGRS5a0hX60tYf1dae4c+FEXbdFRHwhaQt99baBC0beuWDopd1FRBJTUha6c47ntjbw3ilFTB6X43UcEZGYSMpC33O8g30nOrlzobbORcQ/krLQf73tKOmpxrJ55V5HERGJmaQr9FDY8ZttR7lhdqmOPRcRX0m6Qn/jwElOtPdxl4ZbRMRnkq7Qn9t6lPzMNF2IS0R8J6kKvScQ4nc7j3PbvHKy0lO9jiMiElNJVegv7jlBVyCko1tExJeSqtB/vfUo5YVZXD11rNdRRERiLmkKvTsQ5JV9zXx4/gRSdN1zEfGhpCn0zYdOEww7lswo9jqKiMioSJpCX193ktQUo3pKkddRRERGRdIU+oa6U8ybWEhuZprXUURERkVSFHpPIMT2hlaunqadoSLiX0lR6FsOn6Y/5Lhm2jivo4iIjJqkKPQNdSdJMTR+LiK+lhSFvr7+FFdMLCQ/K93rKCIio8b3hd7bH2Lb4VadTCQivuf7Qt96uJVAKKzxcxHxPd8X+ob6k5hBdaW20EXE3/xf6HWnqCovoDBb4+ci4m++LvS+YIgth09ruEVEkoKvC337kTb6gmHtEBWRpODrQt9QNzB+vliFLiJJwNeFvr7+JLPL8hmTo5tBi4j/+bbQA8Ewmw9p/FxEkkdUhW5mS82sxsxqzezB8yz3UTNzZlYdu4gX562jrfT2h7lGF+QSkSQxYqGbWSrwKHArUAWsMLOqYZbLB/4S2BDrkBdjfd0pABZP1Ra6iCSHaLbQFwO1zrk651wAeBpYPsxyXwW+AfTGMN9F21B/itll+YzN1fi5iCSHaAp9InBk0HRDZN5ZZrYQmOScez6G2S7JrqNtzJ9U6HUMEZHLJppCH+6Oyu7sm2YpwLeAB0b8Rmb3mtkmM9vU3NwcfcoL1NzRx8muAHPGF4zazxARiTfRFHoDMGnQdAVwbNB0PnAF8JKZHQSuAVYPt2PUOfeYc67aOVddUlJy8alHsLexHYA54/NH7WeIiMSbaAp9IzDTzKaaWQZwN7D6zJvOuTbnXLFzrtI5VwmsB+5wzm0alcRRqGnsAGC2Cl1EksiIhe6cCwL3A2uBPcAzzrldZvawmd0x2gEvxt7GDorzMhmXl+l1FBGRyyYtmoWcc2uANUPmPfQuy95w6bEuTU1jh4ZbRCTp+O5M0VDYse+ECl1Eko/vCv3gyS76gmGNn4tI0vFdoZ/ZIapDFkUk2fiu0Pc2dpBiMLMsz+soIiKXle8KvaaxncpxuWSlp3odRUTksvJhoXdo/FxEkpKvCr07EOTQqW6Nn4tIUvJVoe870YlzOkNURJKTrwq9RtdwEZEk5qtC39vYQXZ6KpPH5ngdRUTksvNVodc0djCrLI+UlOGu+Csi4m++K3TtEBWRZOWbQj9zUwvtEBWRZOWbQtdNLUQk2fmm0HVTCxFJdr4pdN3UQkSSnW8KXTe1EJFk54tC100tRER8Uui6qYWIiE8KXTe1EBHxSaHrphYiIj4p9P0nOpiim1qISJLzRaHXNXcxvSTX6xgiIp5K+EIPhR31J7uYVqLhFhFJbglf6MdaewgEw0wr1ha6iCS3hC/0A82dANpCF5Gk54NC7wJgmsbQRSTJJXyh1zV3UpCVxrjcDK+jiIh4ygeFPrBD1Ex3KRKR5Jb4hd7SqeEWERESvNA7+4KcaO9junaIiogkdqHXR3aI6qQiEZEEL/S6Fh2yKCJyRkIX+oHmLlIMpozL8TqKiIjnErrQ65o7qSjKITNNF+USEUnwQu/SES4iIhEJW+jhsBs4ZLFY4+ciIpDAhX68vZfe/rC20EVEIqIqdDNbamY1ZlZrZg8O8/5fm9luM9thZr83symxj3quurMX5VKhi4hAFIVuZqnAo8CtQBWwwsyqhiy2Fah2zl0JPAt8I9ZBh6o7ewy6hlxERCC6LfTFQK1zrs45FwCeBpYPXsA5t8451x2ZXA9UxDbmO9U1d5KbkUppfuZo/ygRkYQQTaFPBI4Mmm6IzHs39wC/He4NM7vXzDaZ2abm5uboUw6jrkUX5RIRGSyaQh+uMd2wC5p9CqgGvjnc+865x5xz1c656pKSkuhTDkP3ERUROVc0hd4ATBo0XQEcG7qQmd0MfBm4wznXF5t4w+sJhDja2qNT/kVEBomm0DcCM81sqpllAHcDqwcvYGYLgR8yUOZNsY95rvoW3aVIRGSoEQvdORcE7gfWAnuAZ5xzu8zsYTO7I7LYN4E84Bdmts3MVr/Lt4uJsxfl0klFIiJnpUWzkHNuDbBmyLyHBr2+Oca5zutA08AW+tRibaGLiJyRkGeK1rV0MnFMNtkZuiiXiMgZiVnouiiXiMg7JFyhO+eoa+5kmoZbRETOkXCF3tTRR1cgpEMWRUSGSLhCP6CLcomIDCvhCv3MRbm0hS4icq6EK/TS/ExuqSqjvCDL6ygiInElquPQ48kt7xnPLe8Z73UMEZG4k3Bb6CIiMjwVuoiIT6jQRUR8QoUuIuITKnQREZ9QoYuI+IQKXUTEJ1ToIiI+Yc4Ne7/n0f/BZs3AoYv88mKgJYZxvJDo66D83kv0dVD+izPFOVcy3BueFfqlMLNNzrlqr3NcikRfB+X3XqKvg/LHnoZcRER8QoUuIuITiVroj3kdIAYSfR2U33uJvg7KH2MJOYYuIiLvlKhb6CIiMoQKXUTEJxKu0M1sqZnVmFmtmT3odZ6RmNnjZtZkZjsHzRtrZi+a2f7Ic5GXGc/HzCaZ2Toz22Nmu8zsryLzE2kdsszsTTPbHlmHv4vMn2pmGyLr8K9mluF11vMxs1Qz22pmz0emEya/mR00s7fMbJuZbYrMS5jPEICZjTGzZ81sb+Tfw/vibR0SqtDNLBV4FLgVqAJWmFmVt6lGtApYOmTeg8DvnXMzgd9HpuNVEHjAOTcXuAa4L/I7T6R16ANucs7NBxYAS83sGuD/At+KrMNp4B4PM0bjr4A9g6YTLf+NzrkFg47dTqTPEMB3gN855+YA8xn4bxFf6+CcS5gH8D5g7aDpLwFf8jpXFLkrgZ2DpmuA8sjrcqDG64wXsC6/AT6UqOsA5ABbgKsZOMsvLTL/nM9WvD2ACgYK4ybgecASLP9BoHjIvIT5DAEFQD2RA0nidR0SagsdmAgcGTTdEJmXaMqcc8cBIs+lHueJiplVAguBDSTYOkSGK7YBTcCLwAGg1TkXjCwS75+lbwNfBMKR6XEkVn4H/LuZbTazeyPzEukzNA1oBp6IDHv9i5nlEmfrkGiFbsPM03GXl4GZ5QG/BP6bc67d6zwXyjkXcs4tYGBLdzEwd7jFLm+q6JjZMqDJObd58OxhFo3L/BFLnHOLGBguvc/Mrvc60AVKAxYB33fOLQS68Hp4ZRiJVugNwKRB0xXAMY+yXIoTZlYOEHlu8jjPeZlZOgNl/qRz7leR2Qm1Dmc451qBlxjYHzDGzNIib8XzZ2kJcIeZHQSeZmDY5dskTn6cc8ciz03Acwz8UU2kz1AD0OCc2xCZfpaBgo+rdUi0Qt8IzIzs3c8A7gZWe5zpYqwGPhN5/RkGxqXjkpkZ8CNgj3Pu/w16K5HWocTMxkReZwM3M7BDax3w0chicbsOzrkvOecqnHOVDHzm/+Cc+1MSJL+Z5ZpZ/pnXwC3AThLoM+ScawSOmNnsyKwPAruJt3XwemfDReycuA3Yx8AY6Je9zhNF3qeA40A/A3/l72Fg/PP3wP7I81ivc54n/7UM/K/8DmBb5HFbgq3DlcDWyDrsBB6KzJ8GvAnUAr8AMr3OGsW63AA8n0j5Izm3Rx67zvy7TaTPUCTvAmBT5HP0a6Ao3tZBp/6LiPhEog25iIjIu1Chi4j4hApdRMQnVOgiIj6hQhcR8QkVuoiIT6jQRUR84v8DJhvFE0caLowAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    range(len(pca_mnist.explained_variance_ratio_)),\n",
    "    np.cumsum(pca_mnist.explained_variance_ratio_)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ajustemos un PCA de sólo 2 componentes para visualizar el conjunto de datos en un gráfico de dispersión."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 2)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_mnist_2d = sklearn.decomposition.PCA(2)\n",
    "mnist_2d=pca_mnist_2d.fit_transform(mnist.iloc[:,:-1])\n",
    "mnist_2d.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cada uno de los números tienden a acumularse juntos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1480dc87c88>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    mnist_2d[:,0],\n",
    "    mnist_2d[:,1],\n",
    "    c=mnist.label,\n",
    "    cmap='tab10'\n",
    ")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2)\n",
    "\n",
    "axs[0].imshow(\n",
    "    mnist.iloc[0,:-1].values.reshape(8,-1),\n",
    "    cmap=\"gray\"\n",
    ")\n",
    "axs[0].set_title(\"Original image\")\n",
    "\n",
    "axs[1].imshow(\n",
    "    pca_mnist_2d.inverse_transform(mnist_2d)[0].reshape(8,-1),\n",
    "    cmap=\"gray\"\n",
    ")\n",
    "axs[1].set_title(\"Image using 2 principal components\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Actividad 1:**\n",
    "\n",
    "Ajusta un PCA cuyos componentes principales expliquen el 95% de la varianza del conjunto de datos. ¿Cuántos componentes fueron necesarios?, ¿Cómo se ve la imagen de un número al usar ese número de componentes principales?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Ajuste y visualización de un PCA que explique el 95% de la varianza del conjunto de datos\n",
    "# HINT:\n",
    "pca = sklearn.decomposition.PCA(0.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## t-distributed stochastic neighbor embedding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sklearn en la clase sklearn.manifold.TSNE implementa este método y la forma de utilización es exactamente igual al PCA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ajustamos un ebmedding de 2 dimensiones para visualización."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 2)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tsne_mnist_2d = sklearn.manifold.TSNE(2)\n",
    "mnist_2d_tsne=tsne_mnist_2d.fit_transform(mnist.iloc[:,:-1])\n",
    "mnist_2d_tsne.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este método agrupa de mucho mejor manera los números del conjunto de datos MNIST."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAD8CAYAAADQSqd1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOydd3hcxfW/37l3m7qsLluWJfeKm3DBVNNsYsC0hBogBJOE8A0EAukkJPkFQhqEEEKAhE4IYHqzsQHbGOPe5W5LsrrVy9Y7vz9WliVLWq2kXe2uNO/z7CPtvXNnzkq7n5175sw5QkqJQqFQKPoXLdQGKBQKxWBEia9CoVCEACW+CoVCEQKU+CoUCkUIUOKrUCgUIUCJr0KhUIQAJb4KhUIRAIQQPxBC7BBC7BRC3NldeyW+CoVC0UeEEJOBW4FZwFRgkRBijK9rlPgqFApF35kAfCmlbJJSuoHPgMt8XWDqF7P8JCUlRebk5ITaDIVCEQFs3LixUkqZ2pc+rLPmSaO22q+27r27dwL2NoeelFI+2fL7DuB3QohkoBm4CNjgq7+wEt+cnBw2bPBpr0KhUAAghDjS1z6M2mqSn3jJr7Zl86fbpZR5nZ2TUu4WQjwELAMagK2A21d/yu2gUCgUAUBK+bSUcoaU8kygCtjnq31YzXwVCoUiUhFCpEkpy4UQ2cDlwFxf7ZX4KhQKRWB4vcXn6wJul1L6dCYr8VUoFIoAIKU8oyftlc9X0SmOwnoaN5XhaXCG2hSFYkCiZr6Kdrir7ZT9bTOy6cRCrXX8EFJvmhxCqxSKgYea+SraUfZYe+EFcORXU/vRoRBZpFAMTJT4DhKMZjfO4gaM5o6hh55GF/WfF1Hx9HZkY+ehiQ1flATbRIViUKHcDgMcaUhq3jlA4/oy71et28CUHo01NxHpMcBt0LS1AqQEj49+XD5OKhSKHqPEd4BT/2khjRvKwG20HnOXNOEuaepZRwYU/XINms2EZtXRYszEzEwnekY6QhcBtlqhGPgExO0ghEgUQrwmhMgXQuwWQswVQiQJIZYJIfa1/BwSiLEU/uMqbaTukwJwGd039gengVHnxF3RjPNwHTVvH6DyuZ2oCtgKRc8JlM/3EeBDKeV4vOnUdgM/Bj6RUo4BPml5rugnmvOrKP/7FvAETxily8B5qBbHwdqgjaFQDFT6LL5CiHjgTOBpACmlU0pZA1wKPNvS7FlgcV/HUviH4TGoejkfGagZrw+k08BxsCbo4ygUA41A+HxHAhXAv4UQU4GNwA+AdCllCYCUskQIkdbZxUKIJcASgOzs7ACYMziRUmLPr8JZVI+rtBHp6KcFMl2gx1j6ZyyFYgARCPE1ATOAO6SU64QQj9ADF0NLPswnAfLy8pTzsBe4q+2UPbIJaQ9BRIKAqKl9SqmqUAxKAuHzLQKKpJTrWp6/hleMy4QQmQAtP8sDMJaiE8qf2Boa4QUwazSuLcZocoVmfIUiQumz+EopS4FCIcS4lkPnAruAt4EbW47dCLzV17EUHXFX2TFqQ5h/odlD3fICSh/ZpARYoegBgYrzvQN4UQhhAQ4CN+MV9leFELcABcBVARpL0YbOdqyFAqPeSf2aYhLOHxFqUxSKiCAg4iul3AJ0Vl7j3ED0r+gac3o0aAKMELvLDbDvPoazuZENy97kSPVOdJuFUxYuJO/Sy9BN5tDap1CEGSq3Q4QjTBoJi3JDbQYArspm3nz1D+SXr6PRVUtdfQVrX3uZpQ89oDZiKAY8Qoi7hBA7hRA7hBAvCyFsvtor8R0AxJ02jJRvT0FLCG3IV1ntIZrctRhtkkR4DBdHd++i9MDeEFqmUAQXIcQw4P+APCnlZEAHrvZ1jcrtMECwjU4kanIKjWuKgzdIvAnq3dDFJPZo0z7csuOimzQ8lO7fS+bocZ1cpVCEjpEc4HF5hV9tz+u+iQmIEkK4gGjA54dRzXwHECJKD0KnoKfYsOTEY46xdim8ADGmBHTR8ftc003EJatYYMXARUp5FPgj3uCCEqBWSvmxr2uU+A4ktCBkFzMJPNUOnIfrcJU0+myaEzsZ0eEtJbBER5E7vbP1WMXJuF0etiwvYOXzuzmwqRwZ6oVURVtShBAb2jyWHD/RkjjsUiAXGArECCGu99WZcjsMAFzHmjn24m7cxb7FsXed+//ht+pRnJN5DV9WvEOjuxYkJGdkc8lPf4ZuUm+17qgoqOO1hzZitCRD2rXGm8A+OsHCrEW5TDx9KEKo9J0hpFJK2dUs4jzgkJSyAkAI8QZwGvBCV52pT0SEY99TReWzOyH4OXT8IsmawUVZt9LkrkMTOqMeuhARjBn5AEJKSfmRet7886ZW4W1LU62T1f/bh9ttMPWc4SGwUOEHBcAcIUQ00Iw3zHaDrwuU+EYw0iOpfN4/4TWPjMdVUA/u/rmNjTbFA968E+bkqH4ZMxKpr7Lz9iNbqK9qxuPjLsPtNFj39kHGzEwjOt7ajxYq/KElr81rwCbADWymJWdNVyjxjWBqlx/x/pv9wKh1hmQjhhal3mIADTV2dn9RQkOVHZfTTX2lA00X1JQ10VTv8rmQeRxXs4d/37eG2EQrp105mtEz0pQbIoyQUt4P3O9ve/XJiFCklDR+6X9RS88xexCt6QKTQI8e3DvbpJSseW0fW1cU+SWw3XcIDdUOPv7XTtalHeSa+2ej62rdPBJR/7UIRTqN/svZ22vUSv2hLZVs//RoUP4UteXNrH1jf+A7VvQLSnwjFGHWwBze/z7Nqm6stq0s7HQRLVDkry0NWt+K4BLen15Fl7gqm9Cjw1vc9CE+t7YPeAxDUl5QH/QxFJFJeH96FR1o2lFB1f/2giNMYst8YMmKC7UJIeWL1/fhCnKS+9xTUjocKztcx7YVhTTUOMiZksyk04dhUQufYYf6j0QQzbuPUfXynqBWJA4YuiDm1IxQWxEyPG6DHZ8dDeoYZpvOvKvGULSnGqFBbVkTm5cXUlvWxPEkcmUHa9n04REmzBvK+DkZJA2NDapNCv9R4htB1H50ODKEF7BNTMIybPB+0J3N7qC6BIaNS2TkjFT+c99qpI+bII9b4nG72fxxAZs/LsBs1Tjv5omMnNZpPVtFP6J8vhGEpyoE4WK9xDTI/b22GDOaHrwY3KN7alj18j6fwtsZLofBh//awa4vgpj9TuEXSnwjCFOE7BQTFm1Qz3oBhCaIigttfuWukB5Y+/oBtVgXYpT4RhDxC3LAFOY7mjSBFmshalLHhaDBRlRs+G4wcTk82BtUwdNQosQ3gogal0TytRPQk1tu6QWIGBMJi3JJ/c4pmFtmm8KsheY/qwtiZqaRdvs0hEm9tTJGJYTahC4RGljDPFRxoKP++hFG1MRkoiYmd3ou/Y7prbXSyv6yCXdlk//ZzjS8u7B6eScaNT2VpCvHItRW11ayJyQHbXdbXxA6TD5zGLr6ggwp6q8/wBBCIIQg9dYpWHMTQRfeh8D76Owai0bUKano8dbuE7ILENGm1v7Mw+NI/f40kr8xflAKr6PJxbGjDdRXNWMY7b/pho0fgh6GbqKp5wxn7mWjQm3GoEfNfAcoepyF1FunYDS5kC4DKSV1ywqw76lCWHWiJiRjuD0ID0RNTcE6KhGjyU3DqiKadx4DXWA0uDDs3pptlqw4kq4ZjynRm87weIWFwZqr12l3s/yZXRzaVtnu+PBJSSxcMgWzVcds0Zl18UjWvnEgRFa2Z0hmDJffPQNbGPuiBxNKfAc4WpusYklXjfXZVo8xk7Agl4QF3lL0Uko8tU6ESaDHtl+5H6yie5xlz+zk8LZjHY4X7qxi6Z82suj709jxWRGHt1d2cnX/Y7bpXHv/7FCbEXbU1yez6vMb/Gz964COrcRX0SVCiNaZruIEjbUOCnZWdXm+oqCBF+//Eo/b4zNBen+h6YLxczJDbYbiJALmpBNC6EKIzUKId1ue5woh1gkh9gkh/iuECM+gR4WihzTVOrvdQOFsdoeF8AKYLBpzFo8MtRkDGiHEOCHEljaPOiHEnb6uCeQKyQ+A3W2ePwT8RUo5BqgGbgngWApFyEhMj26NKokEXA4P1SVNoTZjQCOl3COlnCalnAbMBJqApb6uCYj4CiGygK8BT7U8F8B84LWWJs8CiwMxlkIRasxWnVO/lttl9EgwtxX3BmnAlk8KQm3GYOJc4ICU8oivRoGa+f4VuJcTUaXJQI2U8niFsSJgWIDGUihCzswFOVxwyySi4k9404QG4+ZkMPbU9BBa1jn7N5RTvK861GZEOilCiA1tHku6aHc18HJ3nfV5wU0IsQgol1JuFEKcffxwJ007vU9reQFLALKzs/tqjkLRb4zJS2dMXkehffqez0NgTfeseC6f6x6Yo4pu9p5KKWWerwYta1uXAD/prrNAzHznAZcIIQ4Dr+B1N/wVSBRCHBf3LKDTNEpSyiellHlSyrzU1NQAmKNQhA5nsxt7g58lpfuZ+mo7zfUqn0OQWQhsklKWddewz+IrpfyJlDJLSpmDd7q9Qkp5HbASuLKl2Y3AW30dS6EId8I9/tlkGXy7EPuZa/DD5QDB3V58H/BDIcR+vD7gp4M4lkIRFpitOhkj47s4p5E8LKafLfKi6YLsiclYbCq0P1gIIaKB84E3/GkfUPGVUn4qpVzU8vtBKeUsKeVoKeVVUkpHIMdSKMKVBbdNITqhfVi7NcbEdQ/MZdai/om31XSB0L0720wWjZThsZx744R+GXuwIqVsklImSylr/WmvvgYVigATk2Dlpt/PozC/iooj9aTnxpM1PgmAoWMSERo9rkDRU9Jy4jn/WxM5VtRAXLKNlEFezDQcUQ4ghSIICM17mz9zYU6r8ALYYs3Mu2I0urlz37Bu1sgcnYAlSu/0vMmsMfX84d2OX3GkDrNFJ3dqqhLeMEXNfBUDhsrKSvLz8xFCMHHiRIYMGUJlZSVLly6ltLQUq9XK3LlzmTdvHpoWunnH1HOzSR+ZwK5VxTQ3OkkeFktDlR1ns4fReWmMmpGGx+lh5Qv5HN5+DGlIhC4wWQQx8Ta2Li/sdgzDIykvqGfEpM5zPytCjxJfRcTicrk4dOgQHo+H4uJi1q5di2EYCCFYuXIls2fPZs2aNa3tm5qa+OSTTzh69ChXX311CC2HjNwEMnK7rnShR2lceOsUPnt5D/lrS3A7DNwOsNc3+tW/lPDe41v52vemKgEOU5T4KsIewzCor6/HZrNhtVqRUvLqq6+ye/dun9e1Fd625Ofnc+zYMZKTw1uUGmsd7F5TjMfduzwS0gMrn8/nxt+fpjZWhCFKfBVhza5du3jvvfdwOBxIKZk4cSLV1dUUFRX1qd81a9ZwySWXBMjK4FBRUI9u0vC4Pb3uo7nBSVOtkxiVGjTsUOKrCFsKCgpYunQpLteJXVnbt28PSN/l5eUB6SeYxA6x9bm8u+GWOO0uYlDiG26oaAdF2LJ69ep2whtI0tPDL/nNyaRkxTIkI6bL7Gn+8vHTuwJjkCKgKPFV9Csul4sdO3awbt06ysp8b3+vru5lFi4pGXHwEDPXb2D03r2Ync4OTc4+++ze9d3PXPx/U0nJiu1TH5WFDRGVf3iwoNwOin6jpKSEZ599FsMwWiv9Tpw4kcWLF3ca+jV8+HAqKip6NVZV0hBmrV+PoWlM3rGT5eedR0N8HEIIrrjiCuLiIiP21RZjDkgyHJfDo7YWhxlq5qvoF6SUvPzyy9jtdpxOJ263G7fbze7du9mxY0en16SlpfVuMCFojonhaNYwTB4PZqeTU9evb7Xj9ddfZ/Pmzb19Kf3KsaMNOJv7mCVNeHNOKMIL9VWoCCoNDQ1s3bqV4uJiGhs7xqi6XC7eeecdli5disViIS8vj3POOQeTycTOnTt7Pa7bbKY8NY3hhUVoQEplJZrHg6HrSCl5++23yczMJCMjow+vLvgEYhuyNcqkQs26IEXG8237uX61/bWqXqyIFA4ePMiLL76IYRg+fY7HF9UcDgdr1qyhtLSUG264gfr6+l6PrbvdxDQ2tD6vSUjAaOPakFKyfv16Lr744l6P0R8kZ8Vismi4HL0PNxs+Man7Rop+R4mvIijs37+fF154oVfXHjhwgN/97nd9inQQUjK0uJijQzMpzMriSE4OnDT7q6ys7HX//YWmCRYsmcw7j23D3RsBFnD6lWMCb5iizyjxVQQEKSUHDx7kyy+/5ODBg3g8vZ+pAb0XXilBSmLr6vhgwQI4Ptvt5La7ubm5Dxb2H0PHDOGbv51L/rpSdnxWRF2FvdN2mgmsUScW6GKGWFl42xS1wSJMUeKr6DOGYfDKK6+wd+/eUJvSKrI1SUmdCm5bampq+sOigBAVZ2H6edlMPy8be4OL2spmdq0+yt6vypBSIhBMOnMYp10xGgBpSHSTWk/vT4QQiXgruE/GW7PyW1LKtV21V+Kr6DO7du3iwIEDoTbjBH4uLplMkfn2t8WascWaSc+J58xrxtFc58QWY8ZkaRPREObljAYojwAfSimvbCmkGe2rcWS++xRhxfbt2/vsZggFHo/HO2vsQqzLysp45513KCkpQUpJWloao0aNYvLkyWRmZvaztZ2j6xqxQ2yhNmPQI4SIB84EbgKQUjqBjrt72qDEV9FndD0yY0idTidOpxOrtb1PVErJihUrWLVqVbvjpaWllJaWsmbNGhISErj99tuxWNqXC1IMaFKEEBvaPH9SSvlky+8jgQrg30KIqcBG4AdSyi5zgCrxVfSZKVOmsGtX5OUP0HUds9kMQH19PZ9++il79uyhoaGhmyuhtraWZ599lltvvTXYZirCh0opZV4X50zADOAOKeU6IcQjwI+BX3TVmRJfRZ85nsA80vIHTJs2DYC3336bTZs29fj6o0ePBtokReRSBBRJKde1PH8Nr/h2iVoOVfQZu90e0rI8veX888/ns88+65XwHifSvnAUwUFKWQoUCiHGtRw6F/B5O6hmvoo+M3z48IhbcJs5cyZWq5V169Z137gLzGaz2raraMsdwIstkQ4HgZt9NVbiq+gzdXV1aJrWmqksEli4cCFSSuz2zjcs+MNFF10UQIsUkY6UcgvQlU+4A5F3r6gIO+x2e9CFNyUlJWCuDZPJREVFBUKIXiXWSUhI4Prrr2f69OkBsUcxOFHiq+gz3SVFDwTDhg0LmMDruo6zJcH6woULWyMe/MVut0dEJQxFeNNn8RVCDBdCrBRC7BZC7BRC/KDleJIQYpkQYl/LzyF9N1cRjuzbty+o/Vut1oBWGpZSMnToUABGjBjBLbfcwsSJE0lMTCQ1NZW8vDzuvvtuvve976F3sgvO5XazviU/sELRWwLh83UDd0spNwkh4oCNQohleHd6fCKlfFAI8WO8YRf3BWA8RZgRExMT1P6dTmdAdpQJIdB1nUWLFrWb7WZkZPD1r3+9Q/vtBw7RLOHkbRSGx8PRkpI+26MY3PRZfKWUJUBJy+/1QojdwDDgUuDslmbPAp+ixHdAMmfOHAoKCoJW7FLXdUaOHNltO03T0HW91Y7ExEQWL15MdXU1e/fuJTY2lry8PL9cBkXNTm4rquESKTGAg6lD2Z86DCSMLS8gMTaxry9LMcgJaLSDECIHmA6sA9JbhBkpZYkQotOaMEKIJcASgOzs7ECao+gnxowZw9lnn83KlSvRNA2XyxWw+FeTycTMmTPRdZ3U1FSfNd1MJhP33HMPHo8Hj8dDbKy38GROTk6PFseaPAbzvtyFIyae4oRktmeN4mhiClLTQUoOpw5lhYBLmuyMjFZ5FRS9I2DiK4SIBV4H7pRS1vkb/9iyN/pJgLy8PBWxHqHMmzePmTNnUlJSQkxMDKtXr2bbtm196lPXdcaPH8/5558PwMUXX8wzzzzTZftrr702ILkWniwsx9Hy+0eTZiMFXuGF1oxpbuD0dfn8fFQm38tWi2+KnhMQ8RVCmPEK74tSyjdaDpcJITJbZr2ZQHkgxlKELzabjdzcXAAOHz7s93WapmGz2XA4HOi6jqZpzJs3j2nTprWrMpyVleWzn5ycnN6Y3YHV1SdyOxg+kgYZwEMHSzgnKZ4JsVEBGVsxeOiz+ArvFPdpYLeU8s9tTr0N3Ag82PLzrb6OFSyklDjcBlaTpnYsBYjjoVy+0HWdmTNnMmfOHJKSkqipqcHhcJCSktJppjRN00hJSem0/E8gXVZTYqNYXdN9ch0Al4Q3yqr5mQ/xPdTk4Bf7i9jbaGdCTBS/Gj2UXOWuGPQEYuY7D7gB2C6E2NJy7Kd4RfdVIcQtQAFwVQDGCihSSv752UEeW7mPRoeH5FgLP7pwHN84Vfme+0p3icrPOOMMZs+e3eqXBe8CWXd885vf5PHHH2+3My0mJoZrrrmm98aexPdGpPFkUQX+bJg2AJcP//byyhqu33649XmB3cXHx+p4fdooThsS1+V1iv6h2lHKfw89FJKxAxHtsBroarroX03mEPH1f65l/eHq1ueVDU7uf2snNpPOpdOHIaVk45FqjjU6mZE9hNQ4VQvLX4YPH87u3bs7PXfjjTe2uid6Snx8PD/60Y/Yu3cvJSUlZGVlMXr06IAm9km1mHl7xhiu33qAao/vjR1RmuDi1K6/NG5qI7zHkcC3dhwm/4wpfbRUEckMytwO24tq+cVb29hSWNfhnN1t8JOl23ngvZ0ca3AhBNhMGoaEb5+Ryz0XjKO22YUhISlGJdLuirPOOov9+/d3CD/Tc0fxszqDSQeKuXlYCkNtPf8b6rrOhAkTmDBhQqDM7cDMhBh2n3kKlU43Fk2wv9HObTsPU+jwvh4B2DTBNZnJzEzoGOd8pNnBlZv34+6i/xq3B4dhYI3AbHCKwDBoxNcwJBsLqnlh7RHe31GMy8c9ZZPTQ5PT20BKaHZ5Zz//WnWQ97eXUlTdhJSS1HgbMRYTHkPytSmZLDlrJPG2nm1VHahkZGRw/fXX8+GHH1JaWorZamVf1FjGbBnC7C+P0GQV3DC7iEcWTWZynM9SVyElxeL9iMxIiGH9aZPY12hnaVk1Tim5KDWBGfEdhdcjJYs27qPC1ZX0ejGr9YVBzYAW3y0F1fzqnV0UVTdRb3cj8M5se4vTLTlUeaIqSEnNCb/jYyv38+K6I6y852wSo9WMGLxbd2+77TYAfvDKFmZ+WgVIBBBnl1z2WQOP23fz+M0zQ2pnTxgTY+Pekb53231R3cCxboRXB+rcHhLNA/ojqPDBgLznKatrZuFfPmfx41+wpbCGygYnDrfRJ+H1h+omF5f9fY1KsN0JIz+rQnBiceD47+PX1eIyBtbfa1+Tne7eaR5g8uod/OFgiXq/DFIGzNduZYODZ9cc4rkvj1Db7HvWEUwOHWvim898xW1njeT00akhsyPc0LvQFw0wXG6wDhx3zQcVtX61cwOPF5YzPjaKS9LUduVIRwhxGKjH+93q9lHvDRgg4nuospFFj66i0Rke1RRW7atk1b5KhiZY+dNV05g1MhldU/69rjCbI7P6cWdIKVlb61+MMIDdkDxRWD7gxddlt1NVXER0YiJxSSmhNieYnCOl7BiI3gkDQnx/vnR72AhvW4prHVz71DqSYiw8es105o0e0G86n9hiTNgb3e1iEiVgsekRWf8tkJQ6gpOQKJQYHg/5az5jx2efUF9ZQX1lOULT8Lhc6GYzaBqGy4XJYmXy/PM5/Rs3YLYOro0nA+Jd/+WhqlCb0CUSONbo5NvPbqC0tvclayKdq+6byckaKwRccW/kLLb5gxCCOB9bkjtjygDbmiyl5I0Hf8Wyfz1G4Y6t1JQW43G7cTudSClxO5247XYMjwdncxOb3nuLl35+DzL8y1ClCCE2tHksOem8BD4WQmzs5FwHBsTM16QJPGG+aOORkv9tLOSO+WNCbUpISEiLYckjZ7H5owKO7q0mc3QiMxeMwGQZOC4HgG31Tdi72ZhxMj8e2fNSRuGKx+1i6R9+w5Ftm3t03bGiQg5v3UTudL9LoIWCym78uPOklMUtGRyXCSHypZSfd9V4QIjvaaOSWbmn61SD4YDTbQzqmS+Ayaxz6qJcTqV3u9vCgtqjsPcD0Mww4WKITmp3en+Tw+vf9/g3GfhmZjITYsM3zrmnLH/qcY5s3dTj66ThoWT/nnAXX59IKYtbfpYLIZYCs4CBJb6PLN/LE58doNllEGXWsJnD33sSbdE5fRD7fAcEnz4Enz0IsmVm+86dcNEfYNatrU3GGnUkNZXx9cpVmA0Xb6XOp9TWedTLw+OyuD4zcOWRQo3L6WDnp8t7d7EQxEbwQpwQIgbQWgpKxAAXAA/4uibixPfXb+/k318cbn3e7DJad6CFK5qAMWmxnD9R5X2NODwuKNkGtUXw6e/xuvWOY8D798CK34PZBh4nk5sqWCVMGEJDkwY/PvwUjw2/lj/l3Nx6lUXAn8dnc2VGUofhIpmKI4d7HbOsmUyMP+2MAFvUr6QDS1uyIpqAl6SUH/q6IKLE12NInl17ONRm9JizxqXyj+tmYtLDf4auaMOeD2HpbWB4wNVEe+Ftg/0YtPEoWaX7RFMJ/1f0ChNmXMZy80hSrSauzkxi1ABMKelo6JgrxW+kpLq0hPTcUYEzqB+RUh4EpvbkmohSg2ONDsJ8Xa0DZl3w1A152AZQLOugoOogvHYT2GvAWQ+y96GMVo+dRZ98n78OqeFno4ZGvPB6DINnjpRw28bd/G1/IRVOb6hc8vARrZU+eorhdvP+3/4YSDPDnoia+SZERd4uKIFEUxssIo+Nz4EngDsl6wrhn2eAyQpzvg/zfwZa5H0hb6lt5OKNe3AhQAjeqrXzhyPlvDR1FGekpDEkcyjVxUd71XdNaQkNVceITRo4fnBfRNTM12rSOX10ZP1jnB7YX+7/jidFmNBQCkYQNj+4HbD6T/DMAm/KvAjC7jG4dNMJ4QVACFyazs1b9uGRkjFz5vW6f8PjZuMHbwfI2vAnosQX4D83z2LOyMhaqHhmzaFQm6DoKaPPA0vHdJEBo+gr+N9NESXAHx+rw2nQqWuhGcFf/vww6998rU9jbP7wHYp27ehTH5FCxImvSdd4Zclcdj9wIcvuOpM1952DRQ/v2/qthTWhNiHyMDze2/66Etj8Amx/DRz1/Tf+hEsgflhwx4UyiakAACAASURBVNj9Dux4PbhjBJAKp6urJUeQkor9e/q8S83jdLLtE59BAgOGiPL5tiXKYmJMehwuj9HyTRyeMwghYEy6qtXlNw0V8O5d3o0Mhsf7BxS6d8FLGpAyDi56GEae1X1fhgGbn4f1T4PbDpMvh7m3g9WP/4fJAkmjoXJv319TV0gPrHsCplwZvDECyNzEWHRkp7XtouxNpFaVBWQcp705IP2EOxErvscx6xrJ0WZK6hyhNqVTbCad75wVmeEz/Y7hgWcuhJojYLQsdkl5YlMDQOUeeO4SSBkLtyyDKB/ZwJbeBvnvtoSJAZ8/7BW7iYu9O9NGnQfDTwW9i4XcmsMBeVk+sfuXfjIcmBgbxQWxFj5scCKPLxZKiZAGl334QpeFHHtKfOrgiIePePEFui7f2c9owLiMWA5UNuHxSEakRPPbxZOZkBkfatMigw1PQ9Uh6DYVOd4Z6b8vghvegLiW3AhSQskW70xZM8Put70z3uMYbmiuho3/9j5f9ScwR8HiJ2DS4o5jDJ8NFfntxT/QjDgteH0HgadnTebfu/bx2P5C6oVOdvFB5q9+nyhX4LbOb/7wHc687iZM5uBXhBF6OrYhP/Sz9XsBHXtAiG9ClIWS2tDOfLOHRPHMzacyOi0OjyFxug2iBljSmEDj8TTTbC/CqiVgfuN22Pdxzzoo3wl/mQxzvw+xGbDsp97ZM3hns+LEkobTJKhIsWBoguQqJ9H2FkF1NcPrSyBpJGSe0r7/0+/C2PwsWjA9WpMjw+XQimEwq/ww33rzaZxNjd237w1SsvmDdzj1kiuC03+YMCDE97Lpw/jDR/n0MJlUwBDAT742gdFpXl+irgklvD6QUnLo8N84cuRJhNAYt6ucjLLm3t3AGC744tGOmyA8J8LEypMt7Bwfh3ddQLA/N4YRhU2MLGjxLRoO+OqfcOnf23edMBSnRcdmD9IbyxwN2XOD03cQkFLy1p9+R8GOrbgdwZ3sNNVFjjumt0RctENnXDs7m5RYa8jG1zXB9OFDQjZ+pFFc/CpHjjyJyd7IxK3FvRfe4/jYfebSBTvHx2HoAkPXWn4KjgyPpi62zdyjtqjDtceOraQmwRy8pdzzfg165Mx/ivfmU7B9S9CFF2DyORcEfYxQMyDE12rSqawPndvh/InpZCRE9pbR/qR09yMMLahi9oZqUqpcQXXZH0uLQXQSS2toUJrW4lPUrN643pNoajrMwRHRuLWOsTS+BVmAbvFGZnSFyQYzb+rG+vBiz9pVuJ3OoI+TM20mycOygj5OqAm6+AohFggh9ggh9gshfhyMMV7+6oi/6VN7RXfi8OOF44M3+EBj5f9j2he7GHOwEbNbBv0NKKddB1rns0tDtNRQjk+HGTd2OB8bOw5nTAxfzRzCsSFmDLyiKwFXVxNWSxxc/Ah8dy189wuYem3HNroVFjzkDWeLENwuFztW9tAn3wPMtijiU9KYf/NtXPGTXwdtnHAiqPc8Qggd+DtwPlAErBdCvC2l3BXIcQ4fawpkdx1YMDmDbUU1HK3pfEX3870V3DA3iLuhBgob/gOf/xG9v3Z1xWaQfMrdyHXvev26bdAMSG+IhtO/C/O+D7aOESlJSWdgsw2jydPM1ikJAJicHswuyZxNnWycERp8ZxUktUkWf9k/4Kz7YMVvoXAdDMmBM+6CUfMD+UqDQn1VJZUFR4hPTaOqqJBghhVlTZzM5ffdH7T+w5FgO5xmAftb0q0hhHgFuBQIqPgunJTBv9ccDmSX7bCYBPPHpfP8uiOdnn9xXQE3zM0J2viRgOFwI90SPaaLmNn1T8H79/YpO5hPhuR6k9ZU7vXOdMcuhMWPY7HGMm7sr9mz936kNJDSg6ZZyRx2OYnn/dpnFi4hNGbO+C/79zxAWfFSQJJS5WLMocbOIyBu+qC98B4nKQeufCpQrzToSMNg2b8eY+fnK9A0DbfLhW4yYXiCV6TWGj34Ji/BFt9hQGGb50XA7LYNWgrNLQHIzs7u1SCzRiYzKjWGAxXBCX15b1spP7uoa9fCgYrBmzjH0+Ck+n97se/3zgRNSTaGXDUWa3abmaSjHj76efCEF6D6EEQlQe5ZMP/nkHWiHM3QoVcxZMhsSsvexfDYSU09j/j4U3x0dgKzOZ4Jk//IhBE/gs//AKXve2ODPTUnEu9Ep8KNb0H6pGC8sn5n04dvs3vNZxhud2vEtccVvArLJquVqectCFr//UnL3f4G4KiUcpGvtsEW386mFe3mDFLKJ4EnAfLy8np9P/rRnWfy8zd38N/1hQFfnTYMybiMrjdKWEwDYt2yx0gpqfjXdtwVzRxPtOyuaKbyqe2k352HKaElAuXoJm/crTvI20abq+DgSij8Eq5fCiNOhHFFRWWTm/O93vcdlw5f+5P3cZymlqrZ0ZGV6Kk7Nn/wTr9ENAAITWPu5VeTNWFyv4zXD/wA2A10u7Mq2KpRBAxv8zwLKA7GQCZd48ErTuHFb88OeE23oUOiOG10CtFdxO5eferwTo8PdJwF9Xiq7Zyc4V56JI1flpw4YEs4sV24P3A1w8c/D/440UkDTngB7I3Bv5NLSMtg1uKr+M4/n2fW4quCPl5/IITIAr4G+OVjCrb4rgfGCCFyhRAW4GogqAk7Txudwj9vyGNseiwmTZCZYOPy6cMYldyxQmyUWWf++FS6q+5z25leP97/vjMXy0mNpw1P4Odfmxgw+yMJT7W9c5+pR+KubDPLPbrpRH6F/qJscKQlDDRSSmSQy8VYo2P49t+e4oxrbiQ6PiGoYwWYFCHEhjaPJSed/ytwL37tjw+y20FK6RZCfB/4CNCBZ6SUO4M5JsBZY1M5a2zHrFdbC6t5+KO97CyuZWhiFD84dwyThiUw/4+f4vGRCu+KGd6Z7aShCeT/5kLe2VrCocpGLjolk7GDOGOZeWgssrMYP7OGZUTLXdfRTfDRT/vXMIDYtP4fM8JwNDWSv+Yz6iorGDp2PLnT86gqKsTlDK7LwdHUiGF40CKvkkellLLT2vZCiEVAuZRyoxDibH86C/r2Ginl+8D7wR7HH6YOH8IL357d4fjvL5/CPa9u7fTralx6LNHWE38mTdO4dHqQ87xGCOa0aKLGDcG+txp5vIK0BlqUiZi8lsxUG54Jvq+3g2HRcOa9/TtmhFF++CCv/voneDzudv5dzWRCBjGqASA+JTUShbc75gGXCCEuAmxAvBDiBSnl9V1dMDhXik7i8hlZfPqjs0mNtaK31FvTNUFyjIVnbp4VYuvCm6RrxxN37nD0RCtajJnomemk3zEdzdbyhdV0LOBjOiyCpiit48KqbgFLrDeudnqX7/kBj5SS+pUrqXrxJVzHOv/7v/fowziaGjssrBnu4Pvmp154UdDH6G+klD+RUmZJKXPwuldX+BJeGCCJdQJBdnIMa38ynxX55eSX1jMiOZoFkzOwmgbcN3RAEbpG/NnZxJ/dRZhgximwJzA3Pg6LYPuEeOrjTCBB90gm7qknpU5A6jj4xosQlxlRO8cCTdP27RRcfwOyRVTLfvMb4hYuIOsvf2ltU3+sktry0lCZyKqXnmP83LOITx3criElvm0w6RoXTMrggkkZoTZl4BCghS8JbJ6SQGOUDi13J4Yu2D4xnln6FcSc/qvWmmsuVzWlZe/idJSTmHgqSUmnI8TAv8mTUlJw3fXIk/Iv1H/wIVXTZ5D0zRsAb3hXSJGS1f99nou+f3do7QgSUspPgU+7a6fEVxFcjh0ISDf1sSbsVq1VeI9j6DqFw6IZ3yK8tbWb2LzlJqT0YBh29KJo4uImM33af9C00GW+6w/qly3vILzHqfzXk63iGzskiaShWVQcCV1h19L9QSzPFCEM/OmAIrRk5bVLat5bHNau+jBoavQKvJQG27Z/H4+nEcPw5uHweJqoq9tK0dGX210lW/JLNDcfZefOH/L5qlmsXXseRUUvtp6LNFzFR7s8ZzS2D/VbdOd9RIUwzCsle0TIxg4XlPgqgssZP/RGH/SR+Ho3sos8DNU169i2/Xbq6rbjdFZ0OG8YDoqLXwWgrm4bX62/jBUrR7Ni5QTWfnkepWXv4HIdo6n5EPv2/569eyMzq1b8hRd2eS5q2rR2z5OGZrHk7/9m0lnnBtusTjnjmo5Z5AYbSnwVwSVpJHx7uXchrA9YnQZDS+1oRmcCbHDs2Er27f89XcW3OxylNDUdYuOmq6mv3waAlE6kdLa7xjCaKS75Lw5nZZ/sDQXmzExi5p/T8YSuk/nb33Q4bLJYSBo2vF99wLrJzJU//y1DMlW4pvL5KoJP2gS48V345xl92uk2tkASf+6D5O+9v9WtcBzDcFBbu77La93uJg4d+geG0f0GAiGsNDbswZqU0mtbQ0X2449T+fQzHHvmGWRTE1HTpzP0t7/BPHRop+2HT5qCyWzG1U+5HC6956eMmDKt+4b9RHx9AfM/vT0kY6uZr6J/SBkNt66A+M5FoDukbqXksvsoKPw3htGbagouysrf8aulw+PEbO2dneFAyi3fYtya1YzfvIkRzzzdpfACZIwaS860PHRzF6lAA8wXr73cfaNBghJfRf+RNgF+uBsW/wPis7zl3f1Bs7Jv4VXsKX+KhsZ8/Nw63wGvi8E3BrCf0XzSkNirMSINIQSL7ryX85fcQTCTpR+npix08cXhhhJfRf8z7Vr44U74ZSXc9D4kjWo50fmH3xEby9H6FRhG/2xTXsF8lpZV98tY4YCm6Uw6cz5X/uw3PpPLB4IhGX3z/Q8klPgqQkvOPPi/TfCLY97HxMu8xSWFjjRHI81RlJx+McLfWXIf0YDT+RzdqO+X8cKJ4v35QXc/JKSpDUzHUQtuil7jdtdTUbEMt6eR5KQziY7uQ+zm8RLqX/8PHN1I866XOFLxOmUpAnfDuwGx118sOMlr+DtS/hMR5JlguOBxu1n/1ut4glyduD+qH0cKSnwVvaK4+DV25/+YE4VJNLKybmbc2L6nj/RkTGTt3neRGf2fV8ONRi3xzHV/QVPTQWJiRnV/0QDA0diA4QluUh3NZCJ7sn/lmwYDyu2g6DF2+1F2599H+4pQBkVFT1Nd/WWf+y8peQMp+6/yhWzz00BjNutOOtM9TmclR4v/S9HRl3A4ygJtYtCxxcZhMgc3IVFM4hAmnX1eUMeIJJT4KnrMjp1d58o9dOhvfe6/ubmoz330BgFY8Iq+Zh5CdLR/s96SkjdZveY08vN/yp49v2D1mnnsibBdcpquM+eKq9EtgRdgS1Q00xYs4oYHH8Fiiwp4/5GKEl9Fjzm+Q6wzmu1d5xfwl9TU8/vch78cn9u6MGEAdqw0E8We5AcwDAcVFcsoK3sPl6um0+sdjgp27f4Rsl1lZklR0XOUlvavr7qv5E7PIz4lNaB9aiYz1zzwB869+TtExXVbU3JQoXy+ih7jK142MfHUPvefmDiD2NiJNDTs6nNf3XF8Oc2EmyPksJwL+Yp53O2pYdXqWS0tJFK6GTPmF2QNuwbDcFBQ8G+KS17F5aqlq7jjPXt/RUaGz+rhYUPx3nxe/sWP6ImrxR80TaOy8Agp2TkB7XcgoGa+ih4hpcenP3bc2MDcbs869U2GD78ZTYsJSH/dIYARHGY0ezBrOuMqfozH04jH09CSJc3Bvn2/paFhL1u23sLBQ4/S3HwEt7vzGTGA213Nrl330tAQ/ukT333kIQItvAAIBkUeByGETQjxlRBiqxBipxCi2w+CEl9FjxBCx9rF1lubLQuTqe8ZzI6PM3bMz8nJ+S79sfOKllFO53PujvkIvZMQM8NwcfjIP6ip2YyU/uVCKCldyvoNl1NVvTbA1gaW+sqO2eD6jKaRmp1D+sjRge87/HAA86WUU4FpwAIhxBxfFyjxVfSY0aPvQ9Ns7Y5pmo1xY38V8LEqK5YTlBlZF5gwmMrWLmb3Hpqbi5DS3sm5rjAwjGby838e1nmCA53ZTNN1Jsw7iyt++kBA+w1XpJeGlqfmlofPf7jy+Sp6TEb6InTNyoGDf6a5uZDo6FxGj/oRyclnBmG0/hespqaCTrOfCWGmrm5nr/q024vweBowmeL6al5QGHHKdA5v2di7i4UgZ9pMxs89g/HzvO8BoWkDsUJxihBiQ5vnT0opnzz+RAihAxuB0cDfpZTrTu6gLUp8Fb0iNfX8oEclSCmR/eRyaIvH03leByldfehVC+syRpfc/VP+88PvUldR3npMM5kwPAZI34mMNF3nou/fTVRseH6xBJBKKWVeVyelN+RlmhAiEVgqhJgspeyyiKESX0VY4nY3cPDgX/sl4iHYCKGTkX4xmha+VZXNFiu3PvYMhbt3cGTLRlJzRrH+ndcpO7Cv22sttihs0f2zMBoJSClrhBCfAgsAJb6KyOFIwVPs3/8w0H+73ILJkCHzGDcuMjZdDJ8wmeETJgOw49Nl3bYXQjDvGzeEviJyiBFCpAKuFuGNAs4DHvJ1jRJfRb9Q56zjjb1vsKl8E7kJuVw97moyY9unF6yv382u3ffR0NA7v2q4YbGkM2Xy30hMnBlqU3rFjIWXcHT3Dp9VLmZfcQ3TLrioH60KWzKBZ1v8vhrwqpTS5y6bPomvEOJh4GLACRwAbpZS1rSc+wlwC+AB/k9K+VFfxlJ0jctw8ca+N9hbtZd5w+ZxzvBzuszGtaV8Cy/nv0yVvYr5w+ezeMxiokzB3fJZ3lTOlW9fSa2jFgODlYUreX7X8zx94dNMT5sOQEPDXjZu+joeT+/LDIUTyUlnM23a06E2o0/kTpvJqZdeybqlr6KbzHjcLgyPgdA10nNGcdb132LY+ImhNjMskFJuA6b35BrRl/AXIcQFwAoppVsI8VCLEfcJISYCLwOzgKHAcmCsbL8HswN5eXlyw4YNvpqEB85GKNkKUUmQNr7fh6911PLC7hd4/+D7lDSU4DppISjOHMe7l71Loi2RwvpCbLqNtOg0Hl7/MC/ufhGjzY4sq25lTuYcrptwHXOHzg2KvXetvIvlBcs7HI81x7L2Wm/867btt1NR8RGhiG4IPBpzZn9ETMzIUBsSEJrqainZt4eouHgyx4wLmzSbQoiNvhbA/GGyLUr+LyfHr7YT9+T3eby29GnmK6X8uM3TL4ErW36/FHhFeiPRDwkh9uMV4vCONO8OtwPe/B7seJ1WkRAmmH4dnPtLiAlOwUW34ebRTY/y7sF3qXfW4/A4kD5Eqt5Vz9mvnu2zzXEcHgefFX3GF8VfcMvkW7h9euCLCXYmvAANrgYe2fgIP5j5A+rqttI74dXobVmh4CCYesqTA0Z4AaLjExg1c1aozRhwBNLn+y3gvy2/D8MrxscpajnWASHEEmAJQHZ2dgDNCTCGB548B8pP8kdKN2x6Fra+Aje9B8P7ntugLceaj7HwjYU0u3tWQscf4W2Ly3DxxLYnmJI6hTOzAhev6/L4Ds96asdTzM+eT5RtOA5HSY/6NpkSOG3up4DB56vyCIdZ88yZb5CYoHLWRgoHMuHrP/FTBm8K7NjdLlEKIZYLIXZ08ri0TZuf4V2afvH4oU666vSTIaV8UkqZJ6XMS00NbEalgLL3Q6jI7/q8xwFPnwev3gxGYGZiLsPFRW9c1GPh7Qv3fnYvHsOnd6hHPLC2+x1Of9r4J3Jzv99h15wvzOZkzjxjA2ZzPB6jJzvOgonAHKDt1YqBT7fiK6U8T0o5uZPHWwBCiBuBRcB18oQDuQgY3qabLKA40Mb3KwdWgG+XtZddb8D79/R5OJfh4muvf40md/8uQDk9TrZXbg9IX7WOWt488Ga37YobiklKmseE8Q+i6/5VDbZYUhDC+/Z1OMoQojcxtMcXpgODyRRLdPTAcTcogkuf3nlCiAXAfcAlUsq2KvE2cLUQwiqEyAXGAF/1ZayQE5Pmf9sNT8OO7kXHF3euuJOSpp7dhgcCl3Rx/xf3B2S2vfxI577ek5mRNgOAjIyLOeP01XhF0RcmsrJuaH0W42fS8/aYyUhf3CrgfUdn0qRHA9ifYqDT13fKY0AcsEwIsUUI8QSAlHIn8CqwC/gQuL27SIewZ9q1PWv/2s3gaOi+XSe4PW4+P/p5r64NBIdqD/Hopkf73I/D41/mrztn3tn6u65HkZl5hc/2CQmnMGzoN1qfm0yx5OR8B+jJ7NeFzdb7MuZmcxrpaYuIjh5DRvqlzJ2znJSg5LZQDFT6JL5SytFSyuFSymktj++0Ofc7KeUoKeU4KeUHfTc1xNgSeniBAX8aD02d5wnwxVsH3+rxNYFEInk5/2WK6vtWzueMYWeg+ZgJCgTXjr+WjJj25cTHj/sdFktXJcbNnDLlnx1mmLk5dzAy9w56kn7ySMFT2Ky9yzUbFzueyZMfYe6cD5k06c9ER4fxYrEiLFH3SP6y8nc9v8ZZD89f1uPL3j/wfs/HCjAe6eG696+jydV7n/Pw+OF8c8I30Tp5m9l0G9nx2dwx/Y4O5zRN47S5K4mPb7szTEMIK+PH/QqLJanDNUIIEhPz0HX/cwxIacdqy6SnHwNNs5E4JLBRLYrBh9pe7C+HeukGKNkMzdUQNcTvS5xG12V6+pMGVwPvH3yfK8dd2X3jLrj71Ls5J/scntv1HKWNpUSZoog1x3L6sNO5ZPQlXe6u03ULp+a9Sm3tZioqlqPpNjLSLyY6OqfLseLjT6GnMb8WSyqxMWNpaPQRydIullhH16PJGnZNj8YJBEftTv54qIRPjtUDMD85jntzMxhq850tbUd9E789UMKm+ibSLCZ+kJ3OlRlDwmazxGBFia+/2Pxbhe+IgLqSHonvOVnnsLVia49jdQON0+PksS2PsTB3ITGW3metmpE+gxnpM3p1bULCdBIS/Nu1qes2xo37Dfn5P8PwM/wsPn4K2cNvZNPm6zrN4avrMYzIvo3ikv/i8TSRnHw2o0bejdns///zZCqcLlZVNxCtaZydFIdN13j8SBkPHirF2RIwNNSsE2MyccjuwCo0rsxI5H8lVTS1eUu8UlrNK6XVDLOa+cfEHCbF2Xi/opYyh4tZCTGcmhBDfqOdSzbtp6kl/LHO7eGO/ALu2VPIzcNS+PHITGy6ugEOBUp8/eXUb0PBFz2/TmiQ6L8/8L2D7/HolkdDLrzHOWY/xpyX55CXnsfDZz1MSlRwdvEFisyMxcTFTqDo6Is0Nu7H5aqmsfEw3vQjJ6ORlroQmy0dkykOp7O9+AphZezYXzM08zJyc/u286/U7uQ7O4+wub4RhwQrYNY1BHBBcjyvl7evBVfs8oDLu0btlgbPFld12fdRh4tLNu/DKrzuF5chMQlBolkHSavwtsUhJc8crWR/s4MXTlHhcaFAfeX5y6TFMHx2z6+beTNYY/1qWt5Uzi+/+CWeMAwM2VC2gcVvLsZl9CWheP8QGzuO8eMeYOaMl5gz+wPmznkfXWu/+UEIC2mpFxIVNRQhdE6Z8gS6HouuRyOEGU2LIjX1XDIzLu1iFP/ZVtfItLW7+LLOK7zgLfjV4DGo9xgdhLe3OCTYDYkHr7iWOd2UubpOy+mUktXV9exrDJdNKoMLJb7+oulw8wcwrAd5NYbPha/90e/my44swwjQ7rhgUOusZdnh7nO8hhvR0blMn/48cXGTAeH12WZdz6RJf2ptk5AwndPnrWbsmPsZNepuZs54iSmT/xaQuN2rtx7scx/Bwm5Izv4qn7t2H6HRE35f+gMZ5XboCZoO3/oQVv0ZvnrSm91s5Nkw93avT3j/x7DjDbDEwKm3wpQroQeLGk6PMyxnvW1ZX7aei0ZGXv7WhIRpzDr1LaQ0ANHpYpPJFMfQob1fXOyKKnd4/089eP3HR+1OXp0+JtTmDBqU+PYU3Qxn3+d9nEzmFDjj7l53fVbWWfx545/7YFzwGZMY2R/OcNyBJgh9SiAJrK1pZF+jnTEx/ufYUHgRQgwHngMy8IbGPCmlfMTXNeH3ThzEjEwcSazZP/9wKDBrZr4+7uuhNiPiGGrpeo6jA78aNZRRUaGv7+YBDjX7tytR0QE3cLeUcgIwB7i9Ja95lyjxDTNumHhD941CQIw5hpcuegmTZsJtuOlLEv5IREpJ3YcfUXDrEo586xZq334b6aeP9LvZXecFyYmycFt2GmvmTGTL3AkkhTDsSwLj1Ky3V0gpS6SUm1p+rwd200Ua3eMot0OY8a3J3+L5Xc/T4OpdXohgMDdzLv88/59sKt/E5W9dzv6a/dhMNq4ccyV3zbwLs24OtYlBQUpJ84YNNKz9kupXXsGoroaWL53mzZup++BDsh7/e7ebFU6Ji+4y5Xuh3YXDMLBqGvfvL6bGE7oF1xEmwaH/Pc8+l5Oxs+cxfNIpaiNGe1KEEG1L7TwppXzy5EZCiBy8JYXW+epMiW+YYTPZ+OvZf+Xby74dalNaKaovYn/Nfr6z7DvYPd6wpGZ3M6/ufZUqexUPnvlgiC0MPIbTSeGtS2jatAlcHcPrZHMzDatWUb9sOfEXnO+zr1kJMWgCjE5uFjQk5U43h5ocvFVRGyjze45hsPhfv2eT046Ukl2frWDM7NNY8L27lACfoLK7MkJCiFjgdeBOKWWdr7bK7RCGzB46m2mp00JtRis5CTk8s+OZDtueHR4HywqWUdlcGSLLgkfVs8/RtGVLp8J7HJeUPP/sS9z7yRf8q7Ccqi5iaoUQTIntfBu1XcIv9xXxmwNHA2J3r5CShPpqTI7mVneSy2Fn37ovKNwZmNzOgwEhhBmv8L4opXyju/ZKfMMQu9vOnuo9oTYDAB2d26bexr7qfRiy4y2xRbP0OftZOFL7xuvgo2R6gy2KW3/2IH+8fgnPadH8bm8Rs9fuYnt954mIXJ1Ne1v4oLKOHQ0h3OggBA0x8ZSltE+x6XI42LdudYiMiiyE9/bgaWC3lNKvkCUlvmHIodpDPlMxBoL06HSsevuELLrQ22UgizZF89dz/srU1KlMTJ6ILjomOXcaTkbEjwi4fdIw8DQ0wFpJ/wAAE6BJREFUen/W11Px+D8o+dWvadywMeBjdTp+N77XFxYspjgljWabd0Zr1zTqPQa37zrSoe2BJjv7u4kiCPXypUc38dnsC9rZITSBbvGdtEfRyjzgBmB+S27zLUIInwHxyucbhiTZkoK+jbesqazDsevHX89t026joK6AJFsSGTEZrf6+W6bcwkeHP2pX1sim27h45MUMsfU+yUxnVL/8MhWPPoqnvgFhNiObT1TVqHnlFcxjRjPq7beD6otMuOQSKp/4B3SxQWLlqafhMncMDzvS7KTM4SLdemIRstDuxCIE9pBLrA+EoCgzh6MZ2WSVFgCgm0xMOuvcEBsWGUgpV9OTZNIo8Q1L0mPSyUvLY33Z+g4iPDFpIgdrD7YufAWSZ3c/y7Zj2/jb/L+RYG2fPH5E/Aj+s+A//GH9H9hasZV4SzzXT7iemyffHFAbapYupeyhPyDt3tcn3R39qK59+8mfNp3s554lZurUgI7vOnqUyn89RdNXXyEsVmQXNfT0LsLMJKCf9KUwISYKhw+3Q7hg6Cb25U4it7ocw/Bw+jU3kpqdE2qzgsokh5MNhwr8ahvor3oRTvGaeXl5csOGDd03HATUOeu497N7WV+6HrNmBgF3z7ybq8ZdxZ0r72RFwYqgZD4TCKalTeO5hc8FvG9/2D//XFzFftZaFYLUu+4kZcmSgIztLCjg0BVXYjQ3Qyei35YXLryUFy66DEeb23INmB4fzXszx3Zof09+IS+XHMNXZLBZGrgNidS7q2EXPG4QzdxII7nTZhKTGNg7mkAjhNjYXfRBd+QN1eWGJf5tbBK/ruvzeG1RM98wJd4SzxPnP0FlcyVV9ipy4nOw6N7b3B/O/CGfF30eFNeERLKtYhsFdQVkx/d/aRxXebn/jaWk8rG/E79gAZbsvtta8cgjGI2NcHJyI03rcOwby99l87hJ7Bo5BkNomC0W4iwmHp/Yuf/7/7d35+FR1ecCx7/vTGYmgSSSBE0CiSTIooCAimxqgha9gF6oFb0uII9VqT4icl2I4vMUrlZrW5dqtS4XvVfUapV6W1Br3cDaCuJSkUVAXNAAgoiQhCWZZN77xzlAQiYbmcyZhPfzPPOQc+ac37w5JG9+53d+y6/75pEdSuKer+o394AzxWTullKyNm/gw8GntmhOkFgJCUwbdiI9UqydNx7sgVuC65rSlT4ZffYnXoCj04/mjlPviLo8TyzUaA0rt61sk7KbEiwoaNHxGolQ/uZbMfnsXe8tq594AQkGObJkJr6sLPD5kORk0gYP5rGvVvI/O77h5/0KeGhAIe+P6N9g4vKJcFNhLs8POoZOvvr/b36fMGj5O3w8YFjcE68fJ/Hec+zRlnjjyGq+7dSYgjEs/Hwh72x8p03KX/vDWsYR/9nLsmfeROn06/a3+TZJBInRbXpSViY126L0WY5EyDj/ArpeVr99Ow84vQWfUZSZRm4oic/31O0zvSeivFE0gZqk+I8WfLhfD4oz0zgiYOkgnqzm207tCu9i+dblbVb+2u3e9DNOLSoi73e/w9+1mStmqJLWxAiz5sqYfCmE6tb8JBQi7czR+FMPfRml2iqqa9iwt/6qGgrsSu4c91rvgNQUxmdnWOL1gCXfdmrWO7MoCzc6erFVyqvK26zspqSedio9nv1Ds44N9e5NIKehZeabR1XZcs+9bLn99gPNDklJEAjQ+ZRTyL399laVX1vQJ/gaem4e58Sb7BPm9OoW1880B1jybYdUlcWli9v0M1ZuW8nOSu/mGgjl55Ny0klNHhcpb/0fie1PzuOHefPQysoDw4lV6XL+RPJ//xC+TgeWIIpUVbH13ntZO2w4nw4cxFeXTqFqQ/2BFQ0J+nycm51ByFc30QbjnHhTfD7mDijk1Iy0uH6uOcCSbztUFalqcTezaKPTGhMhwgvrXmjRObGWNnp0k7XB6q1bUVU0EmHnggV8NXky6y6exFN/fpnZa7/m6U3fU9HEShLfz53rJN7aamrY8exzbH/uj2ith3Abr5vB948/QWTnTqiqYs+yZXw+dhyVX37ZYPnrd+/l4uWf0+Pt5fT7xwq6BvwMP6IzyT4h3e8jJMKILrFp1miOFJ+weGhfRmelx+0zTX0xSb4icqOIqIh0dbdFRB4QkfUi8omIHNq64SaqoC9IkjS/je7SfpdSMrSEZH/L5mpdsmlJS0OLqbTRP4JA4w+gNByG6mo2zZzJ5tlz+Hb1Wv7jx5P5eSiTRzdt5+eflTJ06Wq+3H0guWpVFTU7duyfRKbmhx8aKFzZMmcOa088ifDGjZQvWkTF22/DwQMsIhG+GD+B8rfq97r4tjLMuA/WsWh7OZURZXu4hsc3biM9yc/bQ4/l8QGFLBvRj/8eUNiyi3OIBJg/6Bjr1ZAAWp183eUzzgRqDxMZC/R2X1OBh1v7OeYAEeHKgVc269hOSZ24etDVXHTsRdx/+v0Myx1GRqh5nee7pXrbHhjMz+eoGTOgkd4Mod69qVy/nvI33kT37OHRcy/ku4zM/XMu7I4oO8I1zFjzNZGqKjbeNJM1g09g3fARrOnXn2+mT6/TrBCN7t3L+rHjKL12etSuaACEw5ROu5aNN95ITcWBuZgfL/2OvZG69yl7I8pr35chwGmZaWSHAqQn+Tk9Dk0AqX7f/hWUjbdiUfO9D5hJ3blBJgDz1LEU6CIiuVHPNofkqkFXMem4SchBD2/29f3142dk7khem/gaqUFnBM/I7iOZe9Zcnv/355ssP+gLMum4SbEPvIWyfnoZPV9aSOrYsXWbINz+tllX/YxNs27d3zXtnROGUX1Qd60I8MHOXXxRcgtlCxceSKCqVLz2OpHmrEhRVdXkqDciEcpeepnPTiti19KlAHxctpuqKKNIgyKsPWjJ9rnHF9AjuW2XEwqrcnxa9OktTXy1qn+JiIwHNqrq8oMmOekOfFNru9TdtzlKGVNxasccHYNRSocLn/goGVrC9UOup6yyjNRAKhXhCtJD6c5w5EbkdM5hYu+JzP9sfr33BCEtmMZtp9xG38y+bRV+i4QKC+k2ZzZVV1zOD089za4lS5DkZPD52HR93QVLT171MUuOP4m9yQeaWNIryinYspldb75B1NS2O/r8DYdK9+yh9Jpp9H73nxyXmszSnRWED8q/YVV6dqp769/Z72fp8ON44dvtTlt1TYSy6ho2VoajtvCL+2ru2hedfML1BTmkJXk3fNkc0GTyFZE3cFbkPNitwCzgrGinRdkX9WbHXYbjMXDmdmgqHlNXwBcgKyULgFBS89vxZo+czaj8UTyy/BEqwhWckX8GF/S9gMpIJT3SeuD3ef8LWrNzJ3tWreK7e+9j75o1To21odt+V8m8R1ERfjNpKouGjODa559k3D8XoYEAwar6/Wvb0q533+WK4SN5ZvN2wrWmqAz5hOFHpHJMp/pt8CLCBblZXJCbVWf/37eXM+mTL6hRpwkjSYQp3bPIDwX4r883NzhnxLD0TpTVRDgymMTU/KPsIVsCaTL5quroaPtF5HigENhX680DPhKRoTg13fxah+cBzZwtxcRLcX4xxfnFXodRT015OZtuvoWKxYvrP9xqQqja6So28+lH6fXNl4x9d7Gzr7ptp+iMRqurOTolxJ8G96Jk3TesKN9DwCecn53Bbb3zWlRWUWYaq08dwKvbdlJWXUNxZtr+5N0tJcg1qzbUacv1A38Y2JNiS7YJ65CbHVR1BbB/WVYR+QoYoqrbRGQBME1EngOGATtVtV6TgzHRlE6/jt3LlrU48dYWCIeZuOhVAq0oozW0uprOw4cDMDi9E38b0pdwRPGLM8/DoUhN8jMxJ7Pe/nOOzODs4i4s3VHBa9+XUZgS4pLcTPxR5pAwbUdEngDOAbaq6oCmjm+rMYWvAOOA9cBuILaTvpoOq6p0I3s++qhViRecJ8k+jxIvwSA5t92GP61u74WAr+0GUogIIzLSGGGDJrz0v8CDQLPmY41Z8lXVglpfK3BNrMo2h4/qrVv2L8/eXnWdeiVdJoz3OgwTZ6r6d3fZ+Gax+xKTUJJyctA4PxiLtaoNX9cZFWdMNJZ8TULZ8+GHjQ6qaA/KFi7ks6JiIo2sfmzapa4i8kGtV6uWULHkaxKKhqvbffIFqNm2jS13/crrMExsbVPVIbVej7WmMEu+JqGkFp3mdQgxU/byy16HYBKYzaBsEkpS165kl8xky52/bHWPB69Fdu3yOgTThBXak4K9v23m0ec0+q6IPAuMwmmeKAVmq+rjDR1vNV+TcDIvuYSeCxdwxHk/IVAYn9m+2kRNDXtXr/Y6ChMnqnqRquaqakBV8xpLvGDJ1ySoUM+edLvjDnr99RVy7rzT63AOjQh7VnizEKlJfJZ8TcLL+Mm5ZN/xC2dpn/ZEhEA3m8zPRGfJ17QLmeedxzEvLSQpr7vXoTSbLzWVziNHeh2GSVCWfE27ESwooOf8+SQPGOCscJHAcxdIKETh/Bditqy96Xja2X2cOdz5u3ShcP4L7F27jqoNX7FpZsn+idTjTiTqUGhfamd6LV6MPzXVg6BMe5G4VQdjGpHctw/pZ51FxqRJSEp8V2aQlBSOXbmC4z5dTd4jj5DUvbuTiP1+Op18MoUvvmiJ1zTJar6mXTvqP2cgSX62z3vKmROiGROut4YEg2ROmoS4D//SRhWTNqqYSFUVqOIL2cKUpnms5mvaNfH7OWrGDPq+v4w+S94l+YQT2u7DfD4yLrmEI2dcV/+tYNASr2kRS76mQxC/H39aGkf+bGr9ZgifD0k79HluJRgk2KsXvf/xDtklM+0hmokJa3YwHUpqURHZN93E1nvuAUDDYToXFZHcvx/b7n+g+QUlJRHq04fUotNIGTiQ1OJiS7ompiz5mg4n4+KLOGLieYS//hp/VhZJGRmEt2xh24MPRZ0vIu3ss/GFgpS99DISDKLV1ST370/+Iw/XW43CmFix5Gs6JF8wSKhXr/3bgexsut99NxtvuKHOA7lgYSG5c2Y7TRbTp1O5bh2Bbt3qnGtMW7Dkaw4b6WPH0Pn0Uex8YT7hb78ldVQxnYYMwV19m0BODoGcHI+jNIcLS77msOJPTiZz8iSvwzDGejsYY4wXLPkaY4wHLPkaY0wMiMgYEVkrIutF5Oamjrfka4wxrSQifuAhYCzQD7hIRPo1do4lX2OMab2hwHpV/UJVq4DngAmNnSAaZUo8r4jId8CGGBXXFdgWo7LaksUZO+0hRrA4Y6WHqh7ZmgJE5FWc77M5koHa85c+tm/5eBGZCIxR1Svc7cnAMFWd1lBhCdXVrLUXsjYR+UBVh8SqvLZiccZOe4gRLM5EoqpjYlSURCu+sROs2cEYY1qvFMivtZ0HbGrsBEu+xhjTeu8DvUWkUESCwIXAgsZOSKhmhxh7zOsAmsnijJ32ECNYnB2OqlaLyDTgb4AfeEJVVzV2TkI9cDPGmMOFNTsYY4wHLPkaY4wHOmTyFZFr3WF+q0Tk17X23+IO/VsrIv/mZYz7iMiNIqIi0tXdFhF5wI3zExE50cPYfiMia9w4/k9EutR6L6GuZUuHdsaLiOSLyCIR+dT9ebzO3Z8pIq+LyGfuvxkJEKtfRP4lIi+524Ui8p4b4x/dB0kmRjpc8hWR03FGlgxU1f7A3e7+fjhPIPsDY4Dfu0MCPSMi+cCZwNe1do8FeruvqcDDHoS2z+vAAFUdCKwDboHEu5aHMrQzjqqBG1T1OGA4cI0b283Am6raG3jT3fbadcCntbZ/BdznxvgDcLknUXVQHS75AlcDd6lqJYCqbnX3TwCeU9VKVf0SWI8zJNBL9wEzqdsZewIwTx1LgS4ikutFcKr6mqpWu5tLcfou7osxka5li4d2xouqblbVj9yvy3GSW3ec+J50D3sS+LE3ETpEJA84G5jrbgtwBjDfPcTzGDuajph8+wCnubdLb4vIye7+7sA3tY4rdfd5QkTGAxtVdflBbyVUnLX8FPir+3WixZho8UQlIgXACcB7QLaqbgYnQQNHeRcZAL/FqQjsW2MpC9hR649vQl7T9qxd9vMVkTeAaOu93IrzPWXg3OKdDDwvIj05hOF/rdVEnLOAs6KdFmVfm8XZWIyq+hf3mFtxbp+f2XdalOO97LOYaPHUIyKpwJ+AGapatm/pokQgIucAW1X1QxEZtW93lEMT6pq2d+0y+arq6IbeE5GrgRfV6cC8TEQiOBNntHj4X1vFKSLHA4XAcveXMA/4SESGxjvOxq4lgIhMAc4BfqQHOoXH/Vo2IdHiqUNEAjiJ9xlVfdHdvUVEclV1s9ustLXhEtrcKcB4ERmHM3lMOk5NuIuIJLm134S6ph1BR2x2+DNOWxUi0gcI4szMtAC4UERCIlKI80BrmRcBquoKVT1KVQtUtQAneZyoqt+6cV7q9noYDuzcd3sabyIyBigBxqvq7lpvJcy1dLV4aGe8uG2njwOfquq9td5aAExxv54C/CXese2jqreoap77s3gh8JaqXgIsAia6h3kaY0fULmu+TXgCeEJEVgJVwBS3xrZKRJ4HVuPcQl+jqjUextmQV4BxOA+xdgOXeRjLg0AIeN2toS9V1atUNaGu5aEM7YyjU4DJwAoR+djdNwu4C6dJ7HKc3i7nexRfY0qA50TkF8C/cP6ImBix4cXGGOOBjtjsYIwxCc+SrzHGeMCSrzHGeMCSrzHGeMCSrzHGeMCSrzHGeMCSrzHGeOD/ATk+bv0MCNEeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    mnist_2d_tsne[:,0],\n",
    "    mnist_2d_tsne[:,1],\n",
    "    c=mnist.label,\n",
    "    cmap='tab10'\n",
    ")\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reducción de dimensionalidad de datos de microarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "microarray = pd.read_csv(\"data/gene_expressions.tsv\", sep=\"\\t\", index_col=\"gene\").transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>gene</th>\n",
       "      <th>A1BG</th>\n",
       "      <th>A2M</th>\n",
       "      <th>A2ML1</th>\n",
       "      <th>A4GALT</th>\n",
       "      <th>AAAS</th>\n",
       "      <th>AACS</th>\n",
       "      <th>AADAC</th>\n",
       "      <th>AAED1</th>\n",
       "      <th>AAGAB</th>\n",
       "      <th>AAMP</th>\n",
       "      <th>...</th>\n",
       "      <th>ZSWIM7</th>\n",
       "      <th>ZSWIM8</th>\n",
       "      <th>ZUFSP</th>\n",
       "      <th>ZW10</th>\n",
       "      <th>ZWILCH</th>\n",
       "      <th>ZXDA</th>\n",
       "      <th>ZXDB</th>\n",
       "      <th>ZXDC</th>\n",
       "      <th>ZYG11B</th>\n",
       "      <th>ZZZ3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>786-0</th>\n",
       "      <td>-1.025477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.978677</td>\n",
       "      <td>0.878385</td>\n",
       "      <td>-0.354923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.419631</td>\n",
       "      <td>0.369015</td>\n",
       "      <td>-0.128523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.266154</td>\n",
       "      <td>0.002246</td>\n",
       "      <td>0.482123</td>\n",
       "      <td>0.605908</td>\n",
       "      <td>2.007554</td>\n",
       "      <td>-0.359754</td>\n",
       "      <td>-0.193538</td>\n",
       "      <td>-0.565677</td>\n",
       "      <td>-0.243108</td>\n",
       "      <td>0.456292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A498</th>\n",
       "      <td>-0.925477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>1.588677</td>\n",
       "      <td>0.178385</td>\n",
       "      <td>-0.184923</td>\n",
       "      <td>-0.389323</td>\n",
       "      <td>1.779631</td>\n",
       "      <td>0.249015</td>\n",
       "      <td>-0.198523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.106154</td>\n",
       "      <td>0.042246</td>\n",
       "      <td>0.092123</td>\n",
       "      <td>-0.384092</td>\n",
       "      <td>1.227554</td>\n",
       "      <td>0.770246</td>\n",
       "      <td>0.386462</td>\n",
       "      <td>-0.705677</td>\n",
       "      <td>-0.233108</td>\n",
       "      <td>-0.113708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A549</th>\n",
       "      <td>0.274523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>0.908677</td>\n",
       "      <td>1.658385</td>\n",
       "      <td>-0.074923</td>\n",
       "      <td>0.880677</td>\n",
       "      <td>0.809631</td>\n",
       "      <td>0.649015</td>\n",
       "      <td>0.381477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.366154</td>\n",
       "      <td>-0.627754</td>\n",
       "      <td>-0.047877</td>\n",
       "      <td>0.405908</td>\n",
       "      <td>2.227554</td>\n",
       "      <td>0.040246</td>\n",
       "      <td>0.616462</td>\n",
       "      <td>-0.775677</td>\n",
       "      <td>-0.243108</td>\n",
       "      <td>-0.433708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ACHN</th>\n",
       "      <td>-0.875477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>0.348677</td>\n",
       "      <td>-0.291615</td>\n",
       "      <td>-0.014923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.179631</td>\n",
       "      <td>-0.500985</td>\n",
       "      <td>-1.038523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.266154</td>\n",
       "      <td>0.092246</td>\n",
       "      <td>0.192123</td>\n",
       "      <td>-0.854092</td>\n",
       "      <td>0.947554</td>\n",
       "      <td>-0.259754</td>\n",
       "      <td>-0.533538</td>\n",
       "      <td>-1.125677</td>\n",
       "      <td>-1.633108</td>\n",
       "      <td>-0.203708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BT-549</th>\n",
       "      <td>2.484523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.098677</td>\n",
       "      <td>-0.011615</td>\n",
       "      <td>-2.114923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.379631</td>\n",
       "      <td>-0.630985</td>\n",
       "      <td>-1.168523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.306154</td>\n",
       "      <td>0.702246</td>\n",
       "      <td>0.752123</td>\n",
       "      <td>0.465908</td>\n",
       "      <td>0.887554</td>\n",
       "      <td>-0.199754</td>\n",
       "      <td>-0.083538</td>\n",
       "      <td>-0.785677</td>\n",
       "      <td>-0.773108</td>\n",
       "      <td>0.586292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CAKI-1</th>\n",
       "      <td>1.244523</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.488677</td>\n",
       "      <td>0.568385</td>\n",
       "      <td>-0.504923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.119631</td>\n",
       "      <td>-0.380985</td>\n",
       "      <td>-0.048523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.456154</td>\n",
       "      <td>0.392246</td>\n",
       "      <td>-0.437877</td>\n",
       "      <td>-0.274092</td>\n",
       "      <td>0.897554</td>\n",
       "      <td>0.130246</td>\n",
       "      <td>-0.233538</td>\n",
       "      <td>-0.545677</td>\n",
       "      <td>-0.583108</td>\n",
       "      <td>-0.243708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CCRF-CEM</th>\n",
       "      <td>1.914523</td>\n",
       "      <td>-1.299323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.791323</td>\n",
       "      <td>1.518385</td>\n",
       "      <td>-0.824923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-1.930369</td>\n",
       "      <td>-0.000985</td>\n",
       "      <td>-0.178523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.543846</td>\n",
       "      <td>-0.827754</td>\n",
       "      <td>0.492123</td>\n",
       "      <td>1.005908</td>\n",
       "      <td>1.397554</td>\n",
       "      <td>-0.199754</td>\n",
       "      <td>0.666462</td>\n",
       "      <td>0.454323</td>\n",
       "      <td>-0.493108</td>\n",
       "      <td>0.026292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>COLO205</th>\n",
       "      <td>-1.025477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.041323</td>\n",
       "      <td>0.148385</td>\n",
       "      <td>1.395077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.129631</td>\n",
       "      <td>0.229015</td>\n",
       "      <td>-0.548523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.176154</td>\n",
       "      <td>-0.827754</td>\n",
       "      <td>-0.447877</td>\n",
       "      <td>-0.114092</td>\n",
       "      <td>1.267554</td>\n",
       "      <td>-0.699754</td>\n",
       "      <td>-0.323538</td>\n",
       "      <td>0.224323</td>\n",
       "      <td>-1.613108</td>\n",
       "      <td>-0.803708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DU-145</th>\n",
       "      <td>0.584523</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.601323</td>\n",
       "      <td>0.158385</td>\n",
       "      <td>-0.264923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.189631</td>\n",
       "      <td>-0.120985</td>\n",
       "      <td>-0.938523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.893846</td>\n",
       "      <td>-0.657754</td>\n",
       "      <td>-0.357877</td>\n",
       "      <td>0.315908</td>\n",
       "      <td>1.567554</td>\n",
       "      <td>-0.869754</td>\n",
       "      <td>-0.313538</td>\n",
       "      <td>-0.945677</td>\n",
       "      <td>-1.183108</td>\n",
       "      <td>-0.383708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EKVX</th>\n",
       "      <td>0.094523</td>\n",
       "      <td>0.100677</td>\n",
       "      <td>-1.586062</td>\n",
       "      <td>1.498677</td>\n",
       "      <td>1.038385</td>\n",
       "      <td>0.695077</td>\n",
       "      <td>0.060677</td>\n",
       "      <td>0.459631</td>\n",
       "      <td>0.939015</td>\n",
       "      <td>-0.048523</td>\n",
       "      <td>...</td>\n",
       "      <td>1.276154</td>\n",
       "      <td>1.002246</td>\n",
       "      <td>0.372123</td>\n",
       "      <td>0.645908</td>\n",
       "      <td>1.967554</td>\n",
       "      <td>0.580246</td>\n",
       "      <td>1.026462</td>\n",
       "      <td>-0.695677</td>\n",
       "      <td>1.366892</td>\n",
       "      <td>0.486292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HCC-2998</th>\n",
       "      <td>-0.795477</td>\n",
       "      <td>-1.349323</td>\n",
       "      <td>-1.616062</td>\n",
       "      <td>0.778677</td>\n",
       "      <td>-0.441615</td>\n",
       "      <td>-0.964923</td>\n",
       "      <td>-0.729323</td>\n",
       "      <td>0.359631</td>\n",
       "      <td>-0.010985</td>\n",
       "      <td>-1.678523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.773846</td>\n",
       "      <td>-0.497754</td>\n",
       "      <td>0.532123</td>\n",
       "      <td>-0.204092</td>\n",
       "      <td>0.947554</td>\n",
       "      <td>0.020246</td>\n",
       "      <td>-0.063538</td>\n",
       "      <td>-0.435677</td>\n",
       "      <td>-0.873108</td>\n",
       "      <td>-0.283708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HCT-116</th>\n",
       "      <td>-0.915477</td>\n",
       "      <td>-1.289323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.968677</td>\n",
       "      <td>1.348385</td>\n",
       "      <td>-1.314923</td>\n",
       "      <td>0.060677</td>\n",
       "      <td>0.499631</td>\n",
       "      <td>0.339015</td>\n",
       "      <td>0.541477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.646154</td>\n",
       "      <td>-0.517754</td>\n",
       "      <td>0.892123</td>\n",
       "      <td>0.925908</td>\n",
       "      <td>0.987554</td>\n",
       "      <td>-0.199754</td>\n",
       "      <td>0.306462</td>\n",
       "      <td>-0.265677</td>\n",
       "      <td>0.036892</td>\n",
       "      <td>0.296292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HCT-15</th>\n",
       "      <td>-0.955477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.591323</td>\n",
       "      <td>-0.781615</td>\n",
       "      <td>-0.254923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-0.630369</td>\n",
       "      <td>-0.820985</td>\n",
       "      <td>-1.988523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.453846</td>\n",
       "      <td>-0.007754</td>\n",
       "      <td>1.282123</td>\n",
       "      <td>-0.344092</td>\n",
       "      <td>0.457554</td>\n",
       "      <td>-0.229754</td>\n",
       "      <td>-0.533538</td>\n",
       "      <td>-0.275677</td>\n",
       "      <td>-0.883108</td>\n",
       "      <td>-0.363708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HL-60</th>\n",
       "      <td>-0.625477</td>\n",
       "      <td>-1.349323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.858385</td>\n",
       "      <td>-0.894923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-0.010369</td>\n",
       "      <td>-0.410985</td>\n",
       "      <td>-0.328523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.463846</td>\n",
       "      <td>-1.397754</td>\n",
       "      <td>0.742123</td>\n",
       "      <td>0.175908</td>\n",
       "      <td>-0.022446</td>\n",
       "      <td>-0.569754</td>\n",
       "      <td>-0.133538</td>\n",
       "      <td>0.184323</td>\n",
       "      <td>-0.813108</td>\n",
       "      <td>0.326292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HOP-62</th>\n",
       "      <td>0.584523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.081323</td>\n",
       "      <td>-0.401615</td>\n",
       "      <td>-0.694923</td>\n",
       "      <td>-0.669323</td>\n",
       "      <td>0.689631</td>\n",
       "      <td>-0.630985</td>\n",
       "      <td>-0.418523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.716154</td>\n",
       "      <td>-0.397754</td>\n",
       "      <td>-0.617877</td>\n",
       "      <td>-0.024092</td>\n",
       "      <td>1.047554</td>\n",
       "      <td>-0.679754</td>\n",
       "      <td>0.116462</td>\n",
       "      <td>-1.055677</td>\n",
       "      <td>-0.733108</td>\n",
       "      <td>-0.263708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HOP-92</th>\n",
       "      <td>1.394523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>1.208677</td>\n",
       "      <td>0.958385</td>\n",
       "      <td>-0.354923</td>\n",
       "      <td>-0.779323</td>\n",
       "      <td>0.879631</td>\n",
       "      <td>-0.510985</td>\n",
       "      <td>0.281477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.373846</td>\n",
       "      <td>0.262246</td>\n",
       "      <td>0.072123</td>\n",
       "      <td>0.385908</td>\n",
       "      <td>1.267554</td>\n",
       "      <td>-0.049754</td>\n",
       "      <td>0.266462</td>\n",
       "      <td>-0.665677</td>\n",
       "      <td>0.116892</td>\n",
       "      <td>0.556292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HS-578T</th>\n",
       "      <td>2.754523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.581323</td>\n",
       "      <td>-0.411615</td>\n",
       "      <td>-1.304923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.959631</td>\n",
       "      <td>-0.470985</td>\n",
       "      <td>-0.738523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.066154</td>\n",
       "      <td>-0.347754</td>\n",
       "      <td>-0.387877</td>\n",
       "      <td>-0.134092</td>\n",
       "      <td>1.207554</td>\n",
       "      <td>-0.749754</td>\n",
       "      <td>-1.203538</td>\n",
       "      <td>-1.255677</td>\n",
       "      <td>-0.683108</td>\n",
       "      <td>-0.053708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HT29</th>\n",
       "      <td>-0.965477</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.278677</td>\n",
       "      <td>-1.071615</td>\n",
       "      <td>-0.874923</td>\n",
       "      <td>-0.749323</td>\n",
       "      <td>-0.690369</td>\n",
       "      <td>0.169015</td>\n",
       "      <td>-1.488523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.883846</td>\n",
       "      <td>-1.547754</td>\n",
       "      <td>-0.327877</td>\n",
       "      <td>-0.964092</td>\n",
       "      <td>0.657554</td>\n",
       "      <td>-1.269754</td>\n",
       "      <td>-2.013538</td>\n",
       "      <td>-0.665677</td>\n",
       "      <td>-2.603108</td>\n",
       "      <td>-0.573708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IGR-OV1</th>\n",
       "      <td>0.604523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>2.368677</td>\n",
       "      <td>0.308385</td>\n",
       "      <td>0.295077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.579631</td>\n",
       "      <td>-0.240985</td>\n",
       "      <td>-0.188523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.686154</td>\n",
       "      <td>-0.187754</td>\n",
       "      <td>0.442123</td>\n",
       "      <td>0.375908</td>\n",
       "      <td>0.757554</td>\n",
       "      <td>0.010246</td>\n",
       "      <td>-0.103538</td>\n",
       "      <td>-0.445677</td>\n",
       "      <td>-0.113108</td>\n",
       "      <td>0.196292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K-562</th>\n",
       "      <td>0.564523</td>\n",
       "      <td>-1.379323</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>-2.201323</td>\n",
       "      <td>1.688385</td>\n",
       "      <td>-0.634923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.789631</td>\n",
       "      <td>0.349015</td>\n",
       "      <td>-0.118523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.713846</td>\n",
       "      <td>0.862246</td>\n",
       "      <td>1.072123</td>\n",
       "      <td>0.715908</td>\n",
       "      <td>1.267554</td>\n",
       "      <td>-1.009754</td>\n",
       "      <td>-0.613538</td>\n",
       "      <td>-0.565677</td>\n",
       "      <td>-0.043108</td>\n",
       "      <td>-0.173708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KM12</th>\n",
       "      <td>-0.845477</td>\n",
       "      <td>-1.379323</td>\n",
       "      <td>1.733938</td>\n",
       "      <td>-1.361323</td>\n",
       "      <td>-0.871615</td>\n",
       "      <td>-0.674923</td>\n",
       "      <td>-0.779323</td>\n",
       "      <td>-1.440369</td>\n",
       "      <td>-0.380985</td>\n",
       "      <td>-2.068523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.153846</td>\n",
       "      <td>-1.297754</td>\n",
       "      <td>0.162123</td>\n",
       "      <td>-1.234092</td>\n",
       "      <td>0.037554</td>\n",
       "      <td>-1.389754</td>\n",
       "      <td>-0.923538</td>\n",
       "      <td>-0.825677</td>\n",
       "      <td>-1.823108</td>\n",
       "      <td>-0.613708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LOX-IMVI</th>\n",
       "      <td>-1.025477</td>\n",
       "      <td>-1.379323</td>\n",
       "      <td>-1.626062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.488385</td>\n",
       "      <td>-1.604923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.749631</td>\n",
       "      <td>-0.550985</td>\n",
       "      <td>-0.868523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.063846</td>\n",
       "      <td>-0.517754</td>\n",
       "      <td>0.092123</td>\n",
       "      <td>0.135908</td>\n",
       "      <td>1.297554</td>\n",
       "      <td>-0.469754</td>\n",
       "      <td>-1.263538</td>\n",
       "      <td>-0.825677</td>\n",
       "      <td>-1.913108</td>\n",
       "      <td>-0.103708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M14</th>\n",
       "      <td>0.684523</td>\n",
       "      <td>2.260677</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>-2.201323</td>\n",
       "      <td>1.688385</td>\n",
       "      <td>0.515077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.339631</td>\n",
       "      <td>0.289015</td>\n",
       "      <td>0.151477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.826154</td>\n",
       "      <td>0.202246</td>\n",
       "      <td>-0.467877</td>\n",
       "      <td>1.055908</td>\n",
       "      <td>1.727554</td>\n",
       "      <td>0.180246</td>\n",
       "      <td>0.056462</td>\n",
       "      <td>-0.175677</td>\n",
       "      <td>0.416892</td>\n",
       "      <td>1.076292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MALME-3M</th>\n",
       "      <td>1.984523</td>\n",
       "      <td>5.510677</td>\n",
       "      <td>-1.616062</td>\n",
       "      <td>0.258677</td>\n",
       "      <td>1.118385</td>\n",
       "      <td>1.235077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.259631</td>\n",
       "      <td>0.289015</td>\n",
       "      <td>0.241477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.386154</td>\n",
       "      <td>0.972246</td>\n",
       "      <td>0.122123</td>\n",
       "      <td>0.065908</td>\n",
       "      <td>1.887554</td>\n",
       "      <td>0.320246</td>\n",
       "      <td>0.496462</td>\n",
       "      <td>-0.015677</td>\n",
       "      <td>0.116892</td>\n",
       "      <td>0.516292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MCF7</th>\n",
       "      <td>1.594523</td>\n",
       "      <td>-1.369323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.238677</td>\n",
       "      <td>0.018385</td>\n",
       "      <td>-0.744923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-0.970369</td>\n",
       "      <td>0.229015</td>\n",
       "      <td>-0.568523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.566154</td>\n",
       "      <td>-0.747754</td>\n",
       "      <td>-0.147877</td>\n",
       "      <td>-0.954092</td>\n",
       "      <td>1.557554</td>\n",
       "      <td>-0.609754</td>\n",
       "      <td>-0.633538</td>\n",
       "      <td>-1.215677</td>\n",
       "      <td>-1.703108</td>\n",
       "      <td>-0.523708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MDA-MB-231</th>\n",
       "      <td>0.414523</td>\n",
       "      <td>-1.269323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.508677</td>\n",
       "      <td>-0.101615</td>\n",
       "      <td>0.055077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.249631</td>\n",
       "      <td>-0.700985</td>\n",
       "      <td>0.051477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.916154</td>\n",
       "      <td>-0.027754</td>\n",
       "      <td>0.202123</td>\n",
       "      <td>1.205908</td>\n",
       "      <td>0.247554</td>\n",
       "      <td>0.230246</td>\n",
       "      <td>0.756462</td>\n",
       "      <td>-0.905677</td>\n",
       "      <td>0.066892</td>\n",
       "      <td>0.786292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MDA-MB-435</th>\n",
       "      <td>1.154523</td>\n",
       "      <td>-1.269323</td>\n",
       "      <td>-1.636062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.858385</td>\n",
       "      <td>-0.584923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.869631</td>\n",
       "      <td>0.059015</td>\n",
       "      <td>0.691477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.416154</td>\n",
       "      <td>-0.117754</td>\n",
       "      <td>-0.197877</td>\n",
       "      <td>0.875908</td>\n",
       "      <td>1.887554</td>\n",
       "      <td>-0.859754</td>\n",
       "      <td>-0.133538</td>\n",
       "      <td>-0.515677</td>\n",
       "      <td>-0.213108</td>\n",
       "      <td>0.346292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MDA-MB-468</th>\n",
       "      <td>0.684523</td>\n",
       "      <td>2.380677</td>\n",
       "      <td>-1.296062</td>\n",
       "      <td>-0.241323</td>\n",
       "      <td>-0.711615</td>\n",
       "      <td>-0.264923</td>\n",
       "      <td>0.430677</td>\n",
       "      <td>-0.020369</td>\n",
       "      <td>0.079015</td>\n",
       "      <td>-0.608523</td>\n",
       "      <td>...</td>\n",
       "      <td>1.636154</td>\n",
       "      <td>-0.207754</td>\n",
       "      <td>1.202123</td>\n",
       "      <td>0.565908</td>\n",
       "      <td>0.327554</td>\n",
       "      <td>0.010246</td>\n",
       "      <td>-0.093538</td>\n",
       "      <td>-0.085677</td>\n",
       "      <td>-0.223108</td>\n",
       "      <td>0.846292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MOLT-4</th>\n",
       "      <td>1.644523</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.898385</td>\n",
       "      <td>0.025077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-2.480369</td>\n",
       "      <td>-0.100985</td>\n",
       "      <td>-0.088523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.266154</td>\n",
       "      <td>-0.277754</td>\n",
       "      <td>0.312123</td>\n",
       "      <td>0.935908</td>\n",
       "      <td>0.857554</td>\n",
       "      <td>0.460246</td>\n",
       "      <td>0.296462</td>\n",
       "      <td>0.114323</td>\n",
       "      <td>-0.903108</td>\n",
       "      <td>0.406292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-ADR-RES</th>\n",
       "      <td>0.834523</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.158677</td>\n",
       "      <td>1.168385</td>\n",
       "      <td>-0.454923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-0.380369</td>\n",
       "      <td>0.119015</td>\n",
       "      <td>-0.178523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.063846</td>\n",
       "      <td>0.012246</td>\n",
       "      <td>0.142123</td>\n",
       "      <td>1.635908</td>\n",
       "      <td>1.357554</td>\n",
       "      <td>-0.229754</td>\n",
       "      <td>-0.433538</td>\n",
       "      <td>0.094323</td>\n",
       "      <td>-0.193108</td>\n",
       "      <td>0.376292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-H226</th>\n",
       "      <td>0.124523</td>\n",
       "      <td>-0.379323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.841323</td>\n",
       "      <td>0.848385</td>\n",
       "      <td>0.755077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.909631</td>\n",
       "      <td>0.769015</td>\n",
       "      <td>-0.758523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.033846</td>\n",
       "      <td>0.032246</td>\n",
       "      <td>0.462123</td>\n",
       "      <td>0.345908</td>\n",
       "      <td>1.757554</td>\n",
       "      <td>-0.049754</td>\n",
       "      <td>-0.033538</td>\n",
       "      <td>-0.605677</td>\n",
       "      <td>0.006892</td>\n",
       "      <td>0.666292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-H23</th>\n",
       "      <td>0.324523</td>\n",
       "      <td>0.240677</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>0.498677</td>\n",
       "      <td>1.088385</td>\n",
       "      <td>-0.374923</td>\n",
       "      <td>-0.779323</td>\n",
       "      <td>0.749631</td>\n",
       "      <td>0.669015</td>\n",
       "      <td>0.511477</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.063846</td>\n",
       "      <td>0.012246</td>\n",
       "      <td>0.312123</td>\n",
       "      <td>0.415908</td>\n",
       "      <td>1.997554</td>\n",
       "      <td>0.140246</td>\n",
       "      <td>0.396462</td>\n",
       "      <td>0.044323</td>\n",
       "      <td>-0.003108</td>\n",
       "      <td>0.376292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-H322M</th>\n",
       "      <td>1.414523</td>\n",
       "      <td>-1.159323</td>\n",
       "      <td>0.023938</td>\n",
       "      <td>3.008677</td>\n",
       "      <td>0.568385</td>\n",
       "      <td>-0.134923</td>\n",
       "      <td>-0.599323</td>\n",
       "      <td>-0.060369</td>\n",
       "      <td>0.829015</td>\n",
       "      <td>-0.018523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.996154</td>\n",
       "      <td>0.092246</td>\n",
       "      <td>-0.107877</td>\n",
       "      <td>0.925908</td>\n",
       "      <td>1.377554</td>\n",
       "      <td>0.270246</td>\n",
       "      <td>0.216462</td>\n",
       "      <td>0.174323</td>\n",
       "      <td>-0.223108</td>\n",
       "      <td>0.546292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-H460</th>\n",
       "      <td>-0.005477</td>\n",
       "      <td>-1.339323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.238677</td>\n",
       "      <td>0.818385</td>\n",
       "      <td>-0.744923</td>\n",
       "      <td>0.650677</td>\n",
       "      <td>1.049631</td>\n",
       "      <td>-0.190985</td>\n",
       "      <td>-0.678523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.156154</td>\n",
       "      <td>-1.067754</td>\n",
       "      <td>-0.207877</td>\n",
       "      <td>-0.494092</td>\n",
       "      <td>1.097554</td>\n",
       "      <td>-0.379754</td>\n",
       "      <td>-0.133538</td>\n",
       "      <td>-1.475677</td>\n",
       "      <td>-1.443108</td>\n",
       "      <td>-0.183708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NCI-H522</th>\n",
       "      <td>1.524523</td>\n",
       "      <td>-1.309323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.561323</td>\n",
       "      <td>-0.241615</td>\n",
       "      <td>-1.414923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.869631</td>\n",
       "      <td>-0.670985</td>\n",
       "      <td>-0.968523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.246154</td>\n",
       "      <td>-0.817754</td>\n",
       "      <td>0.042123</td>\n",
       "      <td>-0.324092</td>\n",
       "      <td>0.697554</td>\n",
       "      <td>1.870246</td>\n",
       "      <td>0.036462</td>\n",
       "      <td>-1.395677</td>\n",
       "      <td>-0.643108</td>\n",
       "      <td>-0.643708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OVCAR-3</th>\n",
       "      <td>0.914523</td>\n",
       "      <td>-1.369323</td>\n",
       "      <td>-1.446062</td>\n",
       "      <td>-0.721323</td>\n",
       "      <td>1.158385</td>\n",
       "      <td>0.885077</td>\n",
       "      <td>-0.739323</td>\n",
       "      <td>-0.540369</td>\n",
       "      <td>0.429015</td>\n",
       "      <td>1.281477</td>\n",
       "      <td>...</td>\n",
       "      <td>1.026154</td>\n",
       "      <td>0.462246</td>\n",
       "      <td>0.452123</td>\n",
       "      <td>0.345908</td>\n",
       "      <td>1.697554</td>\n",
       "      <td>0.010246</td>\n",
       "      <td>0.256462</td>\n",
       "      <td>0.694323</td>\n",
       "      <td>-0.183108</td>\n",
       "      <td>0.766292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OVCAR-4</th>\n",
       "      <td>-0.035477</td>\n",
       "      <td>-1.369323</td>\n",
       "      <td>-1.556062</td>\n",
       "      <td>1.468677</td>\n",
       "      <td>0.848385</td>\n",
       "      <td>0.085077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.309631</td>\n",
       "      <td>0.179015</td>\n",
       "      <td>0.711477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.153846</td>\n",
       "      <td>0.312246</td>\n",
       "      <td>0.022123</td>\n",
       "      <td>0.755908</td>\n",
       "      <td>0.857554</td>\n",
       "      <td>-0.039754</td>\n",
       "      <td>0.156462</td>\n",
       "      <td>0.304323</td>\n",
       "      <td>-0.073108</td>\n",
       "      <td>0.526292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OVCAR-5</th>\n",
       "      <td>-1.015477</td>\n",
       "      <td>-1.209323</td>\n",
       "      <td>-1.446062</td>\n",
       "      <td>0.168677</td>\n",
       "      <td>1.108385</td>\n",
       "      <td>-0.544923</td>\n",
       "      <td>-0.689323</td>\n",
       "      <td>0.419631</td>\n",
       "      <td>0.699015</td>\n",
       "      <td>0.451477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.453846</td>\n",
       "      <td>-0.317754</td>\n",
       "      <td>0.332123</td>\n",
       "      <td>1.145908</td>\n",
       "      <td>1.247554</td>\n",
       "      <td>-0.219754</td>\n",
       "      <td>0.016462</td>\n",
       "      <td>-0.305677</td>\n",
       "      <td>0.026892</td>\n",
       "      <td>-0.103708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OVCAR-8</th>\n",
       "      <td>0.514523</td>\n",
       "      <td>-1.349323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.048677</td>\n",
       "      <td>1.118385</td>\n",
       "      <td>0.175077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.969631</td>\n",
       "      <td>-0.220985</td>\n",
       "      <td>0.161477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.693846</td>\n",
       "      <td>0.552246</td>\n",
       "      <td>0.032123</td>\n",
       "      <td>1.775908</td>\n",
       "      <td>1.307554</td>\n",
       "      <td>-0.379754</td>\n",
       "      <td>-0.493538</td>\n",
       "      <td>0.144323</td>\n",
       "      <td>0.656892</td>\n",
       "      <td>0.786292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC-3</th>\n",
       "      <td>-0.905477</td>\n",
       "      <td>-1.289323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.731323</td>\n",
       "      <td>0.878385</td>\n",
       "      <td>-0.184923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.179631</td>\n",
       "      <td>-0.640985</td>\n",
       "      <td>0.151477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.173846</td>\n",
       "      <td>1.472246</td>\n",
       "      <td>0.712123</td>\n",
       "      <td>0.675908</td>\n",
       "      <td>0.867554</td>\n",
       "      <td>0.010246</td>\n",
       "      <td>0.926462</td>\n",
       "      <td>-0.925677</td>\n",
       "      <td>0.086892</td>\n",
       "      <td>0.976292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RPMI-8226</th>\n",
       "      <td>-0.165477</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.661323</td>\n",
       "      <td>1.328385</td>\n",
       "      <td>0.375077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-1.960369</td>\n",
       "      <td>0.379015</td>\n",
       "      <td>-0.428523</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.153846</td>\n",
       "      <td>-0.827754</td>\n",
       "      <td>-0.097877</td>\n",
       "      <td>0.815908</td>\n",
       "      <td>1.607554</td>\n",
       "      <td>-0.329754</td>\n",
       "      <td>0.316462</td>\n",
       "      <td>0.304323</td>\n",
       "      <td>-0.103108</td>\n",
       "      <td>-0.313708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RXF-393</th>\n",
       "      <td>1.014523</td>\n",
       "      <td>-1.329323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>2.668677</td>\n",
       "      <td>0.628385</td>\n",
       "      <td>0.345077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.689631</td>\n",
       "      <td>0.079015</td>\n",
       "      <td>-0.418523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.206154</td>\n",
       "      <td>0.572246</td>\n",
       "      <td>0.572123</td>\n",
       "      <td>0.615908</td>\n",
       "      <td>1.737554</td>\n",
       "      <td>0.540246</td>\n",
       "      <td>0.746462</td>\n",
       "      <td>-0.365677</td>\n",
       "      <td>-0.003108</td>\n",
       "      <td>0.986292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SF-268</th>\n",
       "      <td>0.814523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.131323</td>\n",
       "      <td>1.018385</td>\n",
       "      <td>0.135077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.189631</td>\n",
       "      <td>0.149015</td>\n",
       "      <td>0.101477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.126154</td>\n",
       "      <td>0.372246</td>\n",
       "      <td>0.402123</td>\n",
       "      <td>1.595908</td>\n",
       "      <td>1.187554</td>\n",
       "      <td>0.770246</td>\n",
       "      <td>0.996462</td>\n",
       "      <td>-0.005677</td>\n",
       "      <td>0.866892</td>\n",
       "      <td>0.916292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SF-295</th>\n",
       "      <td>1.424523</td>\n",
       "      <td>-1.289323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.081323</td>\n",
       "      <td>1.068385</td>\n",
       "      <td>-0.314923</td>\n",
       "      <td>0.560677</td>\n",
       "      <td>0.539631</td>\n",
       "      <td>0.459015</td>\n",
       "      <td>0.091477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.053846</td>\n",
       "      <td>-0.357754</td>\n",
       "      <td>0.642123</td>\n",
       "      <td>0.905908</td>\n",
       "      <td>1.697554</td>\n",
       "      <td>-0.569754</td>\n",
       "      <td>-0.153538</td>\n",
       "      <td>-0.375677</td>\n",
       "      <td>0.066892</td>\n",
       "      <td>0.516292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SF-539</th>\n",
       "      <td>1.244523</td>\n",
       "      <td>0.250677</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>-0.511323</td>\n",
       "      <td>0.178385</td>\n",
       "      <td>-0.494923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.639631</td>\n",
       "      <td>0.209015</td>\n",
       "      <td>-0.148523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.723846</td>\n",
       "      <td>0.062246</td>\n",
       "      <td>0.492123</td>\n",
       "      <td>0.435908</td>\n",
       "      <td>1.307554</td>\n",
       "      <td>0.240246</td>\n",
       "      <td>0.486462</td>\n",
       "      <td>0.084323</td>\n",
       "      <td>-0.233108</td>\n",
       "      <td>1.116292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SK-MEL-2</th>\n",
       "      <td>1.554523</td>\n",
       "      <td>4.310677</td>\n",
       "      <td>-1.546062</td>\n",
       "      <td>2.718677</td>\n",
       "      <td>1.408385</td>\n",
       "      <td>0.685077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.539631</td>\n",
       "      <td>0.369015</td>\n",
       "      <td>0.961477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.203846</td>\n",
       "      <td>1.382246</td>\n",
       "      <td>0.352123</td>\n",
       "      <td>-0.084092</td>\n",
       "      <td>1.817554</td>\n",
       "      <td>0.880246</td>\n",
       "      <td>1.466462</td>\n",
       "      <td>0.474323</td>\n",
       "      <td>0.246892</td>\n",
       "      <td>0.786292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SK-MEL-28</th>\n",
       "      <td>1.414523</td>\n",
       "      <td>6.570677</td>\n",
       "      <td>-1.506062</td>\n",
       "      <td>0.778677</td>\n",
       "      <td>0.868385</td>\n",
       "      <td>-0.434923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.439631</td>\n",
       "      <td>0.039015</td>\n",
       "      <td>1.271477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.376154</td>\n",
       "      <td>0.812246</td>\n",
       "      <td>0.452123</td>\n",
       "      <td>0.495908</td>\n",
       "      <td>1.187554</td>\n",
       "      <td>-0.129754</td>\n",
       "      <td>0.066462</td>\n",
       "      <td>0.524323</td>\n",
       "      <td>0.496892</td>\n",
       "      <td>1.166292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SK-MEL-5</th>\n",
       "      <td>1.114523</td>\n",
       "      <td>6.620677</td>\n",
       "      <td>-1.546062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>1.148385</td>\n",
       "      <td>-0.894923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.619631</td>\n",
       "      <td>0.159015</td>\n",
       "      <td>0.141477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.766154</td>\n",
       "      <td>0.452246</td>\n",
       "      <td>-0.007877</td>\n",
       "      <td>0.215908</td>\n",
       "      <td>1.027554</td>\n",
       "      <td>-0.689754</td>\n",
       "      <td>0.006462</td>\n",
       "      <td>-0.125677</td>\n",
       "      <td>-0.343108</td>\n",
       "      <td>0.146292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SK-OV-3</th>\n",
       "      <td>1.754523</td>\n",
       "      <td>-1.379323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>2.278677</td>\n",
       "      <td>1.488385</td>\n",
       "      <td>-0.274923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.549631</td>\n",
       "      <td>0.249015</td>\n",
       "      <td>-0.048523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.423846</td>\n",
       "      <td>0.562246</td>\n",
       "      <td>0.912123</td>\n",
       "      <td>0.865908</td>\n",
       "      <td>1.317554</td>\n",
       "      <td>0.330246</td>\n",
       "      <td>0.656462</td>\n",
       "      <td>0.284323</td>\n",
       "      <td>0.886892</td>\n",
       "      <td>-0.033708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SN12C</th>\n",
       "      <td>2.074523</td>\n",
       "      <td>-1.369323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.051323</td>\n",
       "      <td>0.098385</td>\n",
       "      <td>-0.644923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.289631</td>\n",
       "      <td>-0.800985</td>\n",
       "      <td>-0.408523</td>\n",
       "      <td>...</td>\n",
       "      <td>1.596154</td>\n",
       "      <td>-0.677754</td>\n",
       "      <td>-0.377877</td>\n",
       "      <td>0.205908</td>\n",
       "      <td>1.167554</td>\n",
       "      <td>-0.229754</td>\n",
       "      <td>-0.163538</td>\n",
       "      <td>-0.935677</td>\n",
       "      <td>-0.673108</td>\n",
       "      <td>-0.343708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SNB-19</th>\n",
       "      <td>0.494523</td>\n",
       "      <td>-0.889323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>0.008677</td>\n",
       "      <td>-0.041615</td>\n",
       "      <td>-0.334923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.029631</td>\n",
       "      <td>-0.590985</td>\n",
       "      <td>-0.478523</td>\n",
       "      <td>...</td>\n",
       "      <td>0.156154</td>\n",
       "      <td>-0.287754</td>\n",
       "      <td>0.222123</td>\n",
       "      <td>0.335908</td>\n",
       "      <td>2.057554</td>\n",
       "      <td>0.050246</td>\n",
       "      <td>0.196462</td>\n",
       "      <td>-0.215677</td>\n",
       "      <td>-0.473108</td>\n",
       "      <td>-0.033708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SNB-75</th>\n",
       "      <td>-0.705477</td>\n",
       "      <td>-0.729323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>2.308677</td>\n",
       "      <td>0.638385</td>\n",
       "      <td>-0.154923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.769631</td>\n",
       "      <td>-0.340985</td>\n",
       "      <td>-0.508523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.283846</td>\n",
       "      <td>0.942246</td>\n",
       "      <td>0.562123</td>\n",
       "      <td>1.405908</td>\n",
       "      <td>1.387554</td>\n",
       "      <td>0.690246</td>\n",
       "      <td>0.856462</td>\n",
       "      <td>0.064323</td>\n",
       "      <td>0.766892</td>\n",
       "      <td>1.066292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SR</th>\n",
       "      <td>0.914523</td>\n",
       "      <td>-1.409323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.608385</td>\n",
       "      <td>0.175077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.769631</td>\n",
       "      <td>0.249015</td>\n",
       "      <td>0.341477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.813846</td>\n",
       "      <td>0.402246</td>\n",
       "      <td>0.342123</td>\n",
       "      <td>0.865908</td>\n",
       "      <td>0.617554</td>\n",
       "      <td>0.040246</td>\n",
       "      <td>0.256462</td>\n",
       "      <td>0.034323</td>\n",
       "      <td>-0.263108</td>\n",
       "      <td>0.386292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SW-620</th>\n",
       "      <td>-0.885477</td>\n",
       "      <td>-1.229323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-1.101323</td>\n",
       "      <td>1.968385</td>\n",
       "      <td>0.645077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.229631</td>\n",
       "      <td>0.529015</td>\n",
       "      <td>0.731477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.083846</td>\n",
       "      <td>0.932246</td>\n",
       "      <td>1.372123</td>\n",
       "      <td>1.365908</td>\n",
       "      <td>0.887554</td>\n",
       "      <td>0.810246</td>\n",
       "      <td>1.666462</td>\n",
       "      <td>0.524323</td>\n",
       "      <td>0.236892</td>\n",
       "      <td>0.826292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T-47D</th>\n",
       "      <td>1.524523</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.636062</td>\n",
       "      <td>0.668677</td>\n",
       "      <td>1.218385</td>\n",
       "      <td>0.785077</td>\n",
       "      <td>-0.779323</td>\n",
       "      <td>-0.620369</td>\n",
       "      <td>0.489015</td>\n",
       "      <td>0.161477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.746154</td>\n",
       "      <td>1.232246</td>\n",
       "      <td>-0.407877</td>\n",
       "      <td>1.435908</td>\n",
       "      <td>1.097554</td>\n",
       "      <td>0.350246</td>\n",
       "      <td>0.466462</td>\n",
       "      <td>-0.085677</td>\n",
       "      <td>-0.193108</td>\n",
       "      <td>-0.503708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TK-10</th>\n",
       "      <td>-0.995477</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.181323</td>\n",
       "      <td>0.098385</td>\n",
       "      <td>-0.104923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>1.949631</td>\n",
       "      <td>-0.010985</td>\n",
       "      <td>-0.178523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.353846</td>\n",
       "      <td>-0.687754</td>\n",
       "      <td>-0.007877</td>\n",
       "      <td>-0.784092</td>\n",
       "      <td>1.717554</td>\n",
       "      <td>-0.619754</td>\n",
       "      <td>-0.413538</td>\n",
       "      <td>-0.995677</td>\n",
       "      <td>-0.283108</td>\n",
       "      <td>0.636292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>U251</th>\n",
       "      <td>0.314523</td>\n",
       "      <td>-1.369323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>-0.131323</td>\n",
       "      <td>0.238385</td>\n",
       "      <td>-0.254923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.539631</td>\n",
       "      <td>0.289015</td>\n",
       "      <td>-0.058523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.003846</td>\n",
       "      <td>-0.757754</td>\n",
       "      <td>-0.057877</td>\n",
       "      <td>0.625908</td>\n",
       "      <td>1.517554</td>\n",
       "      <td>-0.129754</td>\n",
       "      <td>0.576462</td>\n",
       "      <td>-0.625677</td>\n",
       "      <td>-0.373108</td>\n",
       "      <td>0.496292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UACC-257</th>\n",
       "      <td>1.774523</td>\n",
       "      <td>5.630677</td>\n",
       "      <td>-1.686062</td>\n",
       "      <td>-2.241323</td>\n",
       "      <td>0.778385</td>\n",
       "      <td>-1.064923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>-0.080369</td>\n",
       "      <td>0.079015</td>\n",
       "      <td>0.341477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.886154</td>\n",
       "      <td>0.092246</td>\n",
       "      <td>-0.447877</td>\n",
       "      <td>0.925908</td>\n",
       "      <td>0.917554</td>\n",
       "      <td>-0.379754</td>\n",
       "      <td>0.106462</td>\n",
       "      <td>-0.125677</td>\n",
       "      <td>0.116892</td>\n",
       "      <td>0.876292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UACC-62</th>\n",
       "      <td>2.104523</td>\n",
       "      <td>3.280677</td>\n",
       "      <td>-1.586062</td>\n",
       "      <td>-1.581323</td>\n",
       "      <td>0.558385</td>\n",
       "      <td>-0.184923</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.129631</td>\n",
       "      <td>-0.680985</td>\n",
       "      <td>0.271477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.433846</td>\n",
       "      <td>-0.337754</td>\n",
       "      <td>0.162123</td>\n",
       "      <td>-0.094092</td>\n",
       "      <td>0.357554</td>\n",
       "      <td>-0.159754</td>\n",
       "      <td>-0.253538</td>\n",
       "      <td>-0.035677</td>\n",
       "      <td>0.126892</td>\n",
       "      <td>-1.153708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UO-31</th>\n",
       "      <td>-0.665477</td>\n",
       "      <td>-1.399323</td>\n",
       "      <td>-1.696062</td>\n",
       "      <td>1.368677</td>\n",
       "      <td>0.508385</td>\n",
       "      <td>0.385077</td>\n",
       "      <td>-0.809323</td>\n",
       "      <td>0.859631</td>\n",
       "      <td>-0.240985</td>\n",
       "      <td>-0.498523</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.333846</td>\n",
       "      <td>-0.157754</td>\n",
       "      <td>0.452123</td>\n",
       "      <td>0.565908</td>\n",
       "      <td>1.467554</td>\n",
       "      <td>-0.399754</td>\n",
       "      <td>-0.413538</td>\n",
       "      <td>-0.615677</td>\n",
       "      <td>-0.723108</td>\n",
       "      <td>0.176292</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>60 rows × 9994 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "gene             A1BG       A2M     A2ML1    A4GALT      AAAS      AACS  \\\n",
       "786-0       -1.025477 -1.409323 -1.696062  1.978677  0.878385 -0.354923   \n",
       "A498        -0.925477 -1.409323 -1.686062  1.588677  0.178385 -0.184923   \n",
       "A549         0.274523 -1.409323 -1.686062  0.908677  1.658385 -0.074923   \n",
       "ACHN        -0.875477 -1.409323 -1.686062  0.348677 -0.291615 -0.014923   \n",
       "BT-549       2.484523 -1.409323 -1.696062  1.098677 -0.011615 -2.114923   \n",
       "CAKI-1       1.244523 -1.399323 -1.696062  1.488677  0.568385 -0.504923   \n",
       "CCRF-CEM     1.914523 -1.299323 -1.696062 -1.791323  1.518385 -0.824923   \n",
       "COLO205     -1.025477 -1.409323 -1.696062 -1.041323  0.148385  1.395077   \n",
       "DU-145       0.584523 -1.399323 -1.696062 -0.601323  0.158385 -0.264923   \n",
       "EKVX         0.094523  0.100677 -1.586062  1.498677  1.038385  0.695077   \n",
       "HCC-2998    -0.795477 -1.349323 -1.616062  0.778677 -0.441615 -0.964923   \n",
       "HCT-116     -0.915477 -1.289323 -1.696062  0.968677  1.348385 -1.314923   \n",
       "HCT-15      -0.955477 -1.409323 -1.696062 -1.591323 -0.781615 -0.254923   \n",
       "HL-60       -0.625477 -1.349323 -1.696062 -2.241323  0.858385 -0.894923   \n",
       "HOP-62       0.584523 -1.409323 -1.696062 -0.081323 -0.401615 -0.694923   \n",
       "HOP-92       1.394523 -1.409323 -1.686062  1.208677  0.958385 -0.354923   \n",
       "HS-578T      2.754523 -1.409323 -1.696062 -1.581323 -0.411615 -1.304923   \n",
       "HT29        -0.965477 -1.399323 -1.696062  0.278677 -1.071615 -0.874923   \n",
       "IGR-OV1      0.604523 -1.409323 -1.686062  2.368677  0.308385  0.295077   \n",
       "K-562        0.564523 -1.379323 -1.686062 -2.201323  1.688385 -0.634923   \n",
       "KM12        -0.845477 -1.379323  1.733938 -1.361323 -0.871615 -0.674923   \n",
       "LOX-IMVI    -1.025477 -1.379323 -1.626062 -2.241323  0.488385 -1.604923   \n",
       "M14          0.684523  2.260677 -1.686062 -2.201323  1.688385  0.515077   \n",
       "MALME-3M     1.984523  5.510677 -1.616062  0.258677  1.118385  1.235077   \n",
       "MCF7         1.594523 -1.369323 -1.696062  1.238677  0.018385 -0.744923   \n",
       "MDA-MB-231   0.414523 -1.269323 -1.696062  1.508677 -0.101615  0.055077   \n",
       "MDA-MB-435   1.154523 -1.269323 -1.636062 -2.241323  0.858385 -0.584923   \n",
       "MDA-MB-468   0.684523  2.380677 -1.296062 -0.241323 -0.711615 -0.264923   \n",
       "MOLT-4       1.644523 -1.399323 -1.696062 -2.241323  0.898385  0.025077   \n",
       "NCI-ADR-RES  0.834523 -1.399323 -1.696062  0.158677  1.168385 -0.454923   \n",
       "NCI-H226     0.124523 -0.379323 -1.696062 -1.841323  0.848385  0.755077   \n",
       "NCI-H23      0.324523  0.240677 -1.686062  0.498677  1.088385 -0.374923   \n",
       "NCI-H322M    1.414523 -1.159323  0.023938  3.008677  0.568385 -0.134923   \n",
       "NCI-H460    -0.005477 -1.339323 -1.696062  0.238677  0.818385 -0.744923   \n",
       "NCI-H522     1.524523 -1.309323 -1.696062 -0.561323 -0.241615 -1.414923   \n",
       "OVCAR-3      0.914523 -1.369323 -1.446062 -0.721323  1.158385  0.885077   \n",
       "OVCAR-4     -0.035477 -1.369323 -1.556062  1.468677  0.848385  0.085077   \n",
       "OVCAR-5     -1.015477 -1.209323 -1.446062  0.168677  1.108385 -0.544923   \n",
       "OVCAR-8      0.514523 -1.349323 -1.696062  0.048677  1.118385  0.175077   \n",
       "PC-3        -0.905477 -1.289323 -1.696062 -1.731323  0.878385 -0.184923   \n",
       "RPMI-8226   -0.165477 -1.409323 -1.696062 -1.661323  1.328385  0.375077   \n",
       "RXF-393      1.014523 -1.329323 -1.696062  2.668677  0.628385  0.345077   \n",
       "SF-268       0.814523 -1.409323 -1.696062 -1.131323  1.018385  0.135077   \n",
       "SF-295       1.424523 -1.289323 -1.696062 -1.081323  1.068385 -0.314923   \n",
       "SF-539       1.244523  0.250677 -1.686062 -0.511323  0.178385 -0.494923   \n",
       "SK-MEL-2     1.554523  4.310677 -1.546062  2.718677  1.408385  0.685077   \n",
       "SK-MEL-28    1.414523  6.570677 -1.506062  0.778677  0.868385 -0.434923   \n",
       "SK-MEL-5     1.114523  6.620677 -1.546062 -2.241323  1.148385 -0.894923   \n",
       "SK-OV-3      1.754523 -1.379323 -1.696062  2.278677  1.488385 -0.274923   \n",
       "SN12C        2.074523 -1.369323 -1.696062 -0.051323  0.098385 -0.644923   \n",
       "SNB-19       0.494523 -0.889323 -1.696062  0.008677 -0.041615 -0.334923   \n",
       "SNB-75      -0.705477 -0.729323 -1.696062  2.308677  0.638385 -0.154923   \n",
       "SR           0.914523 -1.409323 -1.696062 -2.241323  0.608385  0.175077   \n",
       "SW-620      -0.885477 -1.229323 -1.696062 -1.101323  1.968385  0.645077   \n",
       "T-47D        1.524523 -1.399323 -1.636062  0.668677  1.218385  0.785077   \n",
       "TK-10       -0.995477 -1.399323 -1.696062 -0.181323  0.098385 -0.104923   \n",
       "U251         0.314523 -1.369323 -1.696062 -0.131323  0.238385 -0.254923   \n",
       "UACC-257     1.774523  5.630677 -1.686062 -2.241323  0.778385 -1.064923   \n",
       "UACC-62      2.104523  3.280677 -1.586062 -1.581323  0.558385 -0.184923   \n",
       "UO-31       -0.665477 -1.399323 -1.696062  1.368677  0.508385  0.385077   \n",
       "\n",
       "gene            AADAC     AAED1     AAGAB      AAMP  ...    ZSWIM7    ZSWIM8  \\\n",
       "786-0       -0.809323  1.419631  0.369015 -0.128523  ...  0.266154  0.002246   \n",
       "A498        -0.389323  1.779631  0.249015 -0.198523  ...  0.106154  0.042246   \n",
       "A549         0.880677  0.809631  0.649015  0.381477  ...  0.366154 -0.627754   \n",
       "ACHN        -0.809323  1.179631 -0.500985 -1.038523  ...  0.266154  0.092246   \n",
       "BT-549      -0.809323  1.379631 -0.630985 -1.168523  ...  0.306154  0.702246   \n",
       "CAKI-1      -0.809323  0.119631 -0.380985 -0.048523  ...  0.456154  0.392246   \n",
       "CCRF-CEM    -0.809323 -1.930369 -0.000985 -0.178523  ... -0.543846 -0.827754   \n",
       "COLO205     -0.809323  0.129631  0.229015 -0.548523  ...  0.176154 -0.827754   \n",
       "DU-145      -0.809323  1.189631 -0.120985 -0.938523  ... -0.893846 -0.657754   \n",
       "EKVX         0.060677  0.459631  0.939015 -0.048523  ...  1.276154  1.002246   \n",
       "HCC-2998    -0.729323  0.359631 -0.010985 -1.678523  ... -0.773846 -0.497754   \n",
       "HCT-116      0.060677  0.499631  0.339015  0.541477  ...  0.646154 -0.517754   \n",
       "HCT-15      -0.809323 -0.630369 -0.820985 -1.988523  ... -0.453846 -0.007754   \n",
       "HL-60       -0.809323 -0.010369 -0.410985 -0.328523  ... -0.463846 -1.397754   \n",
       "HOP-62      -0.669323  0.689631 -0.630985 -0.418523  ...  0.716154 -0.397754   \n",
       "HOP-92      -0.779323  0.879631 -0.510985  0.281477  ... -0.373846  0.262246   \n",
       "HS-578T     -0.809323  0.959631 -0.470985 -0.738523  ...  0.066154 -0.347754   \n",
       "HT29        -0.749323 -0.690369  0.169015 -1.488523  ... -0.883846 -1.547754   \n",
       "IGR-OV1     -0.809323  0.579631 -0.240985 -0.188523  ...  0.686154 -0.187754   \n",
       "K-562       -0.809323  0.789631  0.349015 -0.118523  ... -0.713846  0.862246   \n",
       "KM12        -0.779323 -1.440369 -0.380985 -2.068523  ... -0.153846 -1.297754   \n",
       "LOX-IMVI    -0.809323  0.749631 -0.550985 -0.868523  ... -0.063846 -0.517754   \n",
       "M14         -0.809323  1.339631  0.289015  0.151477  ...  0.826154  0.202246   \n",
       "MALME-3M    -0.809323  1.259631  0.289015  0.241477  ...  0.386154  0.972246   \n",
       "MCF7        -0.809323 -0.970369  0.229015 -0.568523  ...  0.566154 -0.747754   \n",
       "MDA-MB-231  -0.809323  1.249631 -0.700985  0.051477  ...  0.916154 -0.027754   \n",
       "MDA-MB-435  -0.809323  0.869631  0.059015  0.691477  ...  0.416154 -0.117754   \n",
       "MDA-MB-468   0.430677 -0.020369  0.079015 -0.608523  ...  1.636154 -0.207754   \n",
       "MOLT-4      -0.809323 -2.480369 -0.100985 -0.088523  ...  0.266154 -0.277754   \n",
       "NCI-ADR-RES -0.809323 -0.380369  0.119015 -0.178523  ... -0.063846  0.012246   \n",
       "NCI-H226    -0.809323  0.909631  0.769015 -0.758523  ... -0.033846  0.032246   \n",
       "NCI-H23     -0.779323  0.749631  0.669015  0.511477  ... -1.063846  0.012246   \n",
       "NCI-H322M   -0.599323 -0.060369  0.829015 -0.018523  ...  0.996154  0.092246   \n",
       "NCI-H460     0.650677  1.049631 -0.190985 -0.678523  ...  0.156154 -1.067754   \n",
       "NCI-H522    -0.809323  0.869631 -0.670985 -0.968523  ...  0.246154 -0.817754   \n",
       "OVCAR-3     -0.739323 -0.540369  0.429015  1.281477  ...  1.026154  0.462246   \n",
       "OVCAR-4     -0.809323  0.309631  0.179015  0.711477  ... -0.153846  0.312246   \n",
       "OVCAR-5     -0.689323  0.419631  0.699015  0.451477  ... -0.453846 -0.317754   \n",
       "OVCAR-8     -0.809323  0.969631 -0.220985  0.161477  ... -0.693846  0.552246   \n",
       "PC-3        -0.809323  1.179631 -0.640985  0.151477  ... -0.173846  1.472246   \n",
       "RPMI-8226   -0.809323 -1.960369  0.379015 -0.428523  ... -1.153846 -0.827754   \n",
       "RXF-393     -0.809323  1.689631  0.079015 -0.418523  ...  0.206154  0.572246   \n",
       "SF-268      -0.809323  1.189631  0.149015  0.101477  ...  0.126154  0.372246   \n",
       "SF-295       0.560677  0.539631  0.459015  0.091477  ... -0.053846 -0.357754   \n",
       "SF-539      -0.809323  1.639631  0.209015 -0.148523  ... -0.723846  0.062246   \n",
       "SK-MEL-2    -0.809323  0.539631  0.369015  0.961477  ... -0.203846  1.382246   \n",
       "SK-MEL-28   -0.809323  0.439631  0.039015  1.271477  ...  0.376154  0.812246   \n",
       "SK-MEL-5    -0.809323  0.619631  0.159015  0.141477  ...  0.766154  0.452246   \n",
       "SK-OV-3     -0.809323  1.549631  0.249015 -0.048523  ... -0.423846  0.562246   \n",
       "SN12C       -0.809323  1.289631 -0.800985 -0.408523  ...  1.596154 -0.677754   \n",
       "SNB-19      -0.809323  0.029631 -0.590985 -0.478523  ...  0.156154 -0.287754   \n",
       "SNB-75      -0.809323  1.769631 -0.340985 -0.508523  ... -0.283846  0.942246   \n",
       "SR          -0.809323  1.769631  0.249015  0.341477  ... -0.813846  0.402246   \n",
       "SW-620      -0.809323  0.229631  0.529015  0.731477  ... -0.083846  0.932246   \n",
       "T-47D       -0.779323 -0.620369  0.489015  0.161477  ...  0.746154  1.232246   \n",
       "TK-10       -0.809323  1.949631 -0.010985 -0.178523  ... -0.353846 -0.687754   \n",
       "U251        -0.809323  0.539631  0.289015 -0.058523  ... -0.003846 -0.757754   \n",
       "UACC-257    -0.809323 -0.080369  0.079015  0.341477  ...  0.886154  0.092246   \n",
       "UACC-62     -0.809323  0.129631 -0.680985  0.271477  ... -0.433846 -0.337754   \n",
       "UO-31       -0.809323  0.859631 -0.240985 -0.498523  ... -0.333846 -0.157754   \n",
       "\n",
       "gene            ZUFSP      ZW10    ZWILCH      ZXDA      ZXDB      ZXDC  \\\n",
       "786-0        0.482123  0.605908  2.007554 -0.359754 -0.193538 -0.565677   \n",
       "A498         0.092123 -0.384092  1.227554  0.770246  0.386462 -0.705677   \n",
       "A549        -0.047877  0.405908  2.227554  0.040246  0.616462 -0.775677   \n",
       "ACHN         0.192123 -0.854092  0.947554 -0.259754 -0.533538 -1.125677   \n",
       "BT-549       0.752123  0.465908  0.887554 -0.199754 -0.083538 -0.785677   \n",
       "CAKI-1      -0.437877 -0.274092  0.897554  0.130246 -0.233538 -0.545677   \n",
       "CCRF-CEM     0.492123  1.005908  1.397554 -0.199754  0.666462  0.454323   \n",
       "COLO205     -0.447877 -0.114092  1.267554 -0.699754 -0.323538  0.224323   \n",
       "DU-145      -0.357877  0.315908  1.567554 -0.869754 -0.313538 -0.945677   \n",
       "EKVX         0.372123  0.645908  1.967554  0.580246  1.026462 -0.695677   \n",
       "HCC-2998     0.532123 -0.204092  0.947554  0.020246 -0.063538 -0.435677   \n",
       "HCT-116      0.892123  0.925908  0.987554 -0.199754  0.306462 -0.265677   \n",
       "HCT-15       1.282123 -0.344092  0.457554 -0.229754 -0.533538 -0.275677   \n",
       "HL-60        0.742123  0.175908 -0.022446 -0.569754 -0.133538  0.184323   \n",
       "HOP-62      -0.617877 -0.024092  1.047554 -0.679754  0.116462 -1.055677   \n",
       "HOP-92       0.072123  0.385908  1.267554 -0.049754  0.266462 -0.665677   \n",
       "HS-578T     -0.387877 -0.134092  1.207554 -0.749754 -1.203538 -1.255677   \n",
       "HT29        -0.327877 -0.964092  0.657554 -1.269754 -2.013538 -0.665677   \n",
       "IGR-OV1      0.442123  0.375908  0.757554  0.010246 -0.103538 -0.445677   \n",
       "K-562        1.072123  0.715908  1.267554 -1.009754 -0.613538 -0.565677   \n",
       "KM12         0.162123 -1.234092  0.037554 -1.389754 -0.923538 -0.825677   \n",
       "LOX-IMVI     0.092123  0.135908  1.297554 -0.469754 -1.263538 -0.825677   \n",
       "M14         -0.467877  1.055908  1.727554  0.180246  0.056462 -0.175677   \n",
       "MALME-3M     0.122123  0.065908  1.887554  0.320246  0.496462 -0.015677   \n",
       "MCF7        -0.147877 -0.954092  1.557554 -0.609754 -0.633538 -1.215677   \n",
       "MDA-MB-231   0.202123  1.205908  0.247554  0.230246  0.756462 -0.905677   \n",
       "MDA-MB-435  -0.197877  0.875908  1.887554 -0.859754 -0.133538 -0.515677   \n",
       "MDA-MB-468   1.202123  0.565908  0.327554  0.010246 -0.093538 -0.085677   \n",
       "MOLT-4       0.312123  0.935908  0.857554  0.460246  0.296462  0.114323   \n",
       "NCI-ADR-RES  0.142123  1.635908  1.357554 -0.229754 -0.433538  0.094323   \n",
       "NCI-H226     0.462123  0.345908  1.757554 -0.049754 -0.033538 -0.605677   \n",
       "NCI-H23      0.312123  0.415908  1.997554  0.140246  0.396462  0.044323   \n",
       "NCI-H322M   -0.107877  0.925908  1.377554  0.270246  0.216462  0.174323   \n",
       "NCI-H460    -0.207877 -0.494092  1.097554 -0.379754 -0.133538 -1.475677   \n",
       "NCI-H522     0.042123 -0.324092  0.697554  1.870246  0.036462 -1.395677   \n",
       "OVCAR-3      0.452123  0.345908  1.697554  0.010246  0.256462  0.694323   \n",
       "OVCAR-4      0.022123  0.755908  0.857554 -0.039754  0.156462  0.304323   \n",
       "OVCAR-5      0.332123  1.145908  1.247554 -0.219754  0.016462 -0.305677   \n",
       "OVCAR-8      0.032123  1.775908  1.307554 -0.379754 -0.493538  0.144323   \n",
       "PC-3         0.712123  0.675908  0.867554  0.010246  0.926462 -0.925677   \n",
       "RPMI-8226   -0.097877  0.815908  1.607554 -0.329754  0.316462  0.304323   \n",
       "RXF-393      0.572123  0.615908  1.737554  0.540246  0.746462 -0.365677   \n",
       "SF-268       0.402123  1.595908  1.187554  0.770246  0.996462 -0.005677   \n",
       "SF-295       0.642123  0.905908  1.697554 -0.569754 -0.153538 -0.375677   \n",
       "SF-539       0.492123  0.435908  1.307554  0.240246  0.486462  0.084323   \n",
       "SK-MEL-2     0.352123 -0.084092  1.817554  0.880246  1.466462  0.474323   \n",
       "SK-MEL-28    0.452123  0.495908  1.187554 -0.129754  0.066462  0.524323   \n",
       "SK-MEL-5    -0.007877  0.215908  1.027554 -0.689754  0.006462 -0.125677   \n",
       "SK-OV-3      0.912123  0.865908  1.317554  0.330246  0.656462  0.284323   \n",
       "SN12C       -0.377877  0.205908  1.167554 -0.229754 -0.163538 -0.935677   \n",
       "SNB-19       0.222123  0.335908  2.057554  0.050246  0.196462 -0.215677   \n",
       "SNB-75       0.562123  1.405908  1.387554  0.690246  0.856462  0.064323   \n",
       "SR           0.342123  0.865908  0.617554  0.040246  0.256462  0.034323   \n",
       "SW-620       1.372123  1.365908  0.887554  0.810246  1.666462  0.524323   \n",
       "T-47D       -0.407877  1.435908  1.097554  0.350246  0.466462 -0.085677   \n",
       "TK-10       -0.007877 -0.784092  1.717554 -0.619754 -0.413538 -0.995677   \n",
       "U251        -0.057877  0.625908  1.517554 -0.129754  0.576462 -0.625677   \n",
       "UACC-257    -0.447877  0.925908  0.917554 -0.379754  0.106462 -0.125677   \n",
       "UACC-62      0.162123 -0.094092  0.357554 -0.159754 -0.253538 -0.035677   \n",
       "UO-31        0.452123  0.565908  1.467554 -0.399754 -0.413538 -0.615677   \n",
       "\n",
       "gene           ZYG11B      ZZZ3  \n",
       "786-0       -0.243108  0.456292  \n",
       "A498        -0.233108 -0.113708  \n",
       "A549        -0.243108 -0.433708  \n",
       "ACHN        -1.633108 -0.203708  \n",
       "BT-549      -0.773108  0.586292  \n",
       "CAKI-1      -0.583108 -0.243708  \n",
       "CCRF-CEM    -0.493108  0.026292  \n",
       "COLO205     -1.613108 -0.803708  \n",
       "DU-145      -1.183108 -0.383708  \n",
       "EKVX         1.366892  0.486292  \n",
       "HCC-2998    -0.873108 -0.283708  \n",
       "HCT-116      0.036892  0.296292  \n",
       "HCT-15      -0.883108 -0.363708  \n",
       "HL-60       -0.813108  0.326292  \n",
       "HOP-62      -0.733108 -0.263708  \n",
       "HOP-92       0.116892  0.556292  \n",
       "HS-578T     -0.683108 -0.053708  \n",
       "HT29        -2.603108 -0.573708  \n",
       "IGR-OV1     -0.113108  0.196292  \n",
       "K-562       -0.043108 -0.173708  \n",
       "KM12        -1.823108 -0.613708  \n",
       "LOX-IMVI    -1.913108 -0.103708  \n",
       "M14          0.416892  1.076292  \n",
       "MALME-3M     0.116892  0.516292  \n",
       "MCF7        -1.703108 -0.523708  \n",
       "MDA-MB-231   0.066892  0.786292  \n",
       "MDA-MB-435  -0.213108  0.346292  \n",
       "MDA-MB-468  -0.223108  0.846292  \n",
       "MOLT-4      -0.903108  0.406292  \n",
       "NCI-ADR-RES -0.193108  0.376292  \n",
       "NCI-H226     0.006892  0.666292  \n",
       "NCI-H23     -0.003108  0.376292  \n",
       "NCI-H322M   -0.223108  0.546292  \n",
       "NCI-H460    -1.443108 -0.183708  \n",
       "NCI-H522    -0.643108 -0.643708  \n",
       "OVCAR-3     -0.183108  0.766292  \n",
       "OVCAR-4     -0.073108  0.526292  \n",
       "OVCAR-5      0.026892 -0.103708  \n",
       "OVCAR-8      0.656892  0.786292  \n",
       "PC-3         0.086892  0.976292  \n",
       "RPMI-8226   -0.103108 -0.313708  \n",
       "RXF-393     -0.003108  0.986292  \n",
       "SF-268       0.866892  0.916292  \n",
       "SF-295       0.066892  0.516292  \n",
       "SF-539      -0.233108  1.116292  \n",
       "SK-MEL-2     0.246892  0.786292  \n",
       "SK-MEL-28    0.496892  1.166292  \n",
       "SK-MEL-5    -0.343108  0.146292  \n",
       "SK-OV-3      0.886892 -0.033708  \n",
       "SN12C       -0.673108 -0.343708  \n",
       "SNB-19      -0.473108 -0.033708  \n",
       "SNB-75       0.766892  1.066292  \n",
       "SR          -0.263108  0.386292  \n",
       "SW-620       0.236892  0.826292  \n",
       "T-47D       -0.193108 -0.503708  \n",
       "TK-10       -0.283108  0.636292  \n",
       "U251        -0.373108  0.496292  \n",
       "UACC-257     0.116892  0.876292  \n",
       "UACC-62      0.126892 -1.153708  \n",
       "UO-31       -0.723108  0.176292  \n",
       "\n",
       "[60 rows x 9994 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "microarray"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Actividad 2:**\n",
    "\n",
    "Implementa un método de reducción de dimensionalidad para visualizar cada linea celular como un punto en un gráfico de dispersión bidimensional."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Reducción de dimensionalidad y visualización de cada una de las líneas celulares."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}