2017-10-24 - 16 Principal Component Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "PCA is a dimensionality reduction technique; it lets you distill multi-dimensional data down to fewer dimensions, selecting new dimensions that preserve variance in the data as best it can.\n",
    "\n",
    "We're not talking about Star Trek stuff here; let's make it real - a black & white image for example, contains three dimensions of data: X position, Y position, and brightness at each point. Distilling that down to two dimensions can be useful for things like image compression and facial recognition, because it distills out the information that contributes most to the variance in the data set.\n",
    "\n",
    "Let's do this with a simpler example: the Iris data set that comes with scikit-learn. It's just a small collection of data that has four dimensions of data for three different kinds of Iris flowers: The length and width of both the petals and sepals of many individual flowers from each species. Let's load it up and have a look:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of tuples = 150\n",
      "['setosa', 'versicolor', 'virginica']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris # iris dataset that we are using\n",
    "from sklearn.decomposition import PCA # actual pcs method\n",
    "import pylab as pl # plotting library that we use\n",
    "from itertools import cycle # iteration tool that we use for creating color wheel\n",
    "\n",
    "# load the dataset\n",
    "iris = load_iris()\n",
    "\n",
    "# check dataset features\n",
    "numSamples, numFeatures = iris.data.shape\n",
    "print(\"Number of tuples = \" + str(numSamples))\n",
    "print(list(iris.target_names))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, this tells us our data set has 150 samples (individual flowers) in it and it contains three different species of iris (Setosa, Versicolor and Virginica).\n",
    "\n",
    "Now let's explore the dataset a little deeper. If you take a closer look, you will see that the data of iris consist of **four features** (sepal length, sepal width, petal length and petal width). All four are metric measures (in cm) of different parts of an iris flower. The challange here is, that its **difficult for us to consider 4 dimensions** when doing analysis - our brains are used to 3D problems but 4D is challanging."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                 5.1               3.5                1.4               0.2\n",
       "1                 4.9               3.0                1.4               0.2\n",
       "2                 4.7               3.2                1.3               0.2\n",
       "3                 4.6               3.1                1.5               0.2\n",
       "4                 5.0               3.6                1.4               0.2\n",
       "5                 5.4               3.9                1.7               0.4\n",
       "6                 4.6               3.4                1.4               0.3\n",
       "7                 5.0               3.4                1.5               0.2\n",
       "8                 4.4               2.9                1.4               0.2\n",
       "9                 4.9               3.1                1.5               0.1\n",
       "10                5.4               3.7                1.5               0.2"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "X = iris.data\n",
    "df = pandas.DataFrame(X, columns=list(iris.feature_names))\n",
    "(df.head(11))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "While we can visualize 2 or even 3 dimensions of data pretty easily, visualizing 4D data isn't something our brains can do. So let's distill this down to 2 dimensions, and see how well it works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "pca = PCA(n_components=2, whiten=True).fit(X)\n",
    "X_pca = pca.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "What we have done is distill our 4D data set down to 2D, by projecting it down to two orthogonal 4D vectors that make up the basis of our new 2D projection. We can see what those 4D vectors are, although it's not something you can really wrap your head around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.36158968 -0.08226889  0.85657211  0.35884393]\n",
      " [-0.65653988 -0.72971237  0.1757674   0.07470647]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's see how much information we've managed to preserve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.92461621  0.05301557]\n",
      "0.977631775025\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_ratio_)\n",
    "print(sum(pca.explained_variance_ratio_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "That's pretty cool. Although we have **thrown away two of our four dimensions**, PCA has chosen the remaining two dimensions well enough that we've captured 92% of the variance in our data in a single dimension alone! The second dimension just gives us an additional 5%; altogether we've only really lost less than 3% of the variance in our data by projecting it down to two dimensions.\n",
    "\n",
    "As promised, now that we have a 2D representation of our data, we can plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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ppdKlSxf/e5/lY8CAAcWsOE2bNpUJEyaUKMu4ceOkffv2/vfvvvuuGGNk0qRJ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\nIiIisVLyISIiIrFS8iEiIiKx+v9gCqpnD0XdlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0fd71b860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pylab import *\n",
    "colors = cycle('rgb')\n",
    "\n",
    "# Name of the targe species\n",
    "target_ids = range(len(iris.target_names))\n",
    "\n",
    "pl.figure()\n",
    "\n",
    "for i, c, label in zip(target_ids, colors, iris.target_names):\n",
    "    pl.scatter(X_pca[iris.target == i, 0], X_pca[iris.target == i, 1],\n",
    "        c=c, label=label)\n",
    "    \n",
    "pl.xlabel(\"Principal Component 1\")\n",
    "pl.ylabel(\"Principal Component 2\")\n",
    "pl.title(\"Iris Data reduced to 2 PC\")\n",
    "pl.legend()\n",
    "pl.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "You can see the three different types of Iris are still clustered pretty well. If you think about it, this probably works well because the overall size of an individual flower probably makes both the petal and sepal sizes increase by a similar amount. Although the actual numbers on this graph have no intuitive meaning, what we're probably seeing is measure of the ratio of width to height for petals and sepals - and PCA distilled our data down to that on its own."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Our results suggest we could actually distill this data down to a single dimension and still preserve most of its variance. Try it! Do a PCA down to one component, and measure the results."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}