Principal Component Analysis (PCA).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate 2-dimensional data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(1, 11, 1)\n",
    "y = 1 + (2 * x) + (np.random.normal(0, 1, len(x)) * 4)\n",
    "data = np.column_stack((x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use principal component analysis (PCA) to reduce the number of dimensions of the data from 2 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_scaled = preprocessing.scale(data)\n",
    "w, v = np.linalg.eig(np.cov(data_scaled, rowvar=False))\n",
    "pca_main_axis = v[:,0]\n",
    "projected_data = np.dot(data_scaled, pca_main_axis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct the PCA line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c0 = 0\n",
    "c1 = pca_main_axis[1] / pca_main_axis[0]\n",
    "f = lambda x: c0 + c1*x\n",
    "pca_y = list(map(f, data_scaled[:,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the original data and the PCA line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JgubPYa8QwnbdeY6Cvn6dui2ma1Y9Vrh5XFtLC7R6nVUmDDzqD4cDvy58/FXgzyGEg0MI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\nlk9PklRmDDzSQHbVVXDAAdDU1FILAS6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S1HsGHkmS1HsGHkmS1HsGHkmS1Ht7dF3AYpHk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\nSZLUe/8PGiN9rvvePIoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa572294a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_dpi = 96\n",
    "plt.figure(figsize=(600/my_dpi, 600/my_dpi), dpi=my_dpi)\n",
    "\n",
    "plt.scatter(data_scaled[:,0], data_scaled[:,1], color='b', s=40)\n",
    "plt.plot(data_scaled[:,0], pca_y, color='r', linewidth=3)\n",
    "\n",
    "plt.xlabel('X', fontsize=20)\n",
    "plt.ylabel('Y', fontsize=20)\n",
    "plt.title('Original variables X and Y\\n', fontsize=20)\n",
    "\n",
    "plt.xticks(np.arange(-2, 3, 1), fontsize=20)\n",
    "plt.yticks(np.arange(-2, 3, 1), fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the reduced 1-dimensional data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0EzAAgHYCBgDQTsAAANoJGABAOwEDAGgnYAAA7QQMAKCdgAEAtBMwAIB2AgYA0E7AAADa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\nBQIIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa572294128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = projected_data\n",
    "yy = np.zeros((len(projected_data)))\n",
    "\n",
    "plt.figure(figsize=(600/my_dpi, 600/my_dpi), dpi=my_dpi)\n",
    "\n",
    "plt.scatter(xx, yy, color='b', s=40)\n",
    "\n",
    "plt.xlabel('Z', fontsize=20)\n",
    "plt.title('New variable Z\\n', fontsize=20)\n",
    "\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(np.arange(-1, 1.1, 1), fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}