2_unsupervised-learning-with-sickitlearn/Unsupervised-learning with Scikit-learn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised learning\n",
    "finding patterns in data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering with Kmeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n"
     ]
    },
    {
     "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": [
    "%matplotlib inline\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn import datasets\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "X = iris.data\n",
    "\n",
    "y = iris.target\n",
    "\n",
    "print(iris.feature_names)\n",
    "\n",
    "xs = X[:, 0]\n",
    "ys = X[:, 2]\n",
    "\n",
    "plt.scatter(xs, ys, c=y)\n",
    "\n",
    "\n",
    "model = KMeans(n_clusters=3) # 3 species of iris\n",
    "\n",
    "\n",
    "model.fit(np.c_[xs, ys])\n",
    "\n",
    "\n",
    "centroids = model.cluster_centers_\n",
    "centroids_x = centroids[:,0]\n",
    "centroids_y = centroids[:,1]\n",
    "\n",
    "plt.scatter(centroids_x, centroids_y, s=100, marker='D')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating a clustering\n",
    "- Measuring quality of clustering\n",
    "- A good clustering has tight clusters\n",
    "- Minizing the distance from each sampel to its centroid, by minimizing **model.inertia_**\n",
    "- Choose an elbow in the intertia plot (when it begins to decrease more slowly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "species_df = pd.DataFrame(iris.target)\n",
    "for i in range(3):\n",
    "    species_df.replace(i, iris.target_names[i], inplace=True)\n",
    "species = species_df.values.flatten()\n",
    "\n",
    "\n",
    "df = pd.DataFrame({'labels' : model.fit_predict(X), 'species' : species})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build A cross tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species  setosa  versicolor  virginica\n",
      "labels                                \n",
      "0            50           0          0\n",
      "1             0          48         14\n",
      "2             0           2         36\n"
     ]
    }
   ],
   "source": [
    "ct = pd.crosstab(df['labels'], df['species'])\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding the best clusters count using inertia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "inerias = []\n",
    "clusters = []\n",
    "for k in range(1, 10):\n",
    "    clusters.append(k)\n",
    "    model = KMeans(n_clusters=k)\n",
    "    model.fit(X)\n",
    "    inerias.append(model.inertia_)\n",
    "    \n",
    "plt.plot(clusters, inerias, marker=\"o\")\n",
    "plt.xlabel('nb clusters')\n",
    "plt.ylabel('interia')\n",
    "plt.xticks(clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preprocessing: Transforming features for better clusterings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  class_0  class_1  class_2\n",
      "labels                              \n",
      "0                0       50       19\n",
      "1               46        1        0\n",
      "2               13       20       29\n"
     ]
    }
   ],
   "source": [
    "wines = datasets.load_wine()\n",
    "samples = wines.data\n",
    "varieties = np.array(wines.target).astype(str)\n",
    "\n",
    "for i in range(3):\n",
    "    varieties[varieties == str(i)] = wines.target_names[i]\n",
    "\n",
    "model = KMeans(n_clusters=3)\n",
    "labels = model.fit_predict(samples)\n",
    "\n",
    "df = pd.DataFrame({'labels' : labels, 'varieties' : varieties})\n",
    "\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Features variances\n",
    "- The wines features have very different variances\n",
    "- Variance of a feature measures spread of its values\n",
    "- In Kmeans: feature variance = feature influence\n",
    "- Use StandarScaler to transform each feature to mean 0 and variance 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alcohol                             0.659062\n",
       "malic_acid                          1.248015\n",
       "ash                                 0.075265\n",
       "alcalinity_of_ash                  11.152686\n",
       "magnesium                         203.989335\n",
       "total_phenols                       0.391690\n",
       "flavanoids                          0.997719\n",
       "nonflavanoid_phenols                0.015489\n",
       "proanthocyanins                     0.327595\n",
       "color_intensity                     5.374449\n",
       "hue                                 0.052245\n",
       "od280/od315_of_diluted_wines        0.504086\n",
       "proline                         99166.717355\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data=wines.data, columns=wines.feature_names)\n",
    "df.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alcohol                         1.00565\n",
       "malic_acid                      1.00565\n",
       "ash                             1.00565\n",
       "alcalinity_of_ash               1.00565\n",
       "magnesium                       1.00565\n",
       "total_phenols                   1.00565\n",
       "flavanoids                      1.00565\n",
       "nonflavanoid_phenols            1.00565\n",
       "proanthocyanins                 1.00565\n",
       "color_intensity                 1.00565\n",
       "hue                             1.00565\n",
       "od280/od315_of_diluted_wines    1.00565\n",
       "proline                         1.00565\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler \n",
    "scaler = StandardScaler()\n",
    "\n",
    "scaler.fit(samples)\n",
    "\n",
    "samples_scaled = scaler.transform(samples)\n",
    "\n",
    "df = pd.DataFrame(data=samples_scaled, columns=wines.feature_names)\n",
    "df.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  class_0  class_1  class_2\n",
      "labels                              \n",
      "0               59        3        0\n",
      "1                0        3       48\n",
      "2                0       65        0\n"
     ]
    }
   ],
   "source": [
    "#combining everything in a machine learning pipeline\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "scaler = StandardScaler()\n",
    "model = KMeans(n_clusters=3)\n",
    "\n",
    "steps = [('scaler', scaler), ('clustering', model)]\n",
    "\n",
    "pipeline = Pipeline(steps)\n",
    "\n",
    "pipeline.fit(samples)\n",
    "\n",
    "labels = pipeline.predict(samples)\n",
    "\n",
    "# we can now see the difference after scaling our features !!\n",
    "\n",
    "df = pd.DataFrame({'labels' : labels, 'varieties' : varieties})\n",
    "\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization with hierarchical clustering and t-SNE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical clustering with SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEICAYAAABPgw/pAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAG9BJREFUeJzt3W2sHFd9x/HfiZ1LmtwEQmNu7BBq0iAKAWkNDoWCqq1SqZTHUhUpuKGAgPuqlKcWhfYF5kWrtqpaqj6pmxaCVJaqgtBSREtRym1USiPs3FVNMEncUCCsszYCHDYJ2cScvpgdezyenZ2dOfN05vuRrLnXnplz7q7vf86e+Z//GGutAADtd0HdHQAAuEFABwBPENABwBMEdADwBAEdADxBQAcATxDQAcATBHQA8AQBHQA8sbPKxq644gq7d+/eKpsEgNY7fPjwd6y1u5btV2lA37t3rw4dOlRlkwDQesaYb2TZjykXAPAEAR0APEFABwBPENABwBMEdADwBAEdADxBQAcATxDQAcATlS4s8sVgIA2HdfcCvjlwQNrcrLsXaDNG6DkMh9JoVHcv4JPRiEECimOEnlOvJ21t1d0L+KLfr7sH8AEjdADwBAEdADxBQAcATxDQAcATBHQA8AQBHQA8QUAHAE8Q0AHAEwR0APAEAR0APEFABwBPENABwBMEdADwBAEdADxBQAcATxDQAcATSwO6MebDxpgTxpivRP7uqcaYzxtj7ptvLy+3mwCAZbKM0G+V9PLY390s6XZr7bMk3T7/HgBQo6UB3Vp7h6Tvxv76tZI+Ov/6o5J+yXG/AAAryjuHvmGtPS5J8+3T3HUJAJBH6TdFjTGbxphDxphDJ0+eLLs5AOisvAF9YozZLUnz7YlFO1prB9ba/dba/bt27crZHABgmbwB/dOS3jT/+k2S/slNdwAAee1ctoMx5uOS+pKuMMY8IOkDkn5f0j8YY94q6ZuSXl9mJ4Ekg4E0HNbdCzdGo2Db79faDWcOHJA2N+vuRfcsDejW2jcs+KcbHPcFWMlwGATCXq/unhTnw88QCi9OBPTqLQ3oQJP1etLWVt29QJQvnzLaiKX/AOAJAjoAeIKADgCeIKADgCcI6ADgCQI6AHiCgA4AniCgA4AnCOgA4AkCOgB4goAOAJ4goAOAJwjoAOCJRlZbbHqd6zbUrqYeNdA9jRyhh3Wum6rXa3b96tGo2RdEAOVo5Ahdos51EU3+5ACgPI0coQMAVkdABwBPENABwBMEdADwBAEdADxBQAcATxDQAcATBHQA8AQBHQA80diVogDKV0bdpDJrHVGjKB0jdKDDyqibVFatI2oULVdohG6Mebekt0myko5Ieou19ocuOgagGm2pm0SNouVyj9CNMVdJ+g1J+621z5O0Q9KNrjoGAFhN0SmXnZJ+zBizU9LFksbFuwQAyCN3QLfWflvSH0n6pqTjkk5Za//NVccAAKspMuVyuaTXSnqmpD2SLjHG3JSw36Yx5pAx5tDJkyfz9xQAkKrIlMvPS/q6tfaktfZxSbdJ+pn4TtbagbV2v7V2/65duwo0BwBIUySgf1PSi40xFxtjjKQbJB110y0AwKqKzKHfKekTku5SkLJ4gaSBo34BAFZUKA/dWvsBSR9w1BcAQAEs/UflBuOxhpNJ4fOMptdKkvrbxwqd58DGhjb37CncH6BuBHRUbjiZaDSdqre+Xug8vVuKBXJJGk2nkkRAhxcI6KhFb31dW/v21d0N9be36+4C4AwB3bUyytetavShYNt/V319oCweUDkCumth+boyys1ltNWrMZBLZ8v3EdCBShHQy9CW8nVloSweUAvqoQOAJwjoAOAJAjoAeIKADgCeIKADgCcI6ADgCQI6AHiCgA53BoMgB300Cv70+8GfAVWVgSqwsAjuJK2SZdUoUBkCOtyKr5Jl1ShQGaZcAMATjNDRKK4efpFVWA+9qjK6PEwDZWKEjkYJH35Rld76euEHbWQ1mk4rvVihexiho3Ga8vAL13iYBspGQAdQivF4oMnE3cNeptPgwS3b227r/W9sHNCePX5kYRHQAZRiMhlqOh1pfd3Nw15uucX9g1um0yCtloAOAEusr/e0b99W3d1YaHu7X3cXnOKmKAB4ghE60CHjwViT4dlMm+noWknSdv+YJGnjwIb2bJJW2VYEdKBDJsOJpqOp1ntBquYtvWNn/m06CtJFCejtRUAHOma9t659W+enhW73SatsO+bQAcAThQK6MeYpxphPGGO+Zow5aox5iauOAQBWU3TK5U8l/au19leMMWuSLnbQJwBADrkDujHmMkk/K+nNkmStnUmauekWAGBVRaZcrpF0UtJHjDHbxpi/McZc4qhfAIAVFQnoOyW9QNJfWWv3SXpY0s3xnYwxm8aYQ8aYQydPnizQHAAgTZE59AckPWCtvXP+/SeUENCttQNJA0nav3+/jf/74PBAwyPnFvAZPRgU4enfem7thgPPP6DNF/pRcwEAXMsd0K21DxpjvmWMeba19h5JN0j66qrnGR4ZavTgSL0rzxbw6d18fhGe0YNBER0COgAkK5rl8g5JH5tnuNwv6S15TtK7sqetN2+l7tO/tZ/n1EBurp+eVNbTkbr6FCQX5XnDaosuinQ1oQxvoYBurR1J2u+oL0CjhE9PcvVEozKejBReJLoY0F2U53VV2rcpZXhZ+g+kaPrTk7r+FKSmlOdtShlelv4DgCcI6ADgCQI6AHiCgA4AniCgA4AnCOgA4AnSFgcDaVhsccI5RkE+qvp9d+c8cEDaZIUsgHQE9OEwCMI9NwsMnJ0nFF4gCOhA6fKuPs274tT16lICuhQE4a2tunuRzOVIH0CqvKtP86w4LWN1KQEdQG5pI9q0UWsT6p4sUtXq0zJWlxLQUZ7B4Nx7Cgn3AuIFsJIKWHW1+FSZxoOxJsNzC49NR8Frv90/+9pvHNjQns3Fr33aiHbRqLUpdU98RECvwyo3YvPcZG3KTdTwZ+z1Ft4LiBfAihew6nLxqTJNhhNNR1Ot986+3tGvpbMBPi2gS6uPaJtS98RHBPQ6rHIjdtWbrE27iRren0i5IKUVwOp68akyrffWtW9rceGx6Egd7UBAr0tZN2K5iQp0FguLAMATBHQA8ARTLkDLRDOD4llBZAR1GyN0oGXCzCApuKEcZgaNplOnz0BF+zBCh9eKPOi5yEOdyx4pJ2UGkREEAjq8VuRBz/Fjjs9mmsxmS487dfp0ptEy0yNwjYAO77l60HN/e1uT2SzXxSGOBVPdFC2VkFQaoWhJBAI6sAKXFwd0T7RUQrw0gouSCAR0AKjQolIJLkoiENDbJEsNmKy1X5pS7wWAMwT0NslSAyZL7Zem1XtBI8QrMOapvnjmXDnL6krNLq3bdAT0tnFRA4Z6L0gQr8CYt/qilK+srkRp3aII6ADOSKvAuGr1xTwPiqC0bjGFA7oxZoekQ5K+ba19VfEunWtweKDhkaFGDwZX7v6tfUnSgecf0OYLuYoDXbIo7Y9pmoCLEfo7JR2VdFmWncMAHVoWqMNg3ruyd94xBHQ03aKVqmmrUFlwtFhS2h/TNGcVCujGmKdLeqWk35X0nizHxAN0lkDdu7KnrTdvnfk+DP5A0y1aqbpocRILjpaLT+UwTXNW0RH6hyS9T9KlqxwUD9AhArUjy9Ibs6Q2ktbozCqLkVhwhCJyB3RjzKsknbDWHjbG9FP225S0KUnPeMYztK7iy6Yz62re9rL0xmWpjaQ1Aq1UZIT+UkmvMca8QtJFki4zxvydtfam6E7W2oGkgSTt37/fFmhvdV3O2y6S3khaI9BKuQO6tfb9kt4vSfMR+m/Gg3kjkLcNNFLS4qNFi45cZLGkLXZa1n5cU7NqyEMvA3PYucWzQngij7+SFh8lLTpylcWSttgprf2y+lMGJwHdWrslacvFubzAHHZu8ayQaDYIGSD+ybL4yGUWS9bFTstG89PpKLVfdY3gGzFCT1o81PqFQ8xh57YoK2RZBkhSzndb8r3DvvOJpBnyli6Q6h3BNyKgx3PTWTiEPJJyvtuS753U96b1sWvylC6QVvtE4XrlayMCunRubjr56Mgra853E/O9431vYh/hluuVr40J6ADQRS5XvhLQmyTMjolmwZSd7ZKUkbMoC6ejmTdAWxDQmySeHZM12yUelFcJyEkZOUlZOB3OvAHSxDNi4rnsVWa8ENDT1DFijmbHZM12iQflVQNyloyctL7EX6fBgMAPJ8bjwZkAOR4Pau5NsnhGTDQLpuqMFwJ6mrwj5josC8plpkJGX6fRKPi+ia+Rp5JSHqtId4wH2zKCVnTku2yVZ53KfPDzKvwJ6GXNBecZMXdR+DolvUaDwbmj9+uvX/n0g/G48oDVFvGUx6rSHePBtqxRaJbVmwj4E9CZC26u6IV2OMwV0MMFQ7319VwBa1lJAandi3iiKY9VpjvWGWzDueuyPyW0iT8BXSo+F4zyZKlquewU86CVJ2CllRSQ3I1qfb9wNEl07no6HZ33KWHZzUqpuUW28vIroAMp0hYduRrVVnXhQCCcu06aq067WSk1u8hWXv4H9CwpfeRXw6EqLhxJyrw5Oh6MNR1Nz3y9Z7MdF6S05fs+PrquVQE9VxGvZSl9RefUWZiDhijz5uhkODnn6zoC+mw21mx2QlJzUxjr1qqAnruIV9rcetE5dW7GdkKVWTZFRtpl3hxd71X4+MgEYTCXmp3CWKdWBXSpoUW8uBlbWDyIDcbjzAEz77HRG5jLytYWzbJZRV1piG1ACmO6C+ruACCdH8Tidc3LODZ6Eeitr58TQJPOEY5+F5XkdSlsq6r24IfWjdBbo4s3Y+MLiFZUJC0x77FJNzApW5tfPDe8SG1vrI6AXpayb8Y2UXwBETonniroY2pgkzUuoA8OD87c7Bwcbvmd7DJvxjaVgwVEaLdoqmA8NdD1E3pcWtQ3qboFSNH6OHlel8bNoQ+PDBO/BvIYjMfqb29rNJ1qNJ2qv72twXhcd7c6KzodEz6lJ1zlWbekvkmqtH9hO3lfl8aN0CWdSUsEiiJjpD5Jo03J7RN6XPQtWgMmaSFS1f1LW/26TKUj9JOPnNTowZFGD47Uv7Vf/5RKeBNvNAqmQHLcyEPzucwYCfPRR9MpI/0lio42y1R3Wd7xeKDt7b6m05Gm05GzhVKVBvTvPvpdScEIfPTgqP4plfDGXbSOt28Gg+BixYXLiWg64yqplVWKTzOlXXjGg7G2+9va7m9rOppqOppqu7+t8cDNxSocbZaZPx6OtlcNjNFplUXnjQbd7e2+s8Abv3ns6qJS+Rx6uDDI6bRKdKS9arAKb1z6ejMvmm3j84WrQtGc9VVER/dlzuWvkpc/GU7O1GhZ761rvbeu6Wh6zlL/siQFzDxBs6zRdjTo5vmUEb3QJP1cZVzsGjmHnkWYDbNxyYb0yVi6XFWpgPG8a5ftLjt3NM992SPyeEhHJmU/+afK1aar5OWv99a1b+tsLv52v5o8/PgoVcqf5ljWJ4AsGTuLMmLiU05VaFyWS1bDI0OdeuyUdl+6O/iLcARalqT59jLzrpedO/oMT0bfTkRHtmHQdT2tUuVq0zYIA2b4p01L++MjeOn8jJgqppyiWjNCrz0/PT7fHirzIhI9d9IqzHieu+vR96JPAZJ/q1zn6nryzyLRomDhFE2eejdIl/f5qE3I2InKPUI3xlxtjPmCMeaoMeZuY8w7XXYsrhH56XXOt9exCjPpU4DEJ4EKxW/CtuGmbN3yZJDUnfXiSpER+hOS3mutvcsYc6mkw8aYz1trv7rswOho+6bbbso88l7pRmo4ulw2v9wmLi8kWV+fpNWuzMNXKj49w3RNumWPplukTdM9i+QeoVtrj1tr75p//QNJRyVdleXY6Aj7M/d+JvHvCyO7I13e16dIRhF0fDbLnFJYVFVZNU1U9dx1Uzi5KWqM2Stpn6Q7sx7Tu7J3ZsQd/dqpcHTZpLTEeF54nUGx1wtG5aEs/Sl56qeqIORygVCY952lxMBkNstdJnhV8ayauqZooul7s9nxWtp1mUPeZIUDujFmXdInJb3LWvtQwr9vGmMOGWMOPf7440Wba794FUYXQbHIRSJPf0rMKFoWhFwFYpdz0Ul11dMCaB111bO0FS4ySltgNDs+03Q0XWnhUXROejar7qLS5JWqZSkU0I0xFyoI5h+z1t6WtI+1dmCt3W+t3X/hhRcWaS6/Kpf4Z1mZ6frmatagHH0djkdGSg1bXJUWhFwG4rwLhBadKywv0Na0xHCRUdoCo7Xdazp96vTKC4+WrcosS5VTL3lXrLqU+6aoMcZI+ltJR621f+yuSyVISjks6+ZoPLguai8pDbHAwyHOBOW0G5bRQD+ZSLt3L9432r+G3VBeFCzjKX6k9K0uusioqgVGbRAG67W1jfMWFIVpjnkyZeLpkkUVyXJ5qaQ3SjpijAkTs3/bWvvZwr0qQ5aAF1Xk6TtZVmamzUWXefM2fqEJxX/eEi+Cx2czTWYz5/Pj8dE7Ab09FgXJpphMhjp9+pTW1nqpWTRJnwSiQXttbUNra7vPOW/S13nlDujW2v+UZAr3oG7Hj5+dIpHOLrOvIu87PsXhespjlYtS0s+76kUwo91ra7r30UdLuUlX91RH2eUDpLMXxLA9H+RNNazLKiVu4/cQogE9PJcrrVkpWprJJPgTTd0LR6INmVPObdWLUkt+3roDWlr7VdRfD9sO2/NFkTrgTRd/JF9ZCOhSaSPRRmhJkF5F3oAWnWPfWFvT7rW1UtqvonxA3Z9EfOd6brsqBHSfFJn3b5ksAS1+kzQafCezWe6AnrX9Vfq27O9RrbaWAiCgt9Xx48FUUTRw11HvpcGSUhzjUyFlSgvOi9IvqdXiXpHCW21DQG+r3bule+89P3B7OMVSRN6RtIuR8rLgvKhvrqdToj/L8Vn+qaZlXExTlDHVER9tu7rZ2sRpGT8DeoemHlAOVyPlJsx1R/t/ouBUUxoX0xRlTXWUMdouc1om78XCz4CeZ+oh60Ugut/GRvbFOa6faFSVDl8cVw3GTZ7/PvuzlDvV5CJwljXVMZsd12w2cTqaLquveS8WfgZ0KXnqIS04Zb0IpK22XLQ4JzyujQG9I/PyVUyxtMl4MD7zrFFXD4yu29rabj366L2tucmZ52Lhb0BPsiw4ZZ1/XrTactHinLbz4WdYwqcpljziATxaq6WMB0Y3cf7ZB90K6FL5wSnt/KtM1zRdUpaNQ3VMX7Q1GLuQFMDXe+W9Hm1NC2y67gX0Oq1SHKvpFmXZOOLT9EVblBnAE9trYVpg0xHQq7Zougbn6fKIGcjDyROLAAD1I6ADgCcI6ADgCQI6AHiCgA4AniCgA4AnCOgA4AkCOgB4goAOAJ4goAOAJwjoAOAJAjoAeIKADgCeIKADgCcI6ADgCQI6AHiiUEA3xrzcGHOPMeaYMeZmV50CAKwud0A3xuyQ9BeSflHScyW9wRjzXFcdAwCspsgI/UWSjllr77fWziT9vaTXuukWAGBVRQL6VZK+Ffn+gfnfAQBqYKy1+Q405vWSfsFa+7b592+U9CJr7Tti+21K2px/+2xJ9+TvLgB00k9Ya3ct22lngQYekHR15PunSxrHd7LWDiQNCrQDAMigyJTLlyU9yxjzTGPMmqQbJX3aTbcAAKvKPUK31j5hjPl1SZ+TtEPSh621dzvrGQBgJbnn0AEAzcJKUQDwBAEdADxBQAcATxDQAcATRfLQczHGXG2t/VbaVpKW7RPZ9zuSDkg6IemLkl4n6fsKLlY/yrC9SNJzJN0t6YmMx7g8R9vb/6Gk2yX9+JL35nZJa/O2jkp6jrX2S8aY6yQ9LOkSSZeF/5Zxe72k+3Ie6+IcmY6d/5xXS/pBSX0/rcAP0o4J+zF/f66VdJ2kDUnfy/u+W2sfWfV3tsjvu8tj625/1WOVQSVZLsaY18y/fJGC/4RfTti+QtJnJb1SQQBI2idp+4ikPZI+JemtCv7zPizJSjIZtj1JfybpHZK2Mx7j8hxtbn+PpH9RUMPnoQXvzQ5J/zV/75+sIHg9oiD4HJX0mvn+N0g6LOnS+b9l2V4zP/cLJX1txWNdnCPrsUfnP/tPRn5+l32/QtL/xs6f1o8Tkn5V0l9LerukO1d8362k/5m/d/+u1X9ni/y+Fz227vZXPfYvJb3KWvt2ZVDVCP11kj4i6QWSpgu2T5U0kXS5pPuX7BvdThWUFPiSpDdI+oaCEXrW/5xXKfiPfaOkYxmPcXmONrf/nPnr/jYFq4ST3puH5u/PQ/P394n5e325gv+wF0m6Zf71BQpWIF+ecbsh6R8lvSzHsS7OkfXY6yU9SdIo8vO77PufS7o4dv60fnxPwQj7vyX9co733c7f013K9ztb5Pe96LF1t7/qsd+fv1eZVBXQf89ae58x5riCX+zLdPZjdrh9mrX2i8aYuxT8B7t8vu8lCftGtxuS3qvgyveHkl6ioCSBUbaPj6cUjHJOSHrGvL9Zj3Vxjja3f//8df+t+Tni79mGgmD/uILyDxfNj7lGweh+W9KN1tr/MMa8T9KFkk7OjxvP90nb/py19uPz6YOjKx7r4hxZj92WtG/+ffjzu+z7rvn3JxVMwVyz4JiwH9uSnjl/776e432/QNJjkt5nrf1Ujt/ZIr/vRY+tu/2VjrXWjo0x90mSMWantfYJpbHW1vJH0q8t22bZp2nHdr39Nve97vbb3Pe62+9S39P+VH5TNMJk3K6yb1OO7Xr7be573e23ue91t9+Vvi9E2iIAeKKyEbox5mUK7ra/WtI/S3qxMeZEbHuFpOuMMT+t+Z3ghH0Wbes6tuvtt7nvdbff5r7X3X6X+r5bgaGW2HHw4MFl+zjxwQ9+8NWSrpR0raTZgu1eBXfhn6Tgzm7avk05tuvtt7nvdbff5r7X3X6X+v7wwYMHv3zw4MEfaYkqp1yeLOmIgkUQi7anJH11yT5NO7br7be573W33+a+191+l/p+QhlVGdA/q2Bxw7GU7RcUTAOl7dO0Y7vefpv7Xnf7be573e13qe9PUUY7s+7owIslrUv6KQWdTNpeN+/TYyn7NO3Yrrff5r7X3X6b+153+13q+0wZVTlC3yvp/xQE9UXbHZK+vWSfph3b9fbb3Pe6229z3+tuv0t9nyqjyp5YZIx5sqTnKVgl+tCC7WkFNwK+nrJP047tevtt7nvd7be573W336W+77DW3qEMqpxy+QNJjyoownT7gq0U1KLYmbJP047tevtt7nvd7be573W336W+G0mNC+hfmW93KagMl7Rd09n5okX7NO3Yrrff5r7X3X6b+153+13q+yPKqMqA/mkFFeFmCq42Sdv7FEzLPJayT9OO7Xr7be573e23ue91t9+lvj9XGVVVD/1PFJTc7Cu9jOsDkp4+3ybt07Rju95+m/ted/tt7nvd7Xep73dIstba9yiDC7LsVJS19t2S7rHWvkDS3Qu2n1NQYvV3UvZp2rFdb7/Nfa+7/Tb3ve72u9T3dytYhJRJlVMuu+bbPSnbXQquTGn7NO3Yrrff5r7X3X6b+153+13qe1jLZakq0xZfpuDJRccUpOwkbX92vvsdKfs07diut9/mvtfdfpv7Xnf7Xer7bdbaLyqDygI6AKBclcyhAwDKR0AHAE8Q0AHAEwR0APAEAR0APPH/fzRJxIxvX3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram\n",
    "\n",
    "mergings = linkage(samples_scaled, method='complete')\n",
    "\n",
    "#a tree diagram, especially one showing taxonomic relationships.\n",
    "dendrogram(mergings, labels=varieties, leaf_rotation=90, leaf_font_size=6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  class_0  class_1  class_2\n",
      "labels                              \n",
      "1               51       18        0\n",
      "2                0        3       48\n",
      "3                8       50        0\n"
     ]
    }
   ],
   "source": [
    "#Extracting cluster lables using fcluster depdending on the height of when the merge \n",
    "#did happen\n",
    "\n",
    "from scipy.cluster.hierarchy import fcluster\n",
    "# 400 is the height\n",
    "labels = fcluster(mergings, 9, criterion=\"distance\")\n",
    "\n",
    "df = pd.DataFrame({'labels' : labels, 'varieties' : varieties})\n",
    "\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-SNE for 2-dimensional maps\n",
    "t-distributed stochastic neighbor embedding\n",
    "- Maps samples to 2D spaces (or 3D)\n",
    "- Map apprroximately preserves nearness of samples\n",
    "- Great for inspecting datasets"
   ]
  },
  {
   "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": [
    "from sklearn.manifold import TSNE\n",
    "from sklearn.preprocessing import normalize\n",
    "samples = iris.data\n",
    "\n",
    "#learning is bad when we have everything bunched together!!\n",
    "#try values between 50 and 200\n",
    "model = TSNE(learning_rate=500)\n",
    "\n",
    "#when method that fits and tranforms the data!!! ==> we can't extend the map\n",
    "#include new samples\n",
    "\n",
    "transformed = model.fit_transform(normalize(samples))\n",
    "\n",
    "xs = transformed[:, 0]\n",
    "ys = transformed[:, 1]\n",
    "\n",
    "varieties = np.array(iris.target).astype(str)\n",
    "\n",
    "for i in range(3):\n",
    "    varieties[varieties == str(i)] = iris.target_names[i]\n",
    "\n",
    "\n",
    "plt.scatter(xs, ys, alpha=0.5)\n",
    "    \n",
    "# Annotate the points\n",
    "for x, y, variety in zip(xs, ys, varieties):\n",
    "    plt.annotate(variety, (x, y), fontsize=5, alpha=0.75)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the PCA transformation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimension reduction\n",
    "- Leanrs the principal components of the data\n",
    "- Remove less-informative \"noise\" features\n",
    "- Rotates data samples to be aligned with axes\n",
    "- Shifts data samples so they have mean 0\n",
    "- No information is lot\n",
    "- Steps :\n",
    "    - First step decorrelation (PCA features are not correlated)\n",
    "    - Reduces dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pTqwNhHNuJ7ATwMysgrd8AJh0zn20+PUBM/s1oB9QAyENJYoAo3w+z/DwMF1d\nXWzcuDHS+WGBUWF1h42HrZPUIC0RCdTbbZzrgIFZY3lgWw1qEalbExMTrF17OVNTh0+NpdNt7N8/\nxIUXXljV/EKhwObNfcXbNgOZTA+5XJbW1taKawxb5+67/4IPfvBDVa8vIrVVbxdRnsPp5wCfdBh4\nnZmdUYN6ROpS0AwcY2Z409TUMS65pKvq+VEFXSl4SqSx1VsDISILyOfzxSMJXyQIbzq3+N8vMDV1\nmN27dy96/snAqOnpz5fMnZ7+HPn8w4yPj1dUY/g6H2Nq6nDV64tI7dXbKYzngbZZY23AS865n8/3\nxv7+flasWFEy1tvbS29vb7QVitTY8PBw8U/lQ52GhoZKrm/wmV9J0FUl1yuEr9MWMu63voj4y+Vy\n5HK5krGjR48uer16ayCGgF+fNXZtcXxe27Zt0+O8pSmsXbu2+KfHOR0fDSfDm7q6uhY9vzQwau7c\nSoOhwtc5HDKu4CmRuJX7UD3jcd7+nHOxvQhu43wL8FbgBPDh4tfnFr//SeDeGfMvAH4M/DmwBvgg\n8DLQPc82OgA3MjLiRJpFOt3mYIWD+xwcKv53hUun26qen8n0uFTqrJK5qdRZLpPp8aoxbJ10ui2S\n9UWkeiMjIw5wQIfz/R3v+wavxYPjkieA6Vmvvyl+/0vAnlnvuRIYAX4GjAN9C2xDDYQ0ncnJyWJT\nwKlXOt3mJicnq55fKBRcJtNTMjeT6XGFQsGrxrB1JicnI1lfRKpXTQNhLvglnFhm1gGMjIyM6BSG\nNJ3du3czNDRUcQ6Ez/yogqHC1lHwlEjtzTiF0emcG/V5rxoIERGRJlVNA6HbOEVERMSbGggRERHx\npgZCREREvKmBEBEREW9qIERERMSbGggRERHxpgZCREREvKmBEBEREW9qIERERMSbGggRERHxpgZC\nREREvKmBEBEREW9qIERERMSbGggRERHxpgZCREREvKmBEBEREW9qIERERMSbGggRERHxpgZCRERE\nvKmBEBEREW9qIERERMSbGggRERHxpgZCREREvKmBEBEREW9qIERERMTbsloXIMkzNjbGxMQEq1at\nYvXq1bUuR0REakBHIKRihUKBTZuuY82aNfT09NDe3s6mTddx5MiRWpcmIiJLTA2EVGzz5j4GBvYC\nWeAQkGVgYC+9vdfXuDIREVlqOoUhFRkbGyOff5igedhSHN3C9LQjn+9jfHxcpzNERJqIjkBIRSYm\nJop/unJkynFPAAATaklEQVTWd64C4ODBg0taj4iI1JYaCKnIRRddVPzT47O+8xgAq1atWtJ6RESk\nttRASEXa29vJZHpIpW4lOI3xLJAlldpKJtOj0xciIk0m9gbCzG42s++Z2c/MbK+ZXTLP3KvM7MSs\n17SZvSHuOmVhuVyW7u51QB9wHtBHd/c6crlsjSsTEZGlFutFlGb228Cngd8D9gH9QN7M2p1zL4a8\nzQHtwI9PDTj3wzjrlMq0trayc+dDjI+Pc/DgQeVAiIg0sbjvwugH/so592UAM7sJuA54H/Cped73\ngnPupZhrk0VavXp12cZBAVMiIs0jtlMYZtYCdAKPnBxzzjlgAOia763At8zsOTPbZWaXxVWjREMB\nUyIizSfOayDOBlLA4Vnjh4FzQt7zA+D3gd8E3kVwpd6gmb01riKlegqYEhFpPnUVJOWcGwPGZgzt\nNbOLCE6FvKc2Vcl8FDAlItKc4mwgXgSmgbZZ423A8x7r7AMuX2hSf38/K1asKBnr7e2lt7fXY1Pi\nq5KAKTUQIiK1l8vlyOVyJWNHjx5d9HqxNRDOueNmNgJsAB4AMDMrfv15j6XeSnBqY17btm2jo6Nj\nMaVKFUoDprbM+I4CpkRE6km5D9Wjo6N0dnYuar24T2F8BthRbCRO3sb5GmAHgJl9EniTc+49xa+3\nAt8DvgMsB94PXA1sjLlOWaSTAVMDA7cyPe0Ijjw8Riq1le5uBUyJiDSqWBsI59xXzOxs4M8ITl18\nC8g4514oTjkHOHfGW15NkBvxJuCnwNPABufc7PxkqSO5XJbe3uvJ5/tOjXV39yhgSkSkgVlwZ2Vy\nmVkHMDIyMqJTGDWmgCkRkWSZcQqj0zk36vNePQujyYyNjfH1r3+d8fHxBedu376dvr4+duzYUdEa\nvs2oTy0iIlJnnHOJfgEdgBsZGXESbmpqymUyPY4gKtwBLpPpcYVCYc7cJ5980rW0nFkyt6XlTDc4\nOFh2jYmJiYrX9q1FRETiMzIycvLf4Q7n+ftXRyCahE/YU1fXFRw//uqSucePv5qrr95Ydo1LL73M\nK0hKwVMiIslXV0FSEg+fsKft27dz/PjPgL8umQsO5/qYnv6jOWtMTfUBdy24tm8tIiJSv3QEoglU\nEvZ00uDg4Lxz4fVe4zPX9q1FRETqlxqIJlAa9jTT3LCn9evXzzsXXvAanx0k5VOLiIjULzUQTeBk\n2FMqdSvBqYNngSyp1FYymdKwpxtvvJGWljOBm0vmwi2YtZBK3TFnjXS6rez47LV9axERkfqlBqJJ\n5HJZurvXAX3AeUAf3d3ryoY97dv3BC0tL5fMbWl5mcHBgbJr7N8/VPHavrWIiEh9UpBUk/EJe9qx\nYwePPPIIGzZs4IYbblhwDd8gKQVPiYjUVjVBUroLo8lMTk6yf/9+li1bVvJLe/v27QwODpY0C5dd\ndhltbW1zrktYvXp12V/4vs1o2DoiIlL/1EA0iYmJCdauvZypqcOnxtLpNv7mb/4773737xRv3YRs\nNsv73/8BLrnkbQwNfePU3EwmeLZFa2vrnLULhQKbN/cVb89ceL6IiCSfroFoEkHzcIyZ4U1TU8d4\nxzt+c05o1CuvnMHQ0H4UDCUiImF0BKIJ5PP54pGH0vAmeA74KPBFZodGBRc4XkrwsFQFQ4mISCkd\ngWgCw8PDxT/NDm9qCxk/GQ51cM6YgqFERATUQDSFtWvXFv80O7zpcMj4yXCoVXPGFAwlIiKgUxhN\nIZPJkE63MTV1M8HpiasIfsHfTvA/gdnjtwBnAMPAcuAxUqmtdHeHB0MNDNzK9PTpNcLmi4hIY9AR\niCaxf/8Q6fRyZoY3pdPLefDBv5sTGrVs2c/p6roEBUOJiEgYHYFIiLGxMSYmJioOXcrn8wwPD9PV\n1cXGjRu58MILefHF53nve9/L4OAg11xzDdu3bwfg5Zd/ypvf/GbGx8dpb2/nO9/5DgDvete7+OY3\nv8kVV1zBV7/61VNr9/f3s2fPHjZu3Mhdd91Fa2srO3c+xK5du9i7d++pbUa9TyIiUkecc4l+AR2A\nGxkZcY1oamrKZTI9juAcgwNcJtPjCoVC2fkHDx506XRbyfx0us1ls1ln1lIybtbibrrpJgepkvHg\n61fNGfuDP/gDB8tmjS9zuVzOq0bffRIRkXiMjIyc/He4w/n+/vV9Q729Gr2ByGR6XCp1loOsg0MO\nsi6VOstlMj1l5wfNw4qS+cHXKc/xM7zW8KnRd59ERCQeaiAatIE4cOBA8S8268DNeN3nADc2NlYy\nf+fOnSHzbwwZ/8i868NYmbG7Qub+VkU1+u6TiIjEp5oGQhdR1jHfjIXwvIdCyPj0vOuXy4GA14fM\nfbaiGpUbISLSGNRA1DHfjIXwvIezQsZT865fLgcCXgiZe25FNSo3QkSkMegujDrmm7EQnvfwVYJm\nYfb4fw8Zn5sDEYylgE8QJFheVTKeSg0wPZ1dsEblRoiINAjfcx719qKBr4FwzrlCoeB1x8Lk5GTZ\nuzDuv//+sndhfOhDH3KV3oXxkY98xJW7C+P+++/3qtF3n0REJB7VXANhLvglnFhm1gGMjIyM0NHR\nUetyYjM+Ps7BgwcrzkzYvXs3Q0NDczIZ7rzzTnbt2sW1117Lxz72sVPjmUyG4eFh1q5dSz6fB+DG\nG29kz549JZkRALfddhu7d+8+lQOx2Bp954uISLRGR0fp7OwE6HTOjfq8Vw1EwkUVxlRundtvv51H\nHnlkTrMhIiKNoZoGQtdAJFShUGDz5r7io7QDmUwPuVyW1tbWqtZ529su5cknnwKOA/Doo4/yR3/0\nnxkcHODKK2ffPSEiIs1Id2Ek1ObNfQwM7AWywCEgy8DAXnp7r696nSefHAFeUzLm3GtYv7470n0Q\nEZHkUgORQGNjY+TzDzM9/XlgC8EtlFuYnv4c+fzDjI+PV7HOMYJ8iC+WrA1fwLnj3HnnnTHskYiI\nJI0aiASKKoyp/DqD8669a9euyooUEZGGpgYigaIKYyq/zvp517722msrK1JERBqaGogEOhnGlErd\nSnCdwrNAllRqK5lM5WFM5dc5g9PhUqfXhlswa9HdGCIiAqiBSKxcLkt39zqgDzgP6KO7ex25XLbq\ndd72trcBPy0ZM/spg4MDke6DiIgkV+y3cZrZzcBtwDnAt4EPOef2zzN/PfBp4JcJbgG43Tl3b9x1\nJk1rays7dz5UdRjTfOuEhU6JiIjEGiRlZr8N3Av8HrAP6Af+HdDunHuxzPwLgH8E7ga2A93AZ4Ee\n59zukG00dZCUiIjIYlUTJBX3KYx+4K+cc192zn0XuIng2Pj7QuZ/AJh0zn3UOXfAOfdFgidB9cdc\np4iIiHiIrYEwsxagE3jk5JgLDncMAF0hb1tX/P5M+Xnmi4iISA3EeQTibILL+Q/PGj9McD1EOeeE\nzH+dmZ0RbXkiIiKyWA3zLIz+/n5WrFhRMtbb20tvb2+NKhIREakfuVyOXC5XMnb06NFFrxdnA/Ei\nQSZy26zxNuD5kPc8HzL/Jefcz+fb2LZt23QRpYiISIhyH6pnXETpLbZTGM6548AIsOHkmJlZ8esn\nQt42NHN+0bXFcREREakTcd+F8Rng/Wb2783sl4C/JHjM4w4AM/ukmc3MePhL4BfN7M/NbI2ZfRB4\nd3EdERERqROxXgPhnPuKmZ0N/BnBqYhvARnn3AvFKecQPO7x5Pzvm9l1wDbgVuCfgRudc4pAFBER\nqSOxX0TpnLubIBiq3PfeW2bscYLbP0VERKRO6VkYIiIi4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQ\nIiIi4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi\n4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi4k0N\nhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi4k0NhIiIiHhTAyEiIiLe1ECIiIiINzUQIiIi4k0NhIiI\niHhTAyEiIiLe1ECIiIiINzUQCZLL5WpdwpJpln3VfjYW7WdjaZb9XKzYGggzazWz/2FmR83siJnd\nY2avXeA9XzKzE7NeD8dVY9I00/+Ym2VftZ+NRfvZWJplPxdrWYxr/y3QBmwAXg3sAP4KuH6B930d\nuAGw4tc/j6c8ERERWaxYGggz+yUgA3Q6554qjn0IeMjMbnPOPT/P23/unHshjrpEREQkGnGdwugC\njpxsHooGAAesXeC9683ssJl918zuNrOzYqpRREREFimuUxjnAD+cOeCcmzazQvF7Yb4O/C/ge8BF\nwCeBh82syznnQt6zHOCZZ56puuh6d/ToUUZHR2tdxpJoln3VfjYW7WdjaYb9nPG7c7n3m51zFb8I\nfqGfmOc1DbQDHweeKfP+w8Dve2zvwuK6V88zZzPBkQ299NJLL7300mtxr80+/YBzzvsIxF3AlxaY\nMwk8D7xh5qCZpYCzit+riHPue2b2IrAKeDRkWh7YAnwfOFbp2iIiIsJy4AKC36VevBoI59wUMLXQ\nPDMbAlaa2a/OuA5iA8GdFcOVbs/M/hWQBn6wQE1/W+maIiIiUuKJxbwplosonXPfJehm/trMLjGz\ny4G/AHIz78AoXij5juKfX2tmnzKztWZ2vpltAP4OGGMRnZGIiIjEJ84kys3AdwnuvngQeBz4/Vlz\nVgMrin+eBv4N8PfAAeCvgf3Alc654zHWKSIiIp4s/OYGERERkfL0LAwRERHxpgZCREREvCW+gTCz\nm83se2b2MzPba2aX1LqmqJnZFWb2gJn9v+IDxt5e65qiZmYfN7N9ZvZSMYn0a2bWXuu6omZmN5nZ\nt4sPmTtqZk+Y2aZa1xU3M/tY8X+7n6l1LVEzsz8p8xDAf6p1XXEwszeZ2X1m9qKZ/bT4v+WOWtcV\npeLvk9l/nyfM7C9qXVuUzOxVZvYJM5ss/l0eNLP/5LNGohsIM/tt4NPAnwC/CnwbyJvZ2TUtLHqv\nBb4FfJAg8KMRXUFwp85aoBtoAXaZ2Zk1rSp6zwJ/CHQAncAe4O/N7OKaVhWjYlP/ewT//2xU/0jw\n8MBziq9fq2050TOzlcA3CR5wmAEuBv4DcKSWdcXgbZz+ezwH2Ejw7+5XallUDD5GcGPDB4FfAj4K\nfNTMbql0gURfRGlme4Fh59zW4tdG8A/0551zn6ppcTExsxPAbzjnHqh1LXEqNoE/JLgL5xu1ridO\nZjYF3OacWyikLXHM7F8AI8AHgD8GnnLO/UFtq4qWmf0J8A7nXEN9Ep/NzO4EupxzV9W6lqVkZp8F\nepxzDXVE1Mz+AXjeOff+GWNfBX7qnPv3layR2CMQZtZC8AnukZNjxedlDBA8zEuSbSVB11+odSFx\nKR5C/B3gNcBQreuJyReBf3DO7al1ITFbXTzFOGFmWTM7t9YFxeDfAk+a2VeKpxlHzex3a11UnIq/\nZ7YA22tdSwyeADaY2WoAM3sLcDnwcKULxPUwraVwNpAieL7GTIeBNUtfjkSleCTps8A3nHMNdy7Z\nzH6FoGFYDvwYeGcxfK2hFJujtxIcEm5ke4EbCPJr3gj8F+BxM/sV59xPalhX1H6R4EjSp4HbgUuB\nz5vZz51z99W0svi8kyCr6N5aFxKDO4HXAd81s2mCAwr/0Tl3f6ULJLmBkMZ1N/Bmgm64EX0XeAvB\nP0zvBr5sZlc2UhNRjKH/LNDd6EFwzrmZSbn/aGb7gP8L/BYLPzsoSV4F7HPO/XHx628Xm+GbgEZt\nIN4HfH1mgnID+W2CwMffAf6JoNn/nJk9V2lDmOQG4kWC9Mq2WeNteDywS+qLmX0B6AGucM6FPgMl\nyZxzrxA8dA7gKTO7FNhK8OmuUXQCrwdGi0eUIDhieGXxIq0zXJIvwJqHc+6omY0RPASwkfwAeGbW\n2DPAu2pQS+zM7DyCC7p/o9a1xORTwCedc/+z+PV3zOwCgqdpV9RAJPYaiOKnmhGCh3QBpw59b2CR\nDwaR2io2D+8geHz7oVrXs4ReBZxR6yIiNgD8a4JPNW8pvp4EssBbGrV5gFMXjq5inocAJtQ3mXt6\neA3B0ZZG9D6CU+IVXxOQMK8h+BA+0wk8+oIkH4EA+Ayww8xGgH1AP8EPZUcti4qamb2W4B+kk5/k\nfrF4wUvBOfds7SqLjpndDfQCbwd+YmYnjywddc41zGPazewO4OvAIeAXCC7Qugq4tpZ1Ra147r/k\n+hUz+wkw5Zyb/Sk20czsvwL/QPCL9F8CfwocB3K1rCsG24BvmtnHCW5pXAv8LvD+ed+VQMUPozcA\nO5xzJ2pcTlz+AfhPZvbPwHcIbi3vB+6pdIFENxDOua8Ub/f7M4JTF98CMs65F2pbWeTeBjxKcFeC\nI7iICYILe95Xq6IidhPBvg3OGn8v8OUlryY+byD4e3sjcBR4Gri2Ce5SgMbNMPlXwN8CaeAF4BvA\nOufcVE2riphz7kkzeyfBxXd/DHwP2Opz0V2CdAPn0ljXsMx2C/AJgjul3gA8B/y34lhFEp0DISIi\nIrWR2GsgREREpHbUQIiIiIg3NRAiIiLiTQ2EiIiIeFMDISIiIt7UQIiIiIg3NRAiIiLiTQ2EiIiI\neFMDISIiIt7UQIiIiIg3NRAiIiLi7f8DGkoBCkkZY9gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14101f55dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "corr = 0.962757097051\n"
     ]
    }
   ],
   "source": [
    "#check correlation between features\n",
    "\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "xs = samples[:,2]\n",
    "ys = samples[:,3]\n",
    "\n",
    "plt.scatter(xs, ys)\n",
    "plt.show() \n",
    "\n",
    "\n",
    "correlation, pvalue = pearsonr(xs, ys)\n",
    "print(\"corr =\", correlation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape after transormation (210, 2)\n",
      "corr = 0.86041\n",
      "[ 3.25860476  5.62853333] [ 0.63910027  0.76912343]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZN24c+/btC3RekdFi27ZtzJw5E2CmtXZbtv0UAIgIELJxLoDjOEyfPp3Ukr94\n7xfjOE6ikd2xA046CV5+2X1/zz1w3nmDvgaRchA0ANBywCLis6qd/+p3gxF0gR1273Yz/uON/1e/\nqsZfZBgoABCR4I3zIATK2t+7F97/fnjiCfdX55wDV1456M9O5zgOa9asGZLARmSsUgAgInkb52ee\neWbQjWWgBXY+8xm4/34AXquuZt3ixfQMBCeDF4vFmDt3PtOnT6e5uZnq6mrmzp3P7t1ZVzQXKV25\nMgSL9UKzAERGnN8UOGMmDWTBU2AmfPKsgmyZ+Fu2bLEPLlgwkPH/4vjx9sigMwUKusf8pYNFxipN\nAxSRUPynwE2wcEdBjWWuKX/x+f5btmyxp5/eaE/H2H1e4/862HcyvuDPzUa1+6VcDFcpYBEpUclV\n7VasWOFt/QHuSnfhkwIXLFhMZ+dm3O7+p4BWOjs309KyiKqqKubNm8fll1/B0/d38UssUe+487mY\nLbwBd4ndoUtGHIk8B5GxRAGAiKSoqqriyCOP9N4V1lgGmVXgOA6bO9pZw17ii35/ky/Rxndxlxdp\nx11iN/NzC0niC1M6WKQcKAAQkQyDbSxTn7YdYA1uY55oyB93HH4KxM/0a87icr7hvYsvwBMPNNzP\nnTp1asFJfIGSEEXKiAIAEcng31heTyRyEbW19Xkby0QAcRYwHWgGqr33MG7cOP7tpz9ljrfXIxzB\nQv6LxKhkfAGeA0lupC+//IqswwpBtLW1csopb0Or94mgJEAR8ZeaFBjxTebLZcqUaRYmpmTcu++j\n9oKkLLwXwB7NIWkL8EzMmH2wZcuWQSXx+SUl1tbWq76/lBwlAYrIoMSTAuvq6olEJhLmqdtxHHp7\nnwW+S3IOAHyH2fRxGwaAfcaw8OBJPMXLJD+Vz55dw9atv09ZYveFF17wzl5YXoJfUuJDD/05cO+B\nSKkZV+wLEJHRy3EcHnywi9T6/Qvp67N0dCymp6fHdzggW8b9mzmGXwHjcNcg+ZiFzlcjwHVAH+AQ\nifyMAw44gJNOOinl2NS8hOS1BPLnJcSTEsPeh0gpUw+AiGRV6NQ5vyTCg3mJNXyA+LqC1/Ih7sJ6\nMwU+B3wB+D79/d/xnfI3mCQ+TQEUyaQAQESyKnQ2QHpjHeFJVlHLdP4OwG+Zz5d5k7d38Ea5ra2V\nxsZZhE3iy7yP+MyEVTnvQ6SUKQAQkQzxefbGmIKfupMb62t5M/P4MwCP8WZaOBsiP/D2DB5cJBcr\nSs4PqKiC0DyTAAAgAElEQVSoyNg3WTwgiUSWACeSmJlwKVOmTGPq1Kl5/05ESo0CABEZ4LdYzt69\ne6mvn0nYp+54Y/33a67h8/HzA/N4gpe5kDlzTqOhYU5BwUW8kmCYcfu2tlYqKiYAT5CcCPjii3uV\nCChlSUmAIjIgNVN+NrCBrq6lNDbOwnEcdu7cSWVlZfCG98EHOeyrXwVgL24VgL8CdXX1AwFES8si\nOjoWDxzS2Ng8LPPyn3/+eW9mghIBRUABgIh48mXKw03MmzcvZf9du3ZlDwieeIK+d7+baF8fAJ/k\nE/yOy4ENbNq0lJaWRaxdu5q1a1fT09MTPrgIKUgioAIAKScaAhARIHimvN8wQXo53j/cfz9PHHc8\n0ZdeAuBbzONHrCDb4j6FdOmHpbUARFIpABARIHgDmWuVv1gsRnNTM39vaODNr78GuLn2X+B7aecc\n+el3WgtAJJUCAJESVMhqeUEayHyr/L33ve/jXevu5d3eOXdwDOcB/fwu7dOK89Rd6DRCkVKkHACR\nEhKLxViwYLE3lu9qamr2MuBzT5UDt4HMlZSXb5jgmAe7+IK35UUOpplO/sFSYCluafJ6oItodBmN\njSP/1B2fmTASOQcio50CAJES4pfF39mZSLjLJ18Dmasc7ylAfGb/PuC9XMLjHOtdyyLcp25XmEz/\nvMmGBaiqqlLDL2VPQwAiJSJf93z6cECuYQLrrsqZIdsywceYT9IejTLe2+8iTqCL2719XgZaiEQm\nUlNzUuDiPUGSDUWkcAoARErEYLL46+rq+clPfsLWrVvzNrqp4+jHcCBf4Lf2VSZ50/1uZj++zxJg\nBslj7XPmnEZn57qcT97JQUmuZEMRGQK51gou1guoAWx3d/ewrJUsUop27NjhrQHeasEmve6ygHUc\nx1prbVNTs41GJ3v7PWxhRnztcO81wcIdFp6y0Gqj0cm2qak54/Pq6upt1Eyyv6Jm4MPWMc4eNvmw\nlPMdf/wJ9qabbhr4fD+9vb22qak57Try34uIZOru7o7/N1Rjc7S16gEQKSkR4BKSs/jdBDz3P/XM\nYYLLiD9dJ/58A/Brcg0hxJcJvtLO5my2AbCTY/kA3+G52HOsW7eOVatWUVdXz6OPPsJnPvOZnF34\nmU/7l3q/0ep9IsNFAYBIiXCHAPpxF7tJdL277/vZuXNn2jCBA7QDqTkD7vt2oMfbpx9IbXR37drF\nAuAr/AaAPRzCPNawh2YA9u3bxw9/eCebNv2ZfF34/rkLF3i/VdEekeGiWQAiJSKRof8x4HZgJ1AJ\n/B64j8rKyqTkvg3AZO9n/6dsWAD8YWDrNddcy6xZs6ioqOCtL7/Mj7ztfUQ4h1+ykyrcxh6i0WjO\nssLr1q2jr6+PysrKLLkL1UAD8GlGw/RBkVKkHgCREpGaof974ATg9ymFfFL3ecQ70v8p2+0BSDy9\nb9r0Z/fp/emnOfrii9nP22sJi7nfa/zjn9XnJQRmBhcTAUNTU9NAkuHVV1+b5To+CPwDFe0RGSa5\nEgSK9UJJgCIFicViGcl0NTUn261bt2bZJ2Jhopdc95T350Rve2YC3hvAvnDEEQMbf33U0Smf1dTU\nbGOxmE9CYq+F9CS/Bgt32Gh0sp0yZZqXmJi4jnjyoeM4tr29PSXxb8eOHRnbRMQVNAmw6I2970Up\nABAZlC1bttiampN8G+c4x3HsqlWrbF1dfUbA4P78VEoAYHjS/jxpwx8nT7ax557zbaCtTZ5tcJfX\n2Fd4AcFT3p+TvaDAzeyvra3Peb3W+s8W8NtPpJwpABApY6lT/XJP57PWpjTi2aYTXsF7B97s4lA7\nJTIp6/ms9euN8J/SB10WGPj8XE/2Ye9LpBwpABApU0HrAcT3zf/0/pT9IJ8eONEeDrbV/E/gOfkr\nV6707VFw32Ph84HOE+a+RMqZ6gCIlKkgFQHzldlNrvZ3EkfzY74LQD+G9/NzHKYTdE7+7Nnx6/BP\nNoxEVgZajjdopUMRCUYBgEiJSV2wJ1liDn2+MrvxRYF2bdjAhoMPZoJ3hmXcTCdzMs6XS7ZlhmEJ\nEGHOnNN8M/vT1yoIcl8iEkKu7oFivdAQgMigpHfhx7Pqa2tn2xUrVgTvSj/ppIEd7mA/Cz/OyNIP\nIsjshLhciX7Z7ks5ACIJygEQKWN+De6UKdNS3ruZ+bGMMfn29vbEif71X60F+3+nnmqb58wddPZ9\nviQ/a3Mn+vndl2YBiKQKGgCoEqBICYp34ff09LBz506uuebapLK8s3G70S8BFgGrvaN8utK7uuBX\nv2L8ueeyevLkgfNVVlYWVI2vqqoq72qAuSoIvvDCCyn3Veh1iIhKAYuUtKqqKqy1PPhgF+mNqvuA\nsBg3GHjKv8zuYYfBhRfiOA67fv97KisrmTdv3rBdb5BEv3gQoYZfZHAUAIiUuO3bt3s/Zav57/7Z\n2NickYwXi8VYsGCx91Tuampy96uoqBiS63Mch127dlFZWZmW6LcwaS8l+okMNQUAIiXu1lu/6/20\nCngr7gJBVcQb1ZUrV1JfX+/7RJ06W8AdOujsXEpLyyLWrl2dsX+y5Ibd79zZgouGhjl0dS2lr8+i\nRYBEhlGuBIFivVASoMiQSBTPmZSWADjDwiG2rq4+wLHhCu8ELdebLdmvoWGOEv1EBkFJgCLijalH\nvFdyAuCngVdYsuRi3+NisRgtLfEu+Nzj8elP+kF6DXIl+91332IcxwFuUqKfyDBSACAyxuXqao9E\nIkA/cAt+CYDJ4/jJ57nkks+wfXuP9xv/8fipU6cyd+78lC782trZbNy4gWxZ/D09PVRVVQVK9ps3\nb54afpFhpABAZIwKkqDX39/v/ca/od23b5/vedweg9uAXwNLcQMGdzw+XsFv3rz3sHv36yQ/6W/a\n9KmcnxfvNVCyn0jxqRSwyBiVr5wvFF4WGA7GTRpsBdw1AeBo78+ZwG309r5Gf/8xuA34UcBC+vu/\nlvfzIHt54Gh0Wcq6AOnlgEVkCOVKECjWCyUBiuQUJkHPr3xuJFJh6+rq854HHAvxfS713vvtk1xN\nMGIjkYq85XpzVfULmkgoIpmGZTVAY8zXjTH9aa9Hc+xf77N/nzHmsNCRiogMyDe3P3llvOSV/eJP\n8f39e3jwwa68iX6wAtjs/XwJ7vTB9H2SV+HrAvo57bS3p3xeY+OsjBoD8WqFjuPQ3t6O4zisXbua\nioqKQL0bIjI4heQAPAKcARjv/b48+1ugGvjHwAZrnyvgc0XEk5jbn38MPd7Q1tW9i02buunvvwL4\nILCB7ds/HT8j8AkSDXyX9+cNSef2/yz4C3ACyfP1w5TrTa/ql68ccDyRUEQGp5AAYJ+19vmQxzxv\nrX2pgM8SEU88Sz8ajXqZ9jPwS9Crq8ss6uM4Dhs3ppcDnkd//5uB7cD13qsB+CDR6JdpbGzm1ltv\nSlpLILM4z6RJ0+jtvRS4FEitJlhoud6g5YBFZHAKCQCqjDHPAK8BDwFfstY+nWN/A2w3xuyP23tw\nhbV2UwGfK1KWsmfpfwe4GrerPbHdb26/f6O6mETSX3J9gAdobJw7MJugqqqKWbNm0dKyiI6OxGfF\nG/sXXnhhSOfra4aAyMgIGwBsBs4HdgCHA1cAG4wxJ1hrX/HZ/2/AJ4E/ABNw+xgfMMa801q73Wd/\nEUnjV1jHbaiXAH8EenDH4f8CXMqJJ56YURsgs1F1gMxu9nh9gFtvvSmlRkD66oLJjX08SBiM5OuN\nzxDo7FQ5YJHhFCoAsNZ2JL19xBizBfgr7oDij3z2d3D/TxO32RhzLLAc+Ei+z1u+fDkTJ05M2dbS\n0kJLS0uYyxYZkxzHoaury3c8PLGS3w3AeUAv0eg11NfP4ZJLPpPSW9DQMMf7KYIbOFjc4kAQtpt9\nqFfhy1bL4LbbvsNFFy3x7XEQkYS2tjba2tpStu3ZsyfQsca60+4K5gUB6621Xwm4/3XAadba03Ls\nUwN0d3d3U1NTM6jrExlr/Lv8n8Kdax/3NG6GfUJTUzN79+6lq6ubvr5biPcWGLMEa/+JWw1wFXBf\n0lHJgUX8vVuKdySetOfOnU9n5+aU641Gl9LYOCtUIqGIJGzbto2ZM2cCzLTWbsu236AqARpjDsJd\nWuzHIQ6bgTs0ICI+zj77fWza9DBuY3wk8C6yjYevW7eOffv2UVlZibWW6dOnk95b4Ab5i4HTgQtx\nhwxWAN8mGi1eN3vQbH81/CLDI1QAYIy5Hvhv3G7/I4Argb1Am/f7q4EjrLUf8d4vA57AHZzcHzcH\n4HRgTsbJRYog35K1I/kZsViMs88+x6eWfjPuHPzMhnrOnMR/SmvWrPF+yjanfyfuNL8q3NkDN/CO\ndxzLtm3F6WZXtr9IcYXtATgSuBuYAjwPbARmWWt7vd8fTmo/5X7At4A3Aa8CDwNnWGvT64SKjKgg\ndfRH+jMWLFjMpk3x3rrkRrEVOJfkbH+/hjpf9rzbWZe67Z57/osHH3yQ+++/nzPOOIPzzz8/8P0N\nlrL9RYosV5nAYr1QKWAZZtnWok8vVztSn5EoyXt9ztK8K1euTCnzm/0zE2V4jZlkYUJGad66unfZ\nKVOmpZTbnTJlmn388ceH7O8gH7/rHervQaTcBC0FXPTG3veiFADIMApTR3+kPqO9vd3b/ykLzRYy\na/cHaRT96us3NMyxDQ1zMurqV1QcamFiSoACE+2UKdPy3lt7e/uQ/D3lWg9ARAoTNADQcsBSdvKN\nPT/wwAMFZ57Hx/ufeeaZnJ+RPr6d2h3eCiwiucv/tNPqA43N55qvn7zt8ccfZ+7cufhNL+ztXcz6\n9etT8gtgeIZNcl2viAyzXNFBsV6oB0CGUfan89ssRHI+jWZ7+u3t7bW1tfUpx7rnuiNwV35md/j1\nNhI5yNbW1g/538GVV16Z1OOQfH1PWcBeeeWVGceMxLCJiAyehgBEcvAbe4YJ3nh5ZgOXa3na3t5e\nbyw9szs9dez9Nu+9f4CxZcsWW1NzctbfZws+CumSX7t2bc4hinXr1mV8RmL/HRbarbsM8NANm4jI\n0FAAIJKD39hzrgZx5syTsz791tbOznlsao/AxIxzNDTMybiWmpqT7NatW621NmvwsWvXrkGNnyeC\nluQgyD8HIJGj0JB2T+779vb2jGOGMldARIJTACASgOM4tr293a5cuTJnl7j7mmEhlqOBz3bsSgsr\ncgYJkUhmYBDvWs/W9e4m8U1Iu4YJtqFhTqB7f/zxxwPPAnB7ACIWKmxqL0eFhUhKI58tYNmyZYsC\nApERoABAJIR8Wftwg3Uz85uzBAe5jnWs22WeK0i41PfYjo6OLOe+LnCDnHyPfg3wunXr7JVXXpnR\n7R/m76e2tn6g5yEzYLk9I1BRpr/I8AkaAESypweKlId45n5dXT3R6FLczPinvT+X4Vbi+xxwM+4K\nej3ekV1JZ5mBW10v+dgluItg/h54g7dfeg2s+Dnenba9HoDNmzd779NnE1jcBX1uxc3eP8r78xag\nn66uxLXFYjHmzp3P9OnTaW5uprq6mrlz57N7924A5syZw9e+9rWMrP9k+WZObNrUTUvLooHyvm5t\n//h1/ca7/1biyw93dm6mpWVR1s8LynEc1qxZQ09PT/6dRSRVruigWC/UAyAjwK+rOr1L3H3ij3f7\nx5/W77TJBWuampptJDLJukMEiWMnTz4sbf59xMIkmzrmXuFtvyFkD8DHcvYorFy5cuA+hyJ7P38P\nyfUDn5t6XcNTcyFXUqZIudMQgEge2RrGmTPjmfj+jXJyg7Nlyxa7atWqjCmAyV3iW7ZsscceW50U\nBGQm0UUiB9ls1fD8Ziy4OQP5G9ahLHrkBjoVaQHMZAv1XlCEXbEiPdch99CHX/LgYL47TUkUUQAg\nklOQMW2/ErV1dfW2vb3dbtmyJeMJtK6u3q5atSrH/P54Y3WDhYO8hjPxedmeZrNVy5s9+3Rv2mJq\n2d/kJMDUCoOZDfCqVasC/53FYjGfWgfTMv4OGhrmJP3dPTDkPQAjUclRZCxTACCSQ5CGMVcXc9An\n0HyNVSQyceAYx3HsihUrstb7j89YiP8uSBndIIFOWLW19V6PxXFeD0C+aY2RjEBlME/r+b67QnsV\nREqFAgCRHII+RaY3umGOtTZ/Y1VTc9JAMaFCx7T9rjH1WuP1B9K77mcU9MTs9gTkrn3gOI7t6Oiw\nV155pf35z38+pOP16gEQyU0BgIiP5Klw/tUAJ1qI5GygwjyBBm2shmtMOzEmb1IaYDe58eGCn5iD\nBDbpDf7WrVuHrA6AVhEUyU4BgEgSvydsv1Xy3KS8O3Iu25uZ6Jb7CbShYU7OsfrheKL1u1843sIq\n69YlGNz5gwxtDGeCnlYRFMlOAYBIkmxP2Imu7EuTGsbMxjGzQQ0+ru0GGdkr9g3HmLbf/bq9GzNS\ngpDBNMrZnsLdIYeR6Z7PNfwhUq4UAIh48s9hz9/4Zjaod2Q06n5PoKmfHa8ImLqIzlD3AAS7X7cH\nZDBPzH5P4W9969uHPJgRkXBUCVDEk7uKnfF+9q/QV1lZmaW63YXA9wFYuXIljuOwdu1qKioqcnx2\nFTDP+7MegJ07d1JdXU1TU3NGFcJodBlNTc1UVVUN4f3C0qVLcRyHe+9dl3G9YVRUVHD33XdRW1s/\nsO0vf3nY+yn736eIjA4KAKTkHXvssd5Pq4A1JEr53oMbJPuX8a2rq6eqqipvg3rEEUdkbaQTn527\nQWxra6WxcRawGDgaWExj4yza2lrD3Gqgz1yyZEnooCKbBQsW89BDfya5zC9MwJglDEUwIyLDZ1yx\nL0BkuE2dOpUpU6bR23tp0tYZGNODO+L0Y+Ay3MY3LsKSJRcD6Q3qwqR9/J9q42sLVFZWDjzdd3Yu\npa/P4gYNXUSjy2hsTDSIFRUVrF27mnXr1rF582ZOOeWUnLX5cwn6mYMV7xlxG/r438tC4GWsvZjk\nv8/GxuaCghkRGUa5xgeK9UI5ADKEsiXEjRu3f9pYeXyM/vqMsfcg0856e3t9K/o9/vjjeTPWg9QB\nyLaan5+RyJLPl7y4cuVKJeiJFIGSAEVskIS4Y627IE9qLYC6uvqU8+RrUHt7e72FhLJPf8uVsZ6r\nDsBwFQkaLBXkERmdFACI2PxPqeC3QE8ka438bA1qkMp42WQ2pDtSeiIS6xKMvoVvVJBHZPTRLAAR\n8ifEwQ3Ak96fBwHHAf2ceOKJvuerqqpi3rx5KePojuOwcWP8/P6Jgjt37kzZP3kN+0SS4duB+cB0\noBm4FIiwcWMXfX1fAiYDrwEL6eu7mY6O9oFzDKX068tlKJMXRWRkKQCQkpZtih0swc3+/xzutL7P\nAbcBj1FbWx8qUS7RgEOubP9YLMbcufOZPn06zc3NVFdXM3fufKZOnertuxDYRGpG/cG4/5leihsU\nVOMGCe9wz97VxVDJdn27d+/Oekw8edFxHNrb27NOhxSRUShX90CxXmgIQIaQ3/i92+3/sO+wQJgl\ncq1N7sKfYd1FdvzzCXKN8+cbQnCXEI4nMCYW8sEbIhiK5L7hWo9AREaWcgBE0sTH7zs6OnI2toU0\nqE1NzTYSmZTSMAN2ypRpNhaL5U2Y++xnP5snV+EECzFv220ZeQvxzymUEvpESodyAETSxMfvzzzz\nzCzDAsuAGTz00J9paVkU6txtba3MmXMqsH1gW21tPT09j1FRUZG3mNBPf/pz7322XIWngPg1/RR3\naCAxVNDb+xpnn31OqGtOlu/6knMYhkOYvAMRGSK5ooNivVAPgAwzd037+rRhgWbvKbvwp95sswTy\nT0eMeK+JaUMIk73riu+Xu/ei0Cf1YvUADGaKo4j4Uw+ASA4VFRV8+ctf9N7dCTjAauB5oB8o7KnX\nb5YAZE9GjEaXccghFbhP9LcBM0nOqIdZ3v713pnu8P4c2if1oV6PIKgFCxbT2bmZ5N6Mzs7NoXtg\nRCQ8BQBSFvy6mBNTBKPAFBJT8D4CwDXXXDuQAT8UXdR+U+ZOOeUEXnppN/Bd3AWG7sUNRj7vHXUT\nUEFiKOAX3p/+QwXPPPNMwdc40lP6/BdZGt4pjiKSJFf3QLFeaAhAhkiuLuYdO3bYmpqTbCQyMSmD\nPzUD/vTTG0N1UQcp15s8TJC/UNGdNl5cp6bmZLt169akioPxoYLbbJCliYMazuqByfLdu5YOFimM\nZgGI2OxT29xGlLSX3/h3fFw+cbwxk2xDw5yUz/ELNOrq8s8myJ8bkNmgx2IxW1eXnL8QscZMyrjH\n0T59TzMPRIaHAgApe/kb1/jc+kuzPIk+ELiByrbgUJDpednK6dbV1Wc8iSf3MDiOY1esWJHzGjs6\nOkb1gjwqJSwy9BQASNnL373e7r3PFih8PufxK1eutNbmDzRqa+tzXmeQlfuyDWWsWrUqzz2O7uz6\nkVi1UKTcBA0AxhWWOSAy+qWuA7Aw6TfxhLprcbPsq4EG4NO4/83Ue/usyHn83//+d9asWcMzzzzj\nbffPzN+4sYuenp6smfTxcro9PT3s3LmTyspKrLVs3ryZyspKqqqq0rLlZwMb6OxcyiuvvJznHm8A\nPjiwf0vLItauXZ3y+Y7jsGvXroHPGkl+9z7S1yBStnJFB8V6oR4AGSJ+XcyJUrrxOfbWwu02c1XA\nem9b5nLBEM14ws41jp8voS3etb9ly5aMJ+JEvQL/89fV1fvcYzyxMfvQhebgi5QmDQGI2GAFf+D6\ngcRAd0bA5y10eb/fz3slHx+16YmBbha+XxGfGSmNbrrMRjgzoS8SqfACEf9u/lWrVoVa6yAejKj2\nv0hpUgAg4knkAtxpwcloEONPvo8//nhGQ9rQMMdOnnyYhYOsmyzYmuVp3K8HYYaNRCblbFBTG+Hc\nSYdu0mL2J/rUpMDcyYsjkYEfZEqkiAw9BQAinnyN3bp161L2T54Hn3ls7sTC448/ISUIyFczIMy5\nI5GDbL5s+USw02D9ViasqTk5bb+hn4OvoQWR4lIpYBFPvjK3c+bMSdk/uZxv5iI5yYmFydyku8mT\npwS+ru3b4wsHBTv3qaemlgn2q9KXSHw8DzfBMbms8D+4447vpe3n/1mVlZWB7yOdyvuKjBG5ooNi\nvVAPgAyxMNPNkruuM5/Sd1g42aYnBkYiFfaQQyq8HIL8Y+q9vb120qQpPj0TzRnnTj5HkCp9qYmP\nXRY+byORiRnXMRxz8FXcR6T4NAQg4iO9AU1u7LN1XTc0zLGRyCQbT+hjIMkuPenOeD/HkwyzN3y1\ntbO9feOzEeKN8O12sGV9gwY7wzEHX+V9RYpPdQBEfFRVVVFVVUUsFmPu3Pl0dLQP/G7KlGns3v06\n6XPtTznlbUSjr9Pf/0TS784CdgIXAe/GHVZYitvdvhlYhLu6YD3grtIXn9/uOA4bN8a73n8MXIbb\nRR8X4aabbqK6utp3Xny+efvZ5tY7jpNSW2A45uDnq70wmKEFERliuaKDYr1QD4AMs2yle/3nzsef\n7JOHAXJl61/v/en49gAknpKTz+FYNwnw+qxd5YUm1410Up7K+4oUl4YARLLIv0ZA8lTBB5Iazni3\ndpAV/LDwed+GL/H56d3/bqZ+XV2973UXOm9/pOf7q7yvSHEpABDJIvgaAdYm1gMopAcge8PX1NTs\nk1dA1sWDCk2uK2ZS3kgtKywiqTQNUCSLfFPg4AHcsfkbiERWettm4I7xtwIHeO8/TfK0Qljmbf8G\n5PlPq62tlTlzTgW2D2yrra2np+cxKioqMvbPnI4YVw+4OQZ+Cj1uKCRPpxSR0UdJgFJ24nUBOjuX\n0tdniS/+E4lcQjR6AHv3Xjewb0XFNI4//kR+97vt9PcfQ3Ky3vjxB7B3b2ryHsRwg4AfAw9nXYAn\nbAJeocl1SsoTkWzUAyBlqa2tlcbG1EI5FRUT6O8/gOQCNi++uJfx48f7Pq0/++wzOI5De3s7P/zh\nD4F+3NX3/gi8DVhIX9/NdHS009PT43sdQZ+S8xUzynZ8oceJSOlTD4CUpfQn8Gg0SlNTE24jGX9S\nXkhfn+W++xbjOA5wU8bTekVFBVVVVaxZs8Y75oNpn5Toah9sY9vW1kpLyyI6OhK9Do2NzRnVAIfq\nOBEpbaECAGPM14Gvp23+H2vt8TmOeRfwLeCtuI9V37TW3hnyOkWGRbwuQKIBzz5WnvykHp+LH41G\n6evrIxqNevsPX1d7ofP2h2O+v4iMfYX0ADwCnAEY7/2+bDsaY44Bfgt8D1gANALfN8b8P2vt+gI+\nW2RYBB0rj8ViLFiw2CsgFMHt9ndNnnwYsdjFuMm3bl6BMZdw+ulzhrTBjQctI3WciJSmQgKAfdba\n5wPuexHwuLX2C977HcaYWmA5oABARo1siYHR6DIaGxNj5YmFbmbgdmjdQrxqYCy2BHiV5ERBayeM\n8J2IiARTSBJglTHmGWPMLmNMqzHmqBz7zgI607Z1AKcU8Lkiw8ovMTB5xT3HcejoaKev70u4CYG3\n4PYWHOX9eStuh9g6oB1wgO9z333rsyYBjgTHcVizZk1Rr0FERp+wPQCbgfOBHcDhwBXABmPMCdba\nV3z2fyPwbNq2Z4FDjDETrLWvh/x8kWGTb6w8Maf+MO9P/3wBNwiY5/28PzA0SYBhpQ5XuJqa3OQ/\nv1oDIlJeQgUA1tqOpLePGGO2AH/FTX3+0VBeGMDy5cuZOHFiyraWlhZaWlqG+qNEBmQbK0/kCTzn\n/emfLwDX4nZ+VVDM+faJ4YrUxY386hKIyNjU1tZGW1tbyrY9e/YEOtZYt/RuwbwgYL219is+v+sC\nuq21n03adj5wo7U26yOIMaYG6O7u7qampmZQ1ycylObOnU9n52b6+o7GzQG4mXi+gFsJ8GjcmPhE\n4KNeDsGsEW9wHcdh+vTppE5rxHvvTmtUQqBIadq2bRszZ84EmGmt3ZZtv0EVAjLGHARUAn/LsstD\nuDMGkp3pbRcZcxJ5AtuBF0nOF3Cf+u/DzQ24j/QcgpFUzBLAIjI2hAoAjDHXG2NmG2P+xRhzKvBL\nYGi2EKoAAAksSURBVC/Q5v3+amNM8hz/24G3GGOuNcZMN8ZcDJwLfHuIrl9kRMXzBBzH4cor4yUx\n7sRN+FuN2+3vNrIrV65k7drVRRlvz7fegUoAi0jYHoAjgbuB/wHuAZ4HZllre73fH46bEg2AtfZJ\nYD7u/P/tuNP/Pm6tTZ8ZIDKmVFVV8aEPfch7FwWSu9PdRra+vj79sBGjEsAikk/YJMCc2XfW2o/6\nbNsAzAx5XSKjXtDaAcWiEsAikovWAhAZhNHcyKoEsIjkogBAZBDGQiOrEsAi4kcBgMgQUCMrImON\nAgCRAsRXAwzyxB9mXxGRkTKoOgAi5SYWizF37nymT59Oc3Mz1dXVzJ07n927dw9qXxGRkaYAQCSE\n1PK6TwGtdHZupqVl0aD2FREZaRoCEAkovhpganndhfT1WTo6FtPT0zPQxR9mXxGRYlAPgEhAYcrr\nqhSviIx2CgBEAgpTXleleEVktFMAIBJQmPK6KsUrIqOdAgCREBKrASZWAcy24l+YfUVERpqSAEVC\nCFP5byxUCRSR8qUAQKQAYSr/qUqgiIxGGgIQEREpQwoAREREypACABERkTKkAEBERKQMKQAQEREp\nQwoAREREypACABERkTKkAEBERKQMKQAQEREpQwoAREREypACABERkTKkAEBERKQMKQAQEREpQwoA\nREREypACABERkTKkAEBERKQMKQAQEREpQwoAREREypACABERkTKkAEBERKQMKQAQEREpQwoARERE\nypACABERkTKkAEBERKQMKQAQEREpQwoAREREypACABERkTKkAEBERKQMKQAQEREpQwoAREREypAC\nABERkTKkAEBERKQMKQAQEREpQwoAREREypACABERkTKkAEBERKQMKQAQEREpQ2M6AGhrayv2JRSF\n7ru86L7Li+67vBTzvgcVABhjLjPG9Btjvp1jn3pvn+RXnzHmsMF8NugfTLnRfZcX3Xd50X2PvHGF\nHmiMORm4EPhTgN0tUA38Y2CDtc8V+tkiIiIyOAX1ABhjDgJagQuAFwMe9ry19rn4q5DPFRERkaFR\n6BDAd4H/ttbeF3B/A2w3xvw/Y8w6Y8ypBX6uiIiIDIHQQwDGmA8BM4CTAh7yN+CTwB+ACcAngAeM\nMe+01m7Pcsz+AI899ljOE+/Zs4dt27YFvIzSofsuL7rv8qL7Li/Dcd9Jbef+ufYz1trAJzXGHInb\nkDdaax/xtt0P/NFa+9kQ53kA+Ku19iNZfr8A+K/AFyYiIiLpFlpr7872y7ABwNnAL4A+3G59gChu\nkl8fMMEGOKEx5jrgNGvtaVl+PwVoAp4EXgt8gSIiIrI/cAzQYa3tzbZT2ADgQOBf0jb/J/AY8B/W\n2tx99onzrANestaeG/jDRUREZMiEygGw1r4CPJq8zRjzCtAbb/yNMVcDR8S7940xy4AngL/gRiWf\nAE4H5gz66kVERKQgBdcBSJLehXA4cFTS+/2AbwFvAl4FHgbOsNZuGILPFhERkQKEGgIQERGR0jCm\n1wIQERGRwigAEBERKUOjMgAwxtQZY35jjHnGWzzorDz7D9uCQyPJGPMlY8wWY8xLxphnjTG/NMZU\nBzjuXcaYbmPMa8YYxxjjW19htCrkvkvhOzfGfMoY8ydjzB7vtckYMzfPMWP6u4bw910K37WfIIup\nefuN+e88WbEXkRspxpiv+9zDo3mOGdHvelQGAMCBwHbgYjKTDLOxQBXwRu91+Bhcc6AOuBX4N6AR\nGA+sM8YckO0AY8wxwG+Be4F3ADcD3zfGjKVZFqHv2zPWv/OngS8CNcBM4D7g18aY4/x2LpHvGkLe\nt2esf9cpgi6mVkLfOVDQInJj/Tt/BJhG4h5qs+1YlO/aWjuqX0A/cFaefepxCxEdUuzrHeJ7n+rd\nf22Ofa4FHk7b1ga0F/v6h/m+S/U77wU+Wi7fdcD7LqnvGjgI2AE0APcD386xb8l85yHve8x/58DX\ngW0h9h/x73q09gAUohQXHJqEGwXHcuwzC+hM29YBnDJcFzUCgtw3lNB3boyJeOtsvAF4KMtuJfdd\nB7xvKKHvmnCLqZXSd16Oi8hVeUPZu4wxrcaYo3LsO+Lf9VDUARgNCllwaFQzxhjgJmCjtTbXuNEb\ngWfTtj0LHGKMmWCtfX24rnE4hLjvkvjOjTEn4DZ8+wP/AM6x1v5Plt1L5rsOed8l8V1DQYuplcR3\nXsB9l8J3vhk4H7fX43DgCmCDMeYE6xbVSzfi33VJBADWWgdwkjZtNsYcCywHxmrCzPeA4wHf9RJK\nWKD7LqHv/H9wx/smAucCPzbGzM7RGJaKwPddKt+1cRdTuwl3MbW9xb6ekVLIfZfCd26t7Uh6+4gx\nZgvwV+CDwI+Kc1WpSmkIIN0WoLLYF1EIY8x3gGbgXdbav+XZ/e+4SSbJpuGutTAmng7iQt63nzH3\nnVtr91lrH7fW/tFa+xXc5KhlWXYvme865H37GXPfNW7C46HANmPMXmPMXtyx7mXGmP/zer/SlcJ3\nXsh9+xmL3/kAa+0e3KAm2z2M+HddEj0AWczA7UYaU7xG8Gyg3lr7VIBDHgLmpW07k9zjqaNOAfft\nZ0x+52kiuF2efkriu84i1337GYvfdSfwtrRt/0liMTW/GU+l8J0Xct9+xuJ3PsAYcxBu4//jLLuM\n/Hdd7EzJLNmQB+J2D87AzQb/jPf+KO/31wB3Ju2/DDgLOBZ4K253017cJ8mi30+I+/4esBt3Wty0\npNf+SftcnXbvx+COoV4LTMedOvl/uN1tRb+nYbzvMf+de/dUh7vC5gnev+t9QIP3+/R/52P+uy7w\nvsf8d53j7yIlG74U//su8L7H/HcOXA/M9v6dnwqsxx3TnzJavuvR2gNwEu4/EOu9vuVtvxP4GG6y\nRCkuOPQp3Pt9IG37R0lEjSmLLVlrnzTGzAduBJYC/wt83Fqbnk06moW+b0rjOz8M99/04cAe3Hs4\n0yaypFP+nZfIdw0h75vS+K6zybmYWgl95+nKYRG5I4G7gSnA88BGYJa1ttf7fdG/ay0GJCIiUoZK\nOQlQREREslAAICIiUoYUAIiIiJQhBQAiIiJlSAGAiIhIGVIAICIiUoYUAIiIiJQhBQAiIiJlSAGA\niIhIGVIAICIiUoYUAIiIiJSh/w/QYCoOia2sSAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14102064588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv('data/grains.csv', header=None)\n",
    "grains = df.values\n",
    "\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "model = PCA()\n",
    "\n",
    "model.fit(grains)\n",
    "\n",
    "pca_features = model.transform(grains)\n",
    "\n",
    "print('shape after transormation', pca_features.shape) #same shape\n",
    "\n",
    "xs = grains[:,0]\n",
    "ys = grains[:,1]\n",
    "\n",
    "plt.scatter(xs, ys)\n",
    "\n",
    "correlation, pvalue = pearsonr(xs, ys)\n",
    "# now correlation has to be 0\n",
    "print(\"corr =\", round(correlation, 5))\n",
    "\n",
    "mean = model.mean_\n",
    "first_pc = model.components_[0,:]\n",
    "\n",
    "print(mean, first_pc)\n",
    "\n",
    "#plots the direction in which data varies the most!\n",
    "# Plot first_pc as an arrow, starting at mean\n",
    "plt.arrow(mean[0], mean[1], first_pc[0], first_pc[1], color='red', width=0.01)\n",
    "\n",
    "# Keep axes on same scale\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intrinsic dimension\n",
    "- Intrinsic dimension = number of features needed to approximate the dataset\n",
    "- What is the most compact representation of the samples\n",
    "-  That the intrinsic dimension is the **number of PCA features with significant variance** !!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qTQaa0RQj1rQiU9tD1QoKGUebHZyPJdYq90gu5QISiQT1yGwnqEUcs0I3NTXB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14100b72ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = iris.data\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "\n",
    "#we can see that they all lie very close to a flat, 2d sheet\n",
    "ax.scatter(samples[:, 0], samples[:, 1], samples[:, 2])\n",
    "ax.set_xlabel(iris.feature_names[0])\n",
    "ax.set_ylabel(iris.feature_names[1])\n",
    "ax.set_zlabel(iris.feature_names[2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the variances of PCA features\n",
    "which helps us answer the following question what is its intrinsic dimension?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D7k2yflZxrKp8mvACk+Q04KvASuBxNE+GPpDmKdJaBDb5S0oBkrwJOIWHH1b2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\nK/4/GnUbETCRyMAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x141021ca3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.fit(samples)\n",
    "features = range(model.n_components_)\n",
    "plt.bar(features, model.explained_variance_)\n",
    "plt.xticks(features)\n",
    "plt.xlabel('PCA feature')\n",
    "plt.ylabel('variance')\n",
    "plt.show()\n",
    "\n",
    "#I looks like PCA features 0 and 1 have have significant variances!\n",
    "#Recall that the intrinsic dimension is the number of PCA features with significant variance\n",
    "#So we choose 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimension reduction with PCA\n",
    "- Represents same data using less features\n",
    "- Important part of machine learning piplines\n",
    "- PCA discards low variance PCA features\n",
    "- Assumes that the high variance features are informative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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DMAxi4+LImKTdDLgpJbUh7Mzugyi11j8DPz9iW48kz4cDw+0d04vk6NGjxMXF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1410215c5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "pca.fit(samples)\n",
    "transformed = pca.transform(samples)\n",
    "\n",
    "print(transformed.shape) #we only kept two features!!\n",
    "\n",
    "xs = transformed[:,0]\n",
    "ys = transformed[:,1]\n",
    "\n",
    "plt.scatter(xs, ys, c=iris.target)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['cats', 'chase', 'dogs', 'meow', 'say', 'woof']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import TruncatedSVD \n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "\n",
    "documents = ['cats say meow', 'dogs say woof', 'dogs chase cats']\n",
    "\n",
    "# Create a TfidfVectorizer: tfidf\n",
    "tfidf = TfidfVectorizer() \n",
    "\n",
    "# Apply fit_transform to document: csr_mat\n",
    "csr_mat = tfidf.fit_transform(documents)\n",
    "\n",
    "# Get the words: words\n",
    "words = tfidf.get_feature_names()\n",
    "\n",
    "# Print words\n",
    "print(words)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering Wikipeadia artciles\n",
    "Data set available here https://blog.lateral.io/2015/06/the-unknown-perils-of-mining-wikipedia/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>title</th>\n",
       "      <th>article_text</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HTTP 404</td>\n",
       "      <td>HTTP 404  The 404 or Not Found error message ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alexa Internet</td>\n",
       "      <td>Alexa Internet  Alexa Internet, Inc. is a Cal...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Internet Explorer</td>\n",
       "      <td>Internet Explorer 10  Internet Explorer 10 (I...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HTTP cookie</td>\n",
       "      <td>HTTP cookie  A cookie, also known as an HTTP ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Google Search</td>\n",
       "      <td>Google Search Appliance  The Google Search Ap...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               title                                       article_text\n",
       "0           HTTP 404   HTTP 404  The 404 or Not Found error message ...\n",
       "1     Alexa Internet   Alexa Internet  Alexa Internet, Inc. is a Cal...\n",
       "2  Internet Explorer   Internet Explorer 10  Internet Explorer 10 (I...\n",
       "3        HTTP cookie   HTTP cookie  A cookie, also known as an HTTP ...\n",
       "4      Google Search   Google Search Appliance  The Google Search Ap..."
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Clustering wiki articles\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"data/wikipedia_articles_to_cluster.csv\",  encoding = \"ISO-8859-1\")\n",
    "titles = df.title\n",
    "\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import TruncatedSVD \n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "\n",
    "# Create a TfidfVectorizer: tfidf\n",
    "tfidf = TfidfVectorizer() \n",
    "\n",
    "# Apply fit_transform to document: csr_mat\n",
    "articles = tfidf.fit_transform(df.article_text.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                          article  labels\n",
      "29                               Jennifer Aniston       0\n",
      "31                              Cristiano Ronaldo       1\n",
      "32                                   Arsenal F.C.       1\n",
      "33                                 Radamel Falcao       1\n",
      "34                             Zlatan Ibrahimovi?       1\n",
      "35                Colombia national football team       1\n",
      "36              2014 FIFA World Cup qualification       1\n",
      "37                                       Football       1\n",
      "38                                         Neymar       1\n",
      "39                                  Franck Ribéry       1\n",
      "51                                     Nate Ruess       1\n",
      "52                                     The Wanted       1\n",
      "54                                 Arctic Monkeys       1\n",
      "55                                  Black Sabbath       1\n",
      "56                                       Skrillex       1\n",
      "57                          Red Hot Chili Peppers       1\n",
      "30                  France national football team       1\n",
      "25                                  Russell Crowe       1\n",
      "59                                    Adam Levine       1\n",
      "8                                         Firefox       1\n",
      "7                                   Social search       2\n",
      "1                                  Alexa Internet       2\n",
      "4                                   Google Search       2\n",
      "18  2010 United Nations Climate Change Conference       3\n",
      "40                                    Tonsillitis       3\n",
      "42                                    Doxycycline       3\n",
      "43                                       Leukemia       3\n",
      "44                                           Gout       3\n",
      "47                                          Fever       3\n",
      "49                                       Lymphoma       3\n",
      "6                     Hypertext Transfer Protocol       3\n",
      "5                                          Tumblr       3\n",
      "3                                     HTTP cookie       3\n",
      "2                               Internet Explorer       3\n",
      "46                                     Prednisone       3\n",
      "9                                        LinkedIn       3\n",
      "19  2007 United Nations Climate Change Conference       3\n",
      "11       Nationally Appropriate Mitigation Action       3\n",
      "17  Greenhouse gas emissions by the United States       3\n",
      "10                                 Global warming       3\n",
      "58                                         Sepsis       3\n",
      "16                                        350.org       3\n",
      "0                                        HTTP 404       3\n",
      "12                                   Nigel Lawson       3\n",
      "14                                 Climate change       3\n",
      "15                                 Kyoto Protocol       3\n",
      "20                                 Angelina Jolie       4\n",
      "28                                  Anne Hathaway       4\n",
      "27                                 Dakota Fanning       4\n",
      "13                               Connie Hedegaard       4\n",
      "26                                     Mila Kunis       4\n",
      "50                                   Chad Kroeger       4\n",
      "24                                   Jessica Biel       4\n",
      "53                                   Stevie Nicks       4\n",
      "23                           Catherine Zeta-Jones       4\n",
      "22                              Denzel Washington       4\n",
      "21                             Michael Fassbender       4\n",
      "41                                    Hepatitis B       5\n",
      "45                                    Hepatitis C       5\n",
      "48                                     Gabapentin       5\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import TruncatedSVD\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "svd = TruncatedSVD(n_components=50)\n",
    "kmeans = KMeans(n_clusters=6)\n",
    "\n",
    "pipeline = make_pipeline(svd, kmeans)\n",
    "\n",
    "pipeline.fit(articles)\n",
    "\n",
    "labels = pipeline.predict(articles)\n",
    "\n",
    "df = pd.DataFrame({'labels': labels, 'article': df.title})\n",
    "\n",
    "print(df.sort_values('labels'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-negative matrix factorization (NMF)\n",
    "- In contract to PCA, NMF models are interpretable\n",
    "- Needs all features to be non negative > 0\n",
    "- NMF expresses documents as combinations of topics (or \"themes\")\n",
    "- NMF expresses images as combinations of patterns\n",
    "- NMF has components learned from samples just like PCA\n",
    "- NMF feature values are non-negative as well\n",
    "- A sample can be reconstructed by multiplying components\n",
    "by feature values and add up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5.7528193   2.31736196  5.26603216  1.88949154]\n",
      " [ 3.38130621  2.44971744  0.63732832  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import NMF\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "samples = iris.data\n",
    "\n",
    "model = NMF(n_components=2)\n",
    "\n",
    "model.fit(samples)\n",
    "\n",
    "nmf_features = model.transform(samples)\n",
    "\n",
    "print(model.components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A sample can be reconstructed by multiplying components by feature values and add up.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.1  3.5  1.4  0.2]\n",
      "[ 5.09980563  3.49980804  1.40176904  0.19905119]\n"
     ]
    }
   ],
   "source": [
    "#samples ~= nmf_features.dot(model.components_)\n",
    "\n",
    "print(samples[0, :])\n",
    "print(nmf_features[0, :].dot(model.components_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1    0.462717\n",
      "3    0.023875\n",
      "4    0.022335\n",
      "5    0.021077\n",
      "0    0.009742\n",
      "Name: Anne Hathaway, dtype: float64\n",
      "1    0.200764\n",
      "0    0.167243\n",
      "4    0.153309\n",
      "3    0.054544\n",
      "2    0.007183\n",
      "Name: Denzel Washington, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#Applying NMF to wikipedia articles\n",
    "model = NMF(n_components=6)\n",
    "model.fit(articles)\n",
    "nmf_features = model.transform(articles)\n",
    "\n",
    "df = pd.DataFrame(nmf_features, index=titles)\n",
    "#We Notice that for both actors, the NMF feature 1 has by far the highest value. \n",
    "#This means that both articles are reconstructed using mainly the 2d NMF component.\n",
    "# NMF components represent topics (for instance, acting!)\n",
    "\n",
    "print(df.loc['Anne Hathaway'].nlargest())\n",
    "print(df.loc['Denzel Washington'].nlargest())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NMF learns interpretable parts / Topic-modeling\n",
    "Working with a grayscale images = no colors ony shades of gray measuring pixel brightness beteen 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def show_as_image(vector):\n",
    "    \"\"\"\n",
    "    Given a 1d vector representing an image, display that image in \n",
    "    black and white.  If there are negative values, then use red for \n",
    "    that pixel.\n",
    "    \"\"\"\n",
    "    bitmap = vector.reshape((13, 8))  # make a square array\n",
    "    bitmap /= np.abs(vector).max()  # normalise\n",
    "    bitmap = bitmap[:,:,np.newaxis]\n",
    "    rgb_layers = [np.abs(bitmap)] + [bitmap.clip(0)] * 2\n",
    "    rgb_bitmap = np.concatenate(rgb_layers, axis=-1)\n",
    "    plt.imshow(rgb_bitmap, interpolation='nearest')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAABGVJREFUeJzt3bFt3EAQQNFZQ4FyNaBuVITrs3tQN9eAcmd0oFhnAvo0\ndbr30l0QAxw+lmCwt7ZtG+Bzfpw9AHwHQoKAkCAgJAgICQJCgoCQICAkCDzs2bTWepqZl5m5zMyf\nIweCL+ZxZp5n5nXbtrePNu0Kad4j+hUMBbfq58z8/mhx76vdJRkFbtfl2uLekLzOce+uNuBjAwSE\nBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQ2Hsd183z\nh2rnWmudPcKhnEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQ\nEgSEBAEhQUBIEBASBIQEgbu51+6736v21R19r+DZv68TCQJCgoCQICAkCAgJAkKCgJAgICQICAkC\nQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKC\ngJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQ\nICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAg\nJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQI\nCAkCQoKAkCDwcPYA3Ie11tkjHMqJBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEh\nQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBBwrx3/xbZthz7/7HvznEgQEBIEhAQBIUFASBAQEgSE\nBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQB\nIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFB\nQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBI\nEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQ\nEgSEBAEhQUBIEBASBB7OHoD7sNY6e4RDOZEgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKC\ngJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQ\nICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCOwN6fHQKeDru9rA3pCePz8H3LTn\na4tr27Z/PmGt9TQzLzNzmZk/xVRwIx7nPaLXbdvePtq0KyTgOh8bICAkCAgJAkKCgJAgICQICAkC\nfwHZkCiNPrhPngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c316ec88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "digit_7 = np.array([0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
    "                    0.,  0.,  1.,  1.,  1.,  1.,  0.,  0.,\n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0., \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,\n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,\n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0., \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0., \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  1.,  0., \n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
    "                    0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])\n",
    "show_as_image(digit_7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMj8bICAkCAgJAkKCgJAgICQICAkC/wAifiKBJninagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2eff940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4DIfGyAgJAgICQJCgoCQICAkCAgJAh9LOCKBIaXcKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c319b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzvOzAQJCgoCQICAkCAgJAkKCgJAg8AcjZyKBao4EhQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2ed3978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMj8bICAkCAgJAkKCgJAgICQICAkC/wB9bSKBtUIVTQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c327e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+dgAASFBQEgQEBIEhAQBIUFASBB4BwC2IoEH86nTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2eea9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAABEFJREFUeJzt2LFNHFEYRtH/WQTkNEA3FOH67B7oZhsgJ3sOECHrkbmr\nZc056Rs9fcnVjGbtvQf4nB/XHgD/AyFBQEgQEBIEhAQBIUFASBAQEgTujjy01nqYmaeZOc3M6yUH\nwRdzPzOPM/O893756KFDIc1bRL+CUXCrfs7M748Oj37anZIpcLtO5w6PhuRzju/ubAN+NkBASBAQ\nEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIE\nhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQE\ngbtrD3i3977o/Wuti97P9+aNBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBI\nEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQ\nEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIE\nhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQE\nASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBC4u/aAd2ut\na0+Af+aNBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQ\nEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBAS\nBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSE\nBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQB\nIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFB\nQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBI\nEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQ\nEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIE\nhASBoyHdX3QFfH1nGzga0uPnd8BNezx3uPbef71hrfUwM08zc5qZ12IV3Ij7eYvoee/98tFDh0IC\nzvOzAQJCgoCQICAkCAgJAkKCgJAg8AfIaSKBrSVlqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c3046160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAABEFJREFUeJzt3LFt21AYRtGfgQv1XkDbeIjMl+zgbbSAe3fPhWspBHwV\nWdY57SOIr7kgwYLbWmuAr/l16wHwEwgJAkKCgJAgICQICAkCQoKAkCDwtOeibdueZ+ZlZk4z837N\nQfDNHGbmODOva623cxftCmk+I/oTjIJ79Xtm/p473Ptqd0qmwP06XTrcG5LXOR7dxQZ8bICAkCAg\nJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQI\nCAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJ\nAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJC\ngoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKA\nkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAg\nICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAk\nCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgI\nCQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkC\nQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKC\ngJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQ\nICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAg\nJAgICQJCgoCQICAkCAgJAkKCgJAgICQICAkCQoKAkCAgJAgICQJCgoCQICAkCAgJAkKCgJAgICQI\nCAkCQoKAkCAgJAgICQJCgoCQICAkCDzdesD/sta69YSHtm3brSdclScSBIQEASFBQEgQEBIEhAQB\nIUFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQeBh/mv30/+rxm15\nIkFASBAQEgSEBAEhQUBIEBASBIQEASFBQEgQEBIEhAQBIUFASBAQEgSEBAEhQUBIEBASBIQEASFB\nQEgQ2BvS4aor4Pu72MDekI5f3wF37XjpcFtr/fMO27Y9z8zLzJxm5r1YBXfiMJ8Rva613s5dtCsk\n4DIfGyAgJAgICQJCgoCQICAkCAgJAh+ITyKBOp8e/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2d86208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import NMF\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "samples = np.loadtxt('data/lcd-digits.csv', delimiter=',')\n",
    "\n",
    "model = NMF(n_components=7)\n",
    "\n",
    "nmf_features = model.fit_transform(samples)\n",
    "\n",
    "#through the plots we notice how NMF has expressed the digit as a sum of the components!\n",
    "for component in model.components_:\n",
    "    show_as_image(component)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA doesn't learn parts\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJAj8B61WLTMJM1tzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2eb1a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGyAgJAgICQJCgoCQICAkCAgJAn8BMZU0TlsspG4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c30b0630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2f39e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c3053240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c31649e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkCAgJAgICQJCgoCQICAkCPwCzNk4ShxGs7gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2e10b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAFKCAYAAABo2wHYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x294c2ea4208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "model = PCA(n_components=7)\n",
    "features = model.fit_transform(samples)\n",
    "for component in model.components_:\n",
    "    show_as_image(component)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building recommender systems using NMF\n",
    "- Finding  similar artciles\n",
    "- Recommend articles similar to one being read\n",
    "- Strategy : apply NMF to word-frequencey array\n",
    "- NMF features values describe the topics (similar artcile have similar NMF features values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "title\n",
      "Cristiano Ronaldo     1.000000\n",
      "Radamel Falcao        1.000000\n",
      "Zlatan Ibrahimovi?    1.000000\n",
      "Franck Ribéry         1.000000\n",
      "Neymar                0.999213\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import NMF\n",
    "nmf = NMF(n_components=6)\n",
    "\n",
    "#apply NMF to word frequence array\n",
    "nmf_features = nmf.fit_transform(articles)\n",
    "\n",
    "#compare nmf features values\n",
    "#using cosine similarity\n",
    "from sklearn.preprocessing import normalize\n",
    "\n",
    "norm_features = normalize(nmf_features)\n",
    "\n",
    "current_article = norm_features[23, :]\n",
    "\n",
    "#results in a cosine similarities\n",
    "similarities = norm_features.dot(current_article)\n",
    "\n",
    "#labling similarities\n",
    "\n",
    "import pandas as pd\n",
    "df = pd.DataFrame(norm_features, index=titles)\n",
    "current_article = df.loc['Cristiano Ronaldo']\n",
    "\n",
    "similarities = df.dot(current_article)\n",
    "\n",
    "print(similarities.nlargest())"
   ]
  }
 ],
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