{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Just some notes on PCA in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Guillermo Moncecchi**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains just some code notes on Principal Component Analysis, based on a very simple example.  If you want the original, much better explanation, refer to [this](http://sebastianraschka.com/Articles/2014_pca_step_by_step.html) page from Sebastian Raschka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "np.set_printoptions(suppress=True,precision=3)\n",
    "from matplotlib.patches import FancyArrowPatch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define a very simple dataset, with 6 people, identified by their heigth, weigth, and the length of their middle finger (?). Each column is an instance, with 3 attributes (we use this format to directly call the np.cov() function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[   1.97    1.8     1.7     1.65    1.75    1.67]\n",
      " [ 110.     70.     90.     52.     65.     58.  ]\n",
      " [   5.      4.8     4.9     4.7     4.8     4.6 ]]\n"
     ]
    }
   ],
   "source": [
    "X_men=np.array([[1.97,110,5],[1.80,70,4.8],[1.70,90,4.9]]).transpose()\n",
    "X_women=np.array([[1.65,52,4.7],[1.75,65,4.8],[1.67,58,4.6]]).transpose()\n",
    "\n",
    "X = np.hstack((X_men,X_women))\n",
    "print (X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Means: [  1.757  74.167   4.8  ]\n",
      "Standard deviations: [  0.108  19.953   0.129]\n",
      "Variances: [   0.012  398.139    0.017]\n"
     ]
    }
   ],
   "source": [
    "mean=np.mean(X,axis=1)\n",
    "std=np.std(X,axis=1)\n",
    "var=np.var(X,axis=1)\n",
    "\n",
    "print (\"Means:\",mean)\n",
    "print (\"Standard deviations:\",std)\n",
    "print (\"Variances:\",var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rescale values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.     0.469  0.156  0.     0.313  0.063]\n",
      " [ 1.     0.31   0.655  0.     0.224  0.103]\n",
      " [ 1.     0.5    0.75   0.25   0.5    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "def scale_linear_byrow(X):\n",
    "    mins = np.min(X, axis=1).reshape(3,1)\n",
    "    maxs = np.max(X, axis=1).reshape(3,1)\n",
    "    rng = maxs - mins\n",
    "    return ((X - mins)/rng)\n",
    "\n",
    "X_r=scale_linear_byrow(X)\n",
    "print(X_r)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2MnzrW9+a/ESnJBOCGSdBCTNZXtR4wWlRSvJuVGxxV61WoWlaJKUrzGR4TcJQ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\nglwuh2azablkqQxB0zTLonC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TnglLAmYXS2p9Vq1WPed0isXrlRczY6kEhVxoovVJrlvx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ac5950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "plt.rcParams['legend.fontsize'] = 10   \n",
    "ax.plot(X_r[0,0:3], X_r[1,0:3], X_r[2,0:3], 'o', markersize=8, color='red', alpha=0.5, label='class1')\n",
    "ax.plot(X_r[0,3:6], X_r[1,3:6], X_r[2,3:6], 'o', markersize=8, color='blue', alpha=0.5, label='class1')\n",
    "\n",
    "\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate mean, standard deviation and variance for every attribute, using the axis property of each of the methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Means: [ 0.333  0.382  0.5  ]\n",
      "Standard deviations: [ 0.336  0.344  0.323]\n",
      "Variances: [ 0.113  0.118  0.104]\n"
     ]
    }
   ],
   "source": [
    "mean=np.mean(X_r,axis=1)\n",
    "std=np.std(X_r,axis=1)\n",
    "var=np.var(X_r,axis=1)\n",
    "\n",
    "print (\"Means:\",mean)\n",
    "print (\"Standard deviations:\",std)\n",
    "print (\"Variances:\",var)\n",
    "#mean_vector = np.array([[mean_x],[mean_y],[mean_z]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, obtain the covariance matrix for our sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.136  0.112  0.102]\n",
      " [ 0.112  0.142  0.122]\n",
      " [ 0.102  0.122  0.125]]\n"
     ]
    }
   ],
   "source": [
    "cvm=np.cov(X_r)\n",
    "print (cvm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate eigenvalues and eigenvectors from the covariance matrix. Since it is symmetric, we know they are real numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue 1 from covariance matrix: 0.3587407970726606\n",
      "Eigenvector:\n",
      "[[ 0.561]\n",
      " [ 0.608]\n",
      " [ 0.562]]\n",
      "Eigenvalue 2 from covariance matrix: 0.033429425967488116\n",
      "Eigenvector:\n",
      "[[ 0.825]\n",
      " [-0.356]\n",
      " [-0.439]]\n",
      "Eigenvalue 3 from covariance matrix: 0.010660453485812363\n",
      "Eigenvector:\n",
      "[[ 0.066]\n",
      " [-0.71 ]\n",
      " [ 0.701]]\n"
     ]
    }
   ],
   "source": [
    "eig_val_cov, eig_vec_cov = np.linalg.eig(cvm)\n",
    "\n",
    "for i in range(len(eig_val_cov)):\n",
    "    eigvec_cov = eig_vec_cov[:,i].reshape(1,3).T\n",
    "\n",
    "    print('Eigenvalue {} from covariance matrix: {}'.format(i+1, eig_val_cov[i]))\n",
    "    print('Eigenvector:')\n",
    "    print(eigvec_cov)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify that the eigenvalue equation holds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for i in range(len(eig_val_cov)):\n",
    "    eigv = eig_vec_cov[:,i].reshape(1,3).T\n",
    "    np.testing.assert_array_almost_equal(cvm.dot(eigv), eig_val_cov[i] * eigv,\n",
    "                                         decimal=6, err_msg='', verbose=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.3587407970726606, array([ 0.561,  0.608,  0.562]))\n",
      "(0.033429425967488116, array([ 0.825, -0.356, -0.439]))\n",
      "(0.010660453485812363, array([ 0.066, -0.71 ,  0.701]))\n"
     ]
    }
   ],
   "source": [
    "#  Sort eigenvectors given their eigenvalue\n",
    "\n",
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_val_cov[i]), eig_vec_cov[:,i]) for i in range(len(eig_val_cov))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs.sort()\n",
    "eig_pairs.reverse()\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "for i in eig_pairs:\n",
    "    print(i)\n",
    "    #    print(i[0])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[ 0.561  0.825]\n",
      " [ 0.608 -0.356]\n",
      " [ 0.562 -0.439]]\n"
     ]
    }
   ],
   "source": [
    "# Just to principal components\n",
    "matrix_w = np.hstack((eig_pairs[0][1].reshape(3,1), eig_pairs[1][1].reshape(3,1)))\n",
    "print('Matrix W:\\n', matrix_w)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transform instances to the new subspace..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.731  0.733  0.907  0.141  0.593  0.098]\n",
      " [ 0.03   0.057 -0.434 -0.11  -0.041  0.015]]\n"
     ]
    }
   ],
   "source": [
    "# Transform instance to the new subspace\n",
    "\n",
    "transformed = np.dot(X_r.T,matrix_w).transpose()\n",
    "print (transformed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SozKzPJw4rOnWrVvHawsWsN2oUW9NmzJqFHfPmlViVGaWlxOHNd3C+fPZf82ajaaNamtj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\nBhkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105a4ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(transformed[0,0:3], transformed[1,0:3], 'o', markersize=7, color='blue', alpha=0.5, label='men')\n",
    "plt.plot(transformed[0,3:6], transformed[1,3:6], '^', markersize=7, color='red', alpha=0.5, label='women')\n",
    "#plt.xlim([-4,4])\n",
    "#plt.ylim([-4,4])\n",
    "plt.xlabel('x_values')\n",
    "plt.ylabel('y_values')\n",
    "#plt.legend()\n",
    "plt.title('Transformed samples with class labels')\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[ 0.561]\n",
      " [ 0.608]\n",
      " [ 0.562]]\n"
     ]
    }
   ],
   "source": [
    "# Just one dimension \n",
    "matrix_w2 = np.hstack((eig_pairs[0][1].reshape(3,1),))\n",
    "print('Matrix W:\\n', matrix_w2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.731  0.733  0.907  0.141  0.593  0.098]]\n"
     ]
    }
   ],
   "source": [
    "transformed2 = np.dot(X_r.T,matrix_w2).transpose()\n",
    "print (transformed2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JxczMcuOkYmZmuXFSMTOz3DipmJlZbpxUzMwsN04qZmaWGycVMzPLjZOKmZnl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\nAeXu8Cd2KHOXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c932d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(transformed2[0,0:3],[0,0,0], 'o', markersize=7, color='blue', alpha=0.5, label='men')\n",
    "plt.plot(transformed2[0,3:6],[0,0,0], '^', markersize=7, color='red', alpha=0.5, label='women')\n",
    "#plt.xlim([-4,4])\n",
    "#plt.ylim([-4,4])\n",
    "plt.xlabel('x_values')\n",
    "plt.ylabel('y_values')\n",
    "plt.legend()\n",
    "plt.title('Transformed samples with class labels')\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": "3.3.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}