{
 "metadata": {
  "name": "BASIC_UFLDL_pca-zca-whitening"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## resources\n",
      "\n",
      "- http://ufldl.stanford.edu/wiki/index.php/Implementing_PCA/Whitening\n",
      "- http://ufldl.stanford.edu/wiki/index.php/Exercise:PCA_in_2D\n",
      "- http://ufldl.stanford.edu/wiki/index.php/Exercise:PCA_and_Whitening\n",
      "\n",
      "Try to use scipy svd and sklearn pca to see if there is any difference"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## DISCUSSION ON PCA on Images and PCA on general data\n",
      "\n",
      "- http://ufldl.stanford.edu/wiki/index.php/PCA\n",
      "- for natural image / signal / text data - (1) removing DC is usually done per example (rowwise) instead of per feature (colwise). (2) variance normalization is NOT always necessary as the pixels (features) in the **stationary** images are usually based on the same statistics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import theano\n",
      "import theano.tensor as T\n",
      "from sklearn import decomposition\n",
      "import numpy as np\n",
      "from numpy import linalg\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 162
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## PCA & ZCA in SVD way - 2D data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## load data\n",
      "data2d = np.loadtxt('data/pca_2d/pcaData.txt').T\n",
      "print data2d.shape\n",
      "plot(data2d[:, 0], data2d[:, 1], 'bo')\n",
      "title('Raw data')\n",
      "print data2d.mean(axis = 0)\n",
      "print data2d.var(axis = 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(45, 2)\n",
        "[ 0.01851256  0.03179579]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "[ 0.088  0.088]\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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DvPnmm/jwww+7bdM1/ImIyNrNF8arV692aD+Swj80NBR1dXXm13V1dVCr1VbtPv/8c2Rm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\nQmCC\n"
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "normalized_data = data2d - data2d.mean(axis = 0) # featurewise/columnwise DC removal\n",
      "print normalized_data.shape\n",
      "plot(normalized_data[:, 0], normalized_data[:, 1], 'bo')\n",
      "title('Normalized (feature-wise) data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(45, 2)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 164,
       "text": [
        "<matplotlib.text.Text at 0x10dd7c50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Li83V+OOPP4qIiAgRFhYm/u3f/s3io30MrfMWlUplldE+htR56NAh\nIZPJxPDhw0V4eLgIDw8X+/bts0h9e/fuFUOHDhUBAQHivffeE0II8be//U387W9/07R55ZVXREBA\ngAgLCxM//PCDRerqbp0zZ84Unp6emv0XGRlpk3W2Z43wF8KwGj/88ENNBlly6HF36rx06ZKYOHGi\nCAsLE8OGDRNbt2697TqNvsiLiIjsF+/hS0QkQQx/IiIJYvgTEUkQw5+ISIIY/kREEsTwJyKSoP8H\nYqMvkjr+BIsAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "## remove DC - instance-wise NOT NCESSARY IN THIS EXAMPLE\n",
      "data2d = data2d - np.mean(data2d, axis = 1).reshape(-1, 1)\n",
      "plot(data2d[:, 0], data2d[:, 1], 'bo')"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## find PCA basis \n",
      "## SVD == Eigen-decomposition for sysmetric & positive definite matrices (covariance matrix)\n",
      "## The PC directions will be the columns of U\n",
      "## The PC vectors will be the PC directions from the CENTER of the normalized data\n",
      "U, S, V = linalg.svd(np.dot(normalized_data.T, normalized_data) / normalized_data.shape[0])\n",
      "print U.shape, S.shape, V.shape\n",
      "center = data2d.mean(axis = 0)\n",
      "pc1, pc2 = U.T\n",
      "print pc1\n",
      "plot(normalized_data[:, 0], normalized_data[:, 1], 'g.')\n",
      "plot([center[0], pc1[0]], [center[1], pc1[1]], 'b->')\n",
      "plot([center[0], pc2[0]], [center[1], pc2[1]], 'b->')\n",
      "title('PC of normalized data')\n",
      "print np.dot(pc1, pc2), ' dot product == 0 means they are othogonal!!'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2, 2) (2,) (2, 2)\n",
        "[-0.70710678 -0.70710678]\n",
        "0.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  dot product == 0 means they are othogonal!!\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 165
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## calcualte xRot - X projection on the PC\n",
      "xRot = np.dot(normalized_data, U)\n",
      "print xRot.shape\n",
      "plot(xRot[:, 0], xRot[:, 1], 'bo')\n",
      "title('xRot')\n",
      "ylim(-0.3, 0.5)\n",
      "xlim(-1, 1.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(45, 2)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 166,
       "text": [
        "(-1, 1.1)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 166
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## dimension reduction by PCA\n",
      "## by selecting only the first pc\n",
      "#xRot_pc1 = xRot[:, 1] = 0 # ignore the second PC ????\n",
      "xRot_pc1 = xRot.copy() ## deep copy\n",
      "xRot_pc1[:, 1] = 0\n",
      "#print xRot\n",
      "#print xRot_pc1\n",
      "xHat = np.dot(xRot_pc1, U.T)\n",
      "print xHat.shape\n",
      "plot(xHat[:, 0], xHat[:, 1], 'bo')\n",
      "title('xHat')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(45, 2)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 172,
       "text": [
        "<matplotlib.text.Text at 0x119b5950>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 172
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## PCA WHITENING - NORMALIZE U by S matrix diagonal elements\n",
      "whitened_pcs = U / np.sqrt(S)\n",
      "print whitened_pcs\n",
      "print U\n",
      "whitened_X = np.dot(normalized_data, whitened_pcs)\n",
      "#whitened_X = np.dot(np.dot(normalized_data, whitened_pcs), U.T)\n",
      "print whitened_X.shape\n",
      "plot(whitened_X[:, 0], whitened_X[:, 1], 'bo')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-1.7638156  -5.71992455]\n",
        " [-1.7638156   5.71992455]]\n",
        "[[-0.70710678 -0.70710678]\n",
        " [-0.70710678  0.70710678]]\n",
        "(45, 2)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 173,
       "text": [
        "[<matplotlib.lines.Line2D at 0x11bf2b90>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 173
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## ZCA WHITENING - NORMALIZE U by S matrix diagonal elements\n",
      "whitened_pcs = U / np.sqrt(S)\n",
      "print whitened_pcs\n",
      "print U\n",
      "whitened_Z = np.dot(np.dot(normalized_data, whitened_pcs), U.T)\n",
      "print whitened_Z.shape\n",
      "plot(whitened_Z[:, 0], whitened_Z[:, 1], 'bo')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-1.7638156  -5.71992455]\n",
        " [-1.7638156   5.71992455]]\n",
        "[[-0.70710678 -0.70710678]\n",
        " [-0.70710678  0.70710678]]\n",
        "(45, 2)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 174,
       "text": [
        "[<matplotlib.lines.Line2D at 0x11c1e8d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 174
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## PCA/ZCA Whitening - natural image data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## load data\n",
      "from scipy import io\n",
      "images = io.loadmat('data/pca_exercise/IMAGES_RAW.mat')['IMAGESr']\n",
      "print images.shape\n",
      "gray()\n",
      "\"\"\"\n",
      "fig, axes = subplots(nrows = 5, ncols = 2, figsize = (1 *2, 1 * 5))\n",
      "axes = axes.flatten()\n",
      "for i in range(images.shape[2]):\n",
      "    axes[i].imshow(images[:,:,i])\n",
      "\"\"\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(512, 512, 10)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 178,
       "text": [
        "'\\nfig, axes = subplots(nrows = 5, ncols = 2, figsize = (1 *2, 1 * 5))\\naxes = axes.flatten()\\nfor i in range(images.shape[2]):\\n    axes[i].imshow(images[:,:,i])\\n'"
       ]
      }
     ],
     "prompt_number": 178
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## get random patches of 10000 x 12 x 12\n",
      "patches = np.zeros((10000, 12, 12))\n",
      "im_index = np.random.randint(low = 0, high = 10, size = 10000)\n",
      "x_index = np.random.randint(low = 0, high = 512 - 12, size = 10000)\n",
      "y_index = np.random.randint(low = 0, high = 512 - 12, size = 10000)\n",
      "for i, (im, x, y) in enumerate(zip(im_index, x_index, y_index)):\n",
      "    patches[i] = images[x:x+12, y:y+12, im]\n",
      "print patches.shape\n",
      "feats = patches.reshape(10000, -1)\n",
      "print feats.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(10000, 12, 12)\n",
        "(10000, 144)\n"
       ]
      }
     ],
     "prompt_number": 179
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## patchwise zero-mean of the data\n",
      "print feats.mean(axis = 1)\n",
      "normalized_feats = feats - feats.mean(axis = 1).reshape(-1, 1)\n",
      "print normalized_feats.shape\n",
      "print normalized_feats.mean(axis = 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.66657157 -0.43762508 -0.40810873 ..., -0.44826995 -0.06041566\n",
        " -0.59098646]\n",
        "(10000, 144)\n",
        "[ -2.46716228e-17  -1.18732185e-16   2.39006346e-17 ...,  -3.55040071e-16\n",
        "   7.95659834e-16   9.86864911e-17]\n"
       ]
      }
     ],
     "prompt_number": 180
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## PCA\n",
      "cov_mat = np.dot(normalized_feats.T, normalized_feats) / normalized_feats.shape[0]\n",
      "U, S, V = linalg.svd(cov_mat)\n",
      "print U.shape, S.shape, V.shape\n",
      "\n",
      "rot_feats = np.dot(normalized_feats, U)\n",
      "rot_mat = np.dot(rot_feats.T, rot_feats) / rot_feats.shape[0]\n",
      "fig, axes = subplots(nrows = 1, ncols = 2, figsize = (3 * 2, 3 * 1))\n",
      "axes[0].imshow(cov_mat, cmap = cm.jet)\n",
      "axes[0].set_title('cov before PC rotation')\n",
      "axes[1].imshow(rot_mat, cmap = cm.jet)\n",
      "axes[1].set_title('cov after PC rotation (diagonal)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(144, 144) (144,) (144, 144)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 210,
       "text": [
        "<matplotlib.text.Text at 0x105826d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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WhcY4kFCgRrHsb+NY2W4+8DaAb5pWRvkMVsbyGFaEk9jtzK2TfQ4YkyAbNzs2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2RwcJCVK1fyxBNPvPGJ04A1h9IAF1H/1Q5fNFPqb/siWBegNKOoGXK6Q2Uw5xwn7HMLwCzYE2CN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\nwQmBYRiGAcAJgWEYhknBCYFhGIYBAPwBVhOGlWPawGgAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 210
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## find k to retain 90% and 99% variance\n",
      "explained_variance = S.cumsum() / S.sum()\n",
      "print explained_variance\n",
      "k90 = np.argwhere(explained_variance >= 0.9)[0][0] + 1\n",
      "k99 = np.argwhere(explained_variance >= 0.99)[0][0] + 1\n",
      "print k90, k99"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.18922609  0.31745002  0.39037621  0.45891456  0.50817309  0.54564181\n",
        "  0.57887362  0.60912939  0.63324278  0.65456544  0.67494109  0.69293414\n",
        "  0.70860297  0.72233561  0.73520842  0.74790019  0.75879333  0.76937143\n",
        "  0.77864098  0.78742064  0.79599283  0.80394317  0.81182299  0.81876492\n",
        "  0.82534819  0.8317731   0.83756571  0.84298248  0.84825989  0.85336287\n",
        "  0.85826534  0.86265742  0.86691114  0.87100746  0.87495375  0.87880224\n",
        "  0.88253274  0.885964    0.88916345  0.89229671  0.89541402  0.89842408\n",
        "  0.90135338  0.90427612  0.90715755  0.90973173  0.91215753  0.91453486\n",
        "  0.91680731  0.91901338  0.92116872  0.92324489  0.92524687  0.92724079\n",
        "  0.92913019  0.93097005  0.93275465  0.93452772  0.93626262  0.93795901\n",
        "  0.93957299  0.94115693  0.94270027  0.94422658  0.94570366  0.94710458\n",
        "  0.94846121  0.94978767  0.95109665  0.95236435  0.95362702  0.95487126\n",
        "  0.95609081  0.95727432  0.95842701  0.95955849  0.96066878  0.96174807\n",
        "  0.96279999  0.96382532  0.96484326  0.9658365   0.96681719  0.96777379\n",
        "  0.96872401  0.96965618  0.97057545  0.97148587  0.97236718  0.97321796\n",
        "  0.97405449  0.97488447  0.9757015   0.97649948  0.97726663  0.97802884\n",
        "  0.97877904  0.97950508  0.98021825  0.98090933  0.98158483  0.98225344\n",
        "  0.98290628  0.9835344   0.98414539  0.98475011  0.98534357  0.9859317\n",
        "  0.98650866  0.98706454  0.98761174  0.9881546   0.98869003  0.98921436\n",
        "  0.9897265   0.99023258  0.99072464  0.9912082   0.99168285  0.9921432\n",
        "  0.99259544  0.99303836  0.99346938  0.99388292  0.99429051  0.99469465\n",
        "  0.99508083  0.99546251  0.9958355   0.99620615  0.99656296  0.99691107\n",
        "  0.99724847  0.99757465  0.99788021  0.99817963  0.99847502  0.99875527\n",
        "  0.99902271  0.99928279  0.99953345  0.99977377  1.          1.        ]\n",
        "43 116\n"
       ]
      }
     ],
     "prompt_number": 182
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## get the ZCA\n",
      "rot_feats90 = rot_feats.copy()\n",
      "rot_feats90[:, k90:] = 0\n",
      "rot_feats99 = rot_feats.copy()\n",
      "rot_feats99[:, k99:] = 0\n",
      "#feats90 = np.dot(rot_feats90, U.T)\n",
      "#feats99 = np.dot(rot_feats99, U.T)\n",
      "print feats90.shape, feats99.shape\n",
      "\n",
      "## plotting - the first 25 patches\n",
      "## original\n",
      "figure()\n",
      "fig, axes = subplots(nrows = 3, ncols = 3, figsize=(1 * 3, 1 * 3))\n",
      "axes = axes.flatten()\n",
      "fig.suptitle('original')\n",
      "for i in xrange(9):\n",
      "    axes[i].imshow(feats[i].reshape(12, 12), interpolation='none')\n",
      "    axes[i].get_xaxis().set_visible(False)\n",
      "    axes[i].get_yaxis().set_visible(False)\n",
      "## 99% variation\n",
      "figure()\n",
      "fig, axes = subplots(nrows = 3, ncols = 3, figsize=(1 * 3, 1 * 3))\n",
      "axes = axes.flatten()\n",
      "fig.suptitle('99%')\n",
      "for i in xrange(9):\n",
      "    axes[i].imshow(feats99[i].reshape(12, 12), interpolation='none')\n",
      "    axes[i].get_xaxis().set_visible(False)\n",
      "    axes[i].get_yaxis().set_visible(False)\n",
      "## 90% variation\n",
      "figure()\n",
      "fig, axes = subplots(nrows = 3, ncols = 3, figsize=(1 * 3, 1 * 3))\n",
      "axes = axes.flatten()\n",
      "fig.suptitle('90%')\n",
      "for i in xrange(9):\n",
      "    axes[i].imshow(feats90[i].reshape(12, 12), interpolation='none')\n",
      "    axes[i].get_xaxis().set_visible(False)\n",
      "    axes[i].get_yaxis().set_visible(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(10000, 144) (10000, 144)\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      },
      {
       "output_type": "display_data",
       "png": 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       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 203
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## ZCA whitening\n",
      "epsilon = 0.1\n",
      "white_U = U / (np.sqrt(S) + epsilon)\n",
      "feats_zca = np.dot(np.dot(feats, white_U), U.T)\n",
      "print feats_zca.shape\n",
      "## plotting - the first 25 patches\n",
      "## original\n",
      "figure()\n",
      "fig, axes = subplots(nrows = 3, ncols = 3, figsize=(1 * 3, 1 * 3))\n",
      "axes = axes.flatten()\n",
      "fig.suptitle('original')\n",
      "for i in xrange(9):\n",
      "    axes[i].imshow(feats[i].reshape(12, 12), interpolation='none')\n",
      "    axes[i].get_xaxis().set_visible(False)\n",
      "    axes[i].get_yaxis().set_visible(False)\n",
      "## ZCA\n",
      "figure()\n",
      "fig, axes = subplots(nrows = 3, ncols = 3, figsize=(1 * 3, 1 * 3))\n",
      "axes = axes.flatten()\n",
      "fig.suptitle('ZCA whitening -- enhanced edges')\n",
      "for i in xrange(9):\n",
      "    axes[i].imshow(feats_zca[i].reshape(12, 12), interpolation='none')\n",
      "    axes[i].get_xaxis().set_visible(False)\n",
      "    axes[i].get_yaxis().set_visible(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(10000, 144)\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ywXrEyAXr8eyT66UXVq5caezjNYfdu3c3tJ6zDLhbZnBpA44T+2s5wi1FPvnk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\n0QX+1wAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 222
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## covariance of pca whitening (with/without reguarlization)\n",
      "epsilon = 0.\n",
      "white_U = U / (np.sqrt(S) + epsilon)\n",
      "feats_pca = np.dot(feats, white_U)\n",
      "figure(figsize = (4, 4))\n",
      "imshow(np.dot(feats_pca.T, feats_pca) / feats_pca.shape[0], cmap = cm.jet)\n",
      "\n",
      "epsilon = 1.\n",
      "white_U = U / (np.sqrt(S) + epsilon)\n",
      "feats_pca = np.dot(feats, white_U)\n",
      "figure(figsize = (4, 4))\n",
      "imshow(np.dot(feats_pca.T, feats_pca) / feats_pca.shape[0], cmap = cm.jet)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 221,
       "text": [
        "<matplotlib.image.AxesImage at 0x15edeb50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 221
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}