pca_notes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Start 5 min q&A\n",
    "#1 min freestyle\n",
    "\n",
    "#dimensionaltiy reduction reasons\n",
    "# 1. Space efficiency - makes data small\n",
    "# 2. Computing efficiency It fastens the time required for performing same computations. \n",
    "# Less dimensions leads to less computing, \n",
    "# also less dimensions can allow usage of algorithms unfit for a large number of dimensions like linear regression\n",
    "# 3. Visualizations!\n",
    "\n",
    "#We'll compare 2 - PCA and T-SNE most popular.\n",
    "#feature selection: you select a subset of the original feature set; while (NO NEED)\n",
    "#feature extraction: you build a new set of features from the original feature set.\n",
    "\n",
    "# Exploration of Principle Component Analysis\n",
    "#PCA finds the principal components of data.\n",
    "\n",
    "#It is often useful to measure data in terms of its principal components \n",
    "#rather than on a normal x-y axis. So what are principal components then? \n",
    "#They’re the underlying structure in the data. They are the directions where there is \n",
    "#the most variance, the directions where the data is most spread out. This is \n",
    "#easiest to explain by way of example. Here’s some triangles in the shape of an oval:\n",
    "#https://georgemdallas.wordpress.com/2013/10/30/principal-component-analysis-4-dummies-eigenvectors-eigenvalues-and-dimension-reduction/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(1) # random seed for consistency, debugging same results every time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#We'll first create 2 classes\n",
    "\n",
    "#each with 3 features\n",
    "# create class 1 random sampled 3 X 20 data set "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.22876583 -0.74996962 -0.4791571  -0.42914228  0.84086156 -0.04970258\n",
      "   0.80884436 -1.68405999 -0.33128317  1.00088142 -0.53223402 -0.72239191\n",
      "  -0.82246719 -0.59384307  1.04499441 -0.10839207  0.8709698  -0.11877117\n",
      "  -0.4189379  -1.40232915]\n",
      " [ 1.61336137  2.0546241   0.35016716  1.20845633 -0.10288722  0.46664327\n",
      "   1.78975468 -1.1601701   0.38653915 -0.38483225  1.1181334   1.09899633\n",
      "   0.72171129 -0.34390071  0.6085147   0.45015551 -0.50845713 -0.19899818\n",
      "  -0.47918492  0.45112294]\n",
      " [-0.37480469  0.05340954  0.01716473  1.1157018   1.14690038  1.03368687\n",
      "   0.45128402  1.35010682 -0.85145566  1.45810824  0.6743961  -0.90163449\n",
      "  -0.625342   -1.00016919 -0.0693287   1.7653351   0.77741921  1.86647138\n",
      "  -1.95210529 -0.6949209 ]]\n"
     ]
    }
   ],
   "source": [
    "#Draw random samples from a multivariate normal distribution.\n",
    "#also called Gaussian distribution\n",
    "#https://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gaussian_2d.png/786px-Gaussian_2d.png\n",
    "#uses mean to define center ,covariance for width, or standard deviation. how wide. how spread.\n",
    "#btw Covariance is a measure of how changes in one variable are associated with changes in a second variable. \n",
    "#Specifically, covariance measures the degree to which two variables are linearly associated.\n",
    "mu_vec1 = np.array([0,0,0])  # sample mean\n",
    "cov_mat1 = np.array([[1,0,0],[0,1,0],[0,0,1]]) # sample covariance\n",
    "#Transpose of a Matrix. A matrix which is \n",
    "#formed by turning all the rows of a given matrix into columns and vice-versa. \n",
    "#convenience, for printing\n",
    "class1_sample = np.random.multivariate_normal(mu_vec1, cov_mat1, 20).T\n",
    "print class1_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create class 2 random sampled 3 x 20 data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.5154138   1.67457071  2.19783084  0.08155996  0.5851531   0.17137202\n",
      "  -0.1077125   1.057121    0.74101715  1.08968641  2.69380911 -0.16400797\n",
      "   0.1911528   2.10717545  1.12837699  1.71304905  1.63658341  0.19381518\n",
      "   0.71100266  0.64659002]\n",
      " [-0.11487105  2.46089238  2.70459417  0.89465529  1.45194604  1.52887975\n",
      "   0.98228168  0.20045251  1.1892932   0.3988432   1.19686978  1.69336623\n",
      "   1.55743945  2.44287693  2.76041518  2.30620607  2.40925339  0.74832579\n",
      "   0.60818376 -0.78791289]\n",
      " [ 0.23269017  1.5924728   2.04008915  1.63019567 -0.57915629 -1.23708651\n",
      "  -0.71939447  0.7084054   0.43621127  1.55607351  1.16986926  0.24193267\n",
      "   1.18103874  0.46031844  1.96653925  0.39539703  2.62091229  1.38271517\n",
      "   1.68400133  1.36184732]]\n"
     ]
    }
   ],
   "source": [
    "mu_vec2 = np.array([1,1,1]) # sample mean\n",
    "cov_mat2 = np.array([[1,0,0],[0,1,0],[0,0,1]]) #sample covariance\n",
    "class2_sample = np.random.multivariate_normal(mu_vec2, cov_mat2, 20).T\n",
    "print class2_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# plot samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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UgIQkFNu23QxfAEvcu0J4iSzfbDbr/o0QiwKRKNLJctiJ9u2EILQsy3U/UxASEl8uvfjS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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f1dc6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab inline\n",
    "\n",
    "#plotting\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#figure, width and height\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "#3d subplot\n",
    "#These are subplot grid parameters encoded as a single integer, so 1x1 grid 1st subplot\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "#fontsize\n",
    "plt.rcParams['legend.fontsize'] = 10\n",
    "\n",
    "#plot samples\n",
    "ax.plot(class1_sample[0,:], class1_sample[1,:], class1_sample[2,:],\n",
    "        'o', markersize=8, color='blue', alpha=0.5, label='class1')\n",
    "ax.plot(class2_sample[0,:], class2_sample[1,:], class2_sample[2,:],\n",
    "        '^', markersize=8, alpha=0.5, color='green', label='class2')\n",
    "\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 1. take the whole data set ignoring classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#make it one big dataset\n",
    "#3 x 40 still 3 features\n",
    "all_samples = np.concatenate((class1_sample, class2_sample), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.62434536, -1.07296862,  1.74481176, -0.24937038, -0.3224172 ,\n",
       "        -1.09989127,  0.04221375,  1.14472371,  0.90085595, -0.93576943,\n",
       "        -0.69166075, -0.84520564, -1.11731035,  0.74204416, -0.74715829,\n",
       "        -0.63699565,  0.12015895, -0.35224985, -0.20889423,  0.93110208,\n",
       "         0.24560206,  0.70190716,  2.13162939, -0.39649634,  1.16003707,\n",
       "        -1.02220122,  1.23009474,  0.79924193,  1.19829972,  1.37756379,\n",
       "         2.19891788,  0.36126959,  0.65614632,  1.69803203,  1.40349164,\n",
       "         1.16938243,  0.73378149,  1.31515939,  1.35054598, -0.61577235],\n",
       "       [-0.61175641,  0.86540763, -0.7612069 ,  1.46210794, -0.38405435,\n",
       "        -0.17242821,  0.58281521,  0.90159072, -0.68372786, -0.26788808,\n",
       "        -0.39675353, -0.67124613,  0.2344157 , -0.19183555,  1.6924546 ,\n",
       "         0.19091548,  0.61720311, -1.1425182 ,  0.58662319,  0.28558733,\n",
       "         2.25286816,  1.48851815,  2.51981682, -0.44411381,  1.87616892,\n",
       "         0.69379599,  1.76201118,  1.18656139,  1.11900865,  1.12182127,\n",
       "         1.18515642,  1.42349435,  1.04359686,  0.55287144,  1.59357852,\n",
       "         1.74055645,  1.03261455,  1.84616065, -0.31228341,  2.12141771],\n",
       "       [-0.52817175, -2.3015387 ,  0.3190391 , -2.06014071,  1.13376944,\n",
       "        -0.87785842, -1.10061918,  0.50249434, -0.12289023,  0.53035547,\n",
       "        -0.6871727 , -0.0126646 ,  1.65980218, -0.88762896,  0.05080775,\n",
       "         2.10025514,  0.30017032, -0.34934272,  0.83898341,  0.88514116,\n",
       "         1.51292982,  0.92442829,  3.18557541,  0.49553414,  1.31563495,\n",
       "         1.82797464,  0.77767186,  1.41005165,  0.32933771,  2.12948391,\n",
       "         0.62471505,  1.07734007,  0.37999916,  2.2245077 , -0.09491185,\n",
       "         0.0462994 , -0.37311732,  0.14048406,  0.96130449,  1.40890054]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.62434536, -0.61175641, -0.52817175],\n",
       "       [-1.07296862,  0.86540763, -2.3015387 ],\n",
       "       [ 1.74481176, -0.7612069 ,  0.3190391 ],\n",
       "       [-0.24937038,  1.46210794, -2.06014071],\n",
       "       [-0.3224172 , -0.38405435,  1.13376944],\n",
       "       [-1.09989127, -0.17242821, -0.87785842],\n",
       "       [ 0.04221375,  0.58281521, -1.10061918],\n",
       "       [ 1.14472371,  0.90159072,  0.50249434],\n",
       "       [ 0.90085595, -0.68372786, -0.12289023],\n",
       "       [-0.93576943, -0.26788808,  0.53035547],\n",
       "       [-0.69166075, -0.39675353, -0.6871727 ],\n",
       "       [-0.84520564, -0.67124613, -0.0126646 ],\n",
       "       [-1.11731035,  0.2344157 ,  1.65980218],\n",
       "       [ 0.74204416, -0.19183555, -0.88762896],\n",
       "       [-0.74715829,  1.6924546 ,  0.05080775],\n",
       "       [-0.63699565,  0.19091548,  2.10025514],\n",
       "       [ 0.12015895,  0.61720311,  0.30017032],\n",
       "       [-0.35224985, -1.1425182 , -0.34934272],\n",
       "       [-0.20889423,  0.58662319,  0.83898341],\n",
       "       [ 0.93110208,  0.28558733,  0.88514116],\n",
       "       [ 0.24560206,  2.25286816,  1.51292982],\n",
       "       [ 0.70190716,  1.48851815,  0.92442829],\n",
       "       [ 2.13162939,  2.51981682,  3.18557541],\n",
       "       [-0.39649634, -0.44411381,  0.49553414],\n",
       "       [ 1.16003707,  1.87616892,  1.31563495],\n",
       "       [-1.02220122,  0.69379599,  1.82797464],\n",
       "       [ 1.23009474,  1.76201118,  0.77767186],\n",
       "       [ 0.79924193,  1.18656139,  1.41005165],\n",
       "       [ 1.19829972,  1.11900865,  0.32933771],\n",
       "       [ 1.37756379,  1.12182127,  2.12948391],\n",
       "       [ 2.19891788,  1.18515642,  0.62471505],\n",
       "       [ 0.36126959,  1.42349435,  1.07734007],\n",
       "       [ 0.65614632,  1.04359686,  0.37999916],\n",
       "       [ 1.69803203,  0.55287144,  2.2245077 ],\n",
       "       [ 1.40349164,  1.59357852, -0.09491185],\n",
       "       [ 1.16938243,  1.74055645,  0.0462994 ],\n",
       "       [ 0.73378149,  1.03261455, -0.37311732],\n",
       "       [ 1.31515939,  1.84616065,  0.14048406],\n",
       "       [ 1.35054598, -0.31228341,  0.96130449],\n",
       "       [-0.61577235,  2.12141771,  1.40890054]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_samples.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 2. compute the d dimensional mean vector, to help compute covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Mean Vector:\\n', array([[ 0.41667492],\n",
      "       [ 0.69848315],\n",
      "       [ 0.49242335]]))\n"
     ]
    }
   ],
   "source": [
    "#mean for each feature\n",
    "mean_x = np.mean(all_samples[0,:])\n",
    "mean_y = np.mean(all_samples[1,:])\n",
    "mean_z = np.mean(all_samples[2,:])\n",
    "\n",
    "#3D mean vector\n",
    "mean_vector = np.array([[mean_x],[mean_y],[mean_z]])\n",
    "print('Mean Vector:\\n', mean_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 3. compute the covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Covariance Matrix:\\n', array([[ 0.9868668 ,  0.26943262,  0.2855759 ],\n",
      "       [ 0.26943262,  0.92914135,  0.30682016],\n",
      "       [ 0.2855759 ,  0.30682016,  1.27528118]]))\n"
     ]
    }
   ],
   "source": [
    "#covariane matrix models relationship between our variables. the variance between each\n",
    "#http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/anova/anova-statistics/what-is-the-variance-covariance-matrix/\n",
    "#http://stats.seandolinar.com/making-a-covariance-matrix-in-r/\n",
    "#Variance is the degree by which a random vairable changes with respect to its expected value\n",
    "#Covariance is the degree by which two different random variables change with respect to each other. \n",
    "#measures relationship between each feature\n",
    "cov_mat = np.cov([all_samples[0,:],all_samples[1,:],all_samples[2,:]])\n",
    "print('Covariance Matrix:\\n', cov_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# note covariance and scatter matricies are idenical except for a scaling factor 1/N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Step 4. computer eigenvectors and eigenvalues\n",
    "#Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and \n",
    "#even Google's PageRank algorithm. \n",
    "#Eigenvectors make understanding linear transformations easy.\n",
    "#They are the \"axes\" (directions) along which a linear transformation acts simply by \n",
    "#\"stretching/compressing\" and/or \"flipping\"; \n",
    "#eigenvalues give you the factors by which this compression occurs.\n",
    "#There are a lot of problems that can be modeled with linear transformations, and \n",
    "#the eigenvectors give very simply solution\n",
    "#The more directions you have along which you understand the behavior of a \n",
    "#linear transformation, the easier it is to understand the linear transformation; \n",
    "#so you want to have as many linearly independent eigenvectors as possible associated \n",
    "#to a single linear transformation.\n",
    "#interactive tool - http://setosa.io/ev/eigenvectors-and-eigenvalues/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvector 1: \n",
      "[[-0.49210223]\n",
      " [-0.47927902]\n",
      " [-0.72672348]]\n",
      "Eigenvalue 1 from scatter matrix: 1.67100943053\n",
      "Eigenvector 2: \n",
      "[[-0.64670286]\n",
      " [-0.35756937]\n",
      " [ 0.67373552]]\n",
      "Eigenvalue 2 from scatter matrix: 0.838325973416\n",
      "Eigenvector 3: \n",
      "[[ 0.58276136]\n",
      " [-0.8015209 ]\n",
      " [ 0.13399043]]\n",
      "Eigenvalue 3 from scatter matrix: 0.68195393031\n"
     ]
    }
   ],
   "source": [
    "# eigenvectors and eigenvalues for the from the scatter matrix\n",
    "eig_val_sc, eig_vec_sc = np.linalg.eig(cov_mat)\n",
    "\n",
    "for i in range(len(eig_val_sc)):\n",
    "    eigvec_sc = eig_vec_sc[:,i].reshape(1,3).T\n",
    "    print('Eigenvector {}: \\n{}'.format(i+1, eigvec_sc))\n",
    "    print('Eigenvalue {} from scatter matrix: {}'.format(i+1, eig_val_sc[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 5. sort eigenvector by decreasing value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.67100943053\n",
      "0.838325973416\n",
      "0.68195393031\n"
     ]
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_val_sc[i]), eig_vec_sc[:,i])\n",
    "             for i in range(len(eig_val_sc))]\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[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 5.2 choose k eigenvectos w largest eigenvalues to form d x k matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Matrix W:\\n', array([[-0.49210223, -0.64670286],\n",
      "       [-0.47927902, -0.35756937],\n",
      "       [-0.72672348,  0.67373552]]))\n"
     ]
    }
   ],
   "source": [
    "#k is 2 \n",
    "matrix_w = np.hstack((eig_pairs[0][1].reshape(3,1),\n",
    "                      eig_pairs[1][1].reshape(3,1)))\n",
    "print('Matrix W:\\n', matrix_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# step 6. use d x k to transform samples to new subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#dot product between orignal matrix and eigen pairs\n",
    "transformed = matrix_w.T.dot(all_samples)\n",
    "assert transformed.shape == (2,40), \"The matrix is not 2x40 dimensional.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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UxI93tQ28L74w/rAzvA5Yv8HrrNiA9+X2FHByzHov430pxMZTANyC15GwEa9D5iUxZXL9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\nAADdBAoAoJtAAQB0ewdmAjZUQZ/6hQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f55b3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(transformed[0,0:20], transformed[1,0:20],\n",
    "         'o', markersize=7, color='green', alpha=0.5, label='class1')\n",
    "plt.plot(transformed[0,20:40], transformed[1,20:40],\n",
    "         '^', markersize=7, color='red', alpha=0.5, label='class2')\n",
    "plt.xlim([-5,5])\n",
    "plt.ylim([-5,5])\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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#comparison?\n",
    "\n",
    "#pros\n",
    "T-SNE gives better visualizations\n",
    "\n",
    "#on every other mark, efifiecny accuracy, PCA is better\n",
    "\n",
    "#PCA is label agnostic -- it treats the entire data set as a whole. \n",
    "#LDA, on the other hand, tries to explicitly model difference between classes \n",
    "#(labels) within the data. \n",
    "\n",
    "#PCA performs unsupervised transformation, while LDA is supervised. \n",
    "\n",
    "\n",
    "Best visualizations\n",
    "T-SNE\n",
    "\n",
    "Best generic dim r method \n",
    "PCA \n",
    "\n",
    "Best for supervised\n",
    "LDA\n",
    "\n",
    "\n",
    "T-SNE\n",
    "Step 1 - Compute similarity matrix between all feature vectors\n",
    "Step 2 - Compute similarity matrix from map points\n",
    "Step 3 - Use gradient descent to minimimze distance between matrices\n",
    "\n",
    "LDA (Linear Discriminant Analysis)\n",
    "\n",
    "Similar to LDA except Compute the  M mean vectors for the different classes from the dataset\n",
    "instead of #Take the whole dataset consisting of dd-dimensional samples ignoring the class labels\n",
    "Compute the dd-dimensional mean vector (i.e., the means for every dimension of the whole dataset).\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}