{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Application of SVD: Whitening\n", "In this notebook we will explore one application of Singular Vector Decomposition(SVD) which deals with whitening of data. Whitening is used to decorrelate signlas between data points, and we will explore how the decorrelation works in this notebook!\n", "\n", "We will first start out by defining our methods which will be used. Note that this notebook follows from the question two of section 08 handout." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Defining our plotting function\n", "def plot(x, set1, set2, x_lim, y_lim, title): #Set1: Red Points, Set2: Blue Points\n", " plt.figure(figsize=(5,5))\n", " ax = plt.gca()\n", " ax.scatter(x[set1, 0], x[set1, 1], s=20, c=\"red\", alpha=0.2)\n", " ax.scatter(x[set2, 0], x[set2, 1], s=20, alpha=0.2)\n", " ax.set_aspect(\"equal\")\n", " ax.set_xlim(x_lim)\n", " ax.set_ylim(y_lim)\n", " ax.set_xlabel(\"$x_1$\")\n", " ax.set_ylabel(\"$x_2$\")\n", " ax.spines[\"top\"].set_visible(False)\n", " ax.spines[\"right\"].set_visible(False)\n", " ax.set_title(title)\n", " \n", "def demean(X):\n", " # Note that this is the same as J = (I - 11^T/n)\n", " ones = np.ones((X.shape[0], 1))\n", " J = np.identity(X.shape[0]) - ((np.matmul(ones, ones.T)) / X.shape[0])\n", " return np.matmul(J, X)\n", "\n", "def project(X, V_trans):\n", " # Note that this is the same as V\n", " return np.matmul(X, V_trans.T)\n", "\n", "def scale(X, S):\n", " # Note that this is the same as S^{-1}\n", " return np.multiply(X, (1 / S))\n", "\n", "def unrotate(X, V):\n", " # Note that this is the same as V^{T}\n", " return np.matmul(X, V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will first begin by generating data from the multivarite guassian. In this case our gaussian is a 2d gaussian." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(1)\n", "mu = [10, 10]\n", "sigma = [[5, 4], [4, 5]]\n", "n = 1000\n", "x = np.random.multivariate_normal(mu, sigma, size=n).T\n", "x = x.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will then get the indices of the most extreme points for see how the datapoints actually changes, to give the viewer a sense of direction." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "set1 = np.arange(x.shape[0])\n", "set2 = list(set(range(n)) - set(set1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the original data point that we obtained before any whitening." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(x, set2, set1, [-10, 20], [-10, 20], 'Original')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first thing we might want to start doing is to demean the data so that we can project it to the singular basis later." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_demean = demean(x)\n", "set1 = np.argsort(np.linalg.norm(x_demean, axis=1))[-40:]\n", "set_t = np.where(x_demean[set1, 0] > 0)\n", "set1= set1[set_t]\n", "set2 = list(set(range(n)) - set(set1))\n", "\n", "plot(x_demean, set1, set2, [-10, 10], [-10, 10], 'Demeaned')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now do the projection of the datapoints into the singular basis vectors. We will first obtain the basis vectors by applying SVD on the dataset." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "U, S, V_trans = np.linalg.svd(x_demean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we will project the data points to the singular basis, and the data points are essentially \"rotated\"." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_proj = project(x_demean, V_trans)\n", "plot(x_proj, set1, set2, [-10, 10], [-10, 10], 'Projected')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now start to scale the projected data points, this is the \"Whitening\" part where we decorrelate the feature dimensions of the datapoints such that their " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_scaled = scale(x_proj, S)\n", "plot(x_scaled, set1, set2, [-0.25, 0.25], [-0.25, 0.25], 'Scaled')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, to recover the original orientation, we will \"unrotate\" the points back. Intuitively, you can think of $V^{T}$ as the oposite basis that we will be projecting into. Remember that we projected to $V$ before now we are projecting back to $V^{T}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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aj9PLYzxPuH+uSVYYGpGHNOrw0GH0JGe0q4Pne4RiKLOcvNkmNBbf96tAubz81uJSvQ6HDrl8z48gF0CdW+pWpSi9k81KTP/h5AqTXBMHHs0wIMk1RWn4zplVfvDB2auLVNaCsZZa5OF7gucJZWlZKXNEYGcnZk+3xsoopTCGc6sjfuDwLPfNtrFYXnxzjXMrEwJPURrLeqHxlWBE8cTuLqOy4JWRh85GSF7w4IU3mJv08F9/He67D1ZWIEng2LHqhE/X+/xIce+mc0vdihSlrcP/zefc/HwzODejgKwwLA1T9k/VSUrNlWEKQBgoHppvc359TF4YtLXcN9vg7MqYVhiwrjPKwuArYa4V0U+rJP5xmnO+N2F0rGTv9JDP3DfD2ZUJD8w1Ob8yZmFtQqY1P3D/LI/u6dCIPJ691CN++CHyV1/jxPE3eSVo8uihQzx55SSdlZUq1cla6PernqjzkeICqHNLfdAUpa3D/7TUAMS+d3U4rbWlUws5MF0Ha7ncz1gepiDCwekGjSigFQWcXx9zZP8UBnhiX5eXFnpM1yNCpXh4d5vlYUI99KmHPscu9REL2lp2t+uEgSL0hD9+Y4ndrRqzzZgr/YyHd1ZbQGfbMcevDPj4ng5aW/xOm1fnDhL0Mmh18Fo+x5baPDNcxZ9MqlzROHbD948gF0CdW+qDpChtDv8DJfginFwcopTwif3TlMZw4tKAwlRJ7w/saFEaS+ArIl8QhEYUcP9ck3roszbOMHA1SH7m/hm0MfhKoY3lxBVhYS2hGfk8vLPFgZkGL1/o0wwDLvYnlNqS5Zpd0xFJUWKxhIECpWiGPv2k6rV6nrA4SDk1yAl0RNnP2d8OUM02+dHn8NMEajX4sR+rfsjx+OY5oS5v9J7i3iHnlttuilKuDf1JwdokJ80059fGzDdj0kJTaMPLF3pMNQJeu7xEPfAYZAWP7uqyuxOTas1cM8b3hElevq3Xm5YGEF671Of8+oSD0w2++MQeEMsgLQiVIteGtSRjuhGSliWeEh7f02VxmDFKStJS89iuLqWpFsfqoc+Dc03+9XNvUhhgZgZWVvjGqT77+n2e+PwXqM91QWt46SU4efKt7Z83ygl1eaP3HBdAndtiOylKClhYn1APPERgcZBxqZciwJu9CZ6CtXHB/uk6Z5bH1AKfsytjtDXEvuLieoo2hsBXfOGx3fieotSGtUnKX5xeY7oZceTgNEqERhzQjH08JWhj2T9d49H1Nn/02hVKK8SB4tHdbb5xYpn/6IEZ9kzXWFgdc/TcGod3NfnM/XOMspJXLg2w2jLXiFkaWBr79iGTCfdNw6thlye9gLpnql1LTz9dBdkb5YRuLUji8kbvGe6dce4KpTb00pzYV5y8MubiYIJYqPsep1aHDNOS779vjkv9hOVRxsoo44H5BiD4SvHyhQGfe3wHrTjAGMv59TG1SPGN41f41slVlkYZe6fq/KXDc7TqAWmur+406ic5X3uxR1aWKF8hebWDqRZ6nLwy4PXLfR7Y0SIMPLS1nF+e8Mn9JSeXR1hr6GclWalZmeTsn50i6MREl9c5tpyQaks9GfO49eg0m9UPe6OcUFcn9J7k3hnnjutNcr51apkTl4e8tNBjvhUzVQtIS80oK5mNQ2YaEYEnRL7Hpd6Y1VFOHFS93E4cMsk1Yqvni3yP0Tjnj08s8u9fWaa0mtVxwTgbsjrK+cuH58kKwzAtSIqSE5eGLPTHrI1yBklJYSzjouDU4pBWHAAG3/eYroc8tLPN+iTj+TfXCJTH4iDn4EyDS/2EN1fHPHdulU/un+EPZZbdxTLzaU4pimO7D/NMXlR5ojcqNuLqhN6TXAB1bqt325FUasO3Ti3z7Ok1RCDwFGuTjPVxwZ6pmH3TdYw1FCUYC9YazqyMqQUea8Oc6WbIH524gqeEX3v2PE/s7dKuB0zXAs4sTRjnBcvDnMIYlocJy4OUQZLz9MEZdnYjXr+Uc25txKuX+qyMCiJPEfoKay1KwYPzLdYmOedWx3TigKQoiUOPQClyrUmKktmNude1UYa1YDGYMMR/4AHY0yCKIsYrffLVM/jjUZVc/8gj174Qm3VCX3jh7QVJnLuWe3ec22ZrSpIAD+5sve0YjUlecmpxROAJ7VrIMNUMkpy90zU6tYBSG/ZN10kKzWwzZH1S9SC7jYhTiyO+e2GNdhSwqxszSquqTJ86OE0WeBijWRpmaGupBYrVUdVLbUcBg6zg/3vxEgp4c23CJCnRxjAuDdoqrDF4nse51RGP75nijaUha5OMXUXM/XNNwkDx8fkmv/v8BS71JmhjsEgVXH2PA1N1xBOKMKK0gtdpET72g7C0WNUSfeWVqnrT1oUiVyf0nuPeIee22LojKcdwYnHAKxcHPLq3zZN7p67Z2qk8QW0s5sy1QtYnGcYYtDHs7tQIfMXB2QafONAlCjwWhylFaRhnBUvDnGFScnmYMFMLSUrL64sDVoYhl/oJ2ljWJwUKi7FCpx5Sj33atYCzKyOaoWI40QShT83CJNdMMkMcwI52TLcecHplxM5OzHQtYJSWvLE05AuP7SbyPQ7ONnj98oAL6wmeUjww16QeeSwNU2xm6Y1zapG/kcol8MYbVbWmzWH69QtF19cJdWlNdzX3jji31OaQvdzYkeSHwvGVEY3QR6HxRK7Z2lkPfR7a0ebk0pDL/ZS00Dyyu8Xubo20qPI2jbV4SujGIfXIY6et8YcnrnBmdUTsC/XIZ32SsaQzamHAJNOM0gkP72hxemnE/ul4o0JTdYpnI/Sq77eW0q37TIqCyFegLMZCYcEWsLA6xtgG1lrun68z1YgIPI/9UzVOLg/xRZhvxUzXQ144v44SQYmwOsxYWE341KFpRFXFnjv1oMoBLQrKdoe8NIRhhN/rVelL09NvD5Auremu5wKoc8tcP2RPS42XC1pbUNVqeTMK6Cf51fOScm345IEpSq3JCgNY9k838BQ8vLOJsZbAU/STHAPsaEb87skLrE9yFMIn90/z2pUBpYFMG+qhIclLrAiDTNNthBTaEvoKVRhKo/n26VVEYL4VYbEUpWaQlJQGNOABrcjDAGlRsKMZsjTMif2UtXE1HzrXCtkzVeNjO9v4yru6sv/AfJNjF3s8uLPJg/PNq8WeP3P/DHEU0bMer1wcoYMAr9/j8YUTdKDqkW4NkO+W1uR6pncF98o7t8SNioikpaEoDOO8xFjLwzs7lKY60G2SlbywOLwabBHhkwe65NpwZnnMycUhl2czHt3TwVMaBBbWRvyrb51Ha0NalNQiRVYa2rWAvNR4CgJPuNxPODDTJAoUYmGmHpJrhRLF6jjHWMjykiUgDjxQPsYUKIHAg1bkM8k1xsJwYmnHEbG2rI9zaqHPpd6YXpLx5tqYYVby2K7u1RqigyRHW8sTu6aY5JrTKyN64xyL5al9Uxzf+QDxmZP46Zj+mXP8xYGP8QOz88Rlfm2AvFla02DgeqZ3CRdAnVviRkVEIl/x1P4uH9vV5o2lIbnWaN5+flE/zTl+eUA7DjizPEbEog28vtjn2bMrPLSzxWO7O3znzCqhp2jUwqq25yhlfTQm8Gw1ZWAVeanR1hB4itVhBiJcHk7QpcUi7O3GDLKS9UlJqg2dOECwVVFlZdElFNqirUUsKKVYGqb0kpyZRkjsK95YHrOrU8NXMFOPyEvDIzvb/LXHd1GPPBqRj1KWN5ZGCDBVr8rqvbiwjsR11GNP8PypK1xowmQUkVzM+OyuiE66ZTj/TmlNnucS7u8i7hV3bonri4hM8oLSWEJP0e6GzLWiq+lMW4OtNtWw/fzyhHqkWJ+U9JOcRuSzqx0xTEuGScnZlTELqwk7OzGX+indRojGct9MnVPLQ7SpAt84L9EGVkYTvE6dSV6QpBZtNIW1KCVM10KWBym5tvTTnEYYEHhCHHisj3KSQlNqCH0QVS1wlaWhNykYZwUzjZjdnZhJrjm/PuG++SaFsVdriB6abfLG0pDeOGeqHl3dnz/OqpX+11YmrGiPZiREyrCYlnz3TJ/vv/ha9R9yczh/o7QmrV3C/V3EveLOLbG1iMjiIGVhfcL+qTpH31y/WlB5a/qS5wmro4xza2PWhilL45T74gYWi9HVvOTCekIzDqhHPu04oJ/lHArr5NqQ5AXaWh7f2+X8esIgHTPONcpajMCF9Qn9xCBYfF+RJAWTTJPnhkFSUAsUgqUwGlHQ8H0s0K571MKIJNcYa8lLCJTCiEVEyAsDtjoOZHe3zuIgYWFtwr7pGp1aSGkM59fHfPrgFEYbwtCjFiqyUhMGioPTTV69OGSiLe1duzjUW6IYjUmWzpM/+Sj+zh3X9iqvT2sqS5dwfxdxAdS5ZTr1gCP7p/jm6RWe2jdFPfTfsaDy3k6N33juPL2kBIRAKZQnfGxHi28OV7jcTymN5eB0g2Uy9nTqfGxHm6QoWRtlJEXJgZkGr14aUBSGQhustRTWkheGiYZRnhB6ik4UoI2t9sYbg28Uoecx3/FZG2X4njDTCJhqhIxSTTMOGKY5JxdHFNogoqj7HlEojDNF4MHaOCf0FEWpEeDsygQhYf90HYtlmGmMwKsXBlixPDjf4tOHZmhEHh/f3+GNK0M6tRC1c4pkrY+KQM3NVS/O1l7l5gF1m1zC/V3FverOLWWoemz1sPrVur6g8sow5c9Pr/LG4pBXLvbZM1Xn4HQTawxnF4cshD6NyCPXhtnYY5xrdnZjzqwMeGr/NPVQqt1K45KlwYRjFzKGaUGgIEcwpiqUrLGUuaVAM06rRaiaD/PdGu0g4MIgoauEQ3NNxBrWk4Jm5BF4lpVhhrEWUeAZVaVTeYrSCLun6qwMMjJtMNrwxaf2EAceWaFZHGQcv9JnRyumN85pNwKOHJwiKTRpqYl8wfcUn9w/TaENpxfHJGWJ50cUvs/Ry2Me39GgY/Kb9ypdwv1dw73yzra80xbNmxVUXhml/PZzF3izNyZQgrXw+uKA08sjmlHAyrjkvnrIjuk6k1wT+EJeQC306Y3yqibo5YSiNFzqj0kyTZJpJkV5NVdURGGswRooBbDVFlBjweZwpZeR1A3DSYExlnYcIlLNyV4Z5EyyElHCfDOmGXpoH/ZP18lLzdIwZ0crIvIUmYF6ICwNUna2a7y40KPUhqpoHnzj9UUO72gTeMLuTh0Ri68URw5M06kH/JWP7eBTB6uznDq1kPq+Btlrxzl2dsIzcyH+kU/ePDBen3Dv3BHuHXDet5sdGrc5F/rdhXVWxxk13+OJfVWKzUsLPYxYWlFAURqWRhmTXNMIfGqBx3QzIPI90kKznuSMkgLPEy71FFGgUAgX1iccPb9GqatczXGuSQuDxYI1lKUh8D2impBtDO3Tssrt1EBpDIu9DIEq91NX13hKMacUU80IJcIwL2iGAUZgnJX4voeI5dTSmHbs064HYOHE5QGt2GdHJ2RxkGFKy8qwGt6neUkq8Oq4z9MHp/AVvHB+jSf2d/CVwleKyPeq3nrYxv/EJxiuDFm5f5bZdmP7/zldjuiHxr26zvvyXg6Ns1isgFiw1ZHr5LrqFVar8JqVUUY98LEGUMIkNwQKzq2OEREKrVkaZBycqTPTCtjRivn6K5cJpJomSAq9MXQXcgOIZaYeogTGRYkx1Tc2VQ4/AJ6t6hlbqhX2rIS0MFeLlGSlxssUe6ZqjNMSFSqKQlOr+RSFISkMw7SstpCOMgIRClM9xyArCZUQBh4WoRV5TAqNrxRpUTLISl67NOTE4oBnz67SiUMOztXxVbXAlBeGFxbWOL824fSg4PDONp8+NPP+TzN1u5c+VB/8mETne8rVFCT/rXxPre3VnUWbAbYR+uzq1mmEPscu9RhMck6vjEgKzTgzrE1yEKER+dw322CuVQW/3iSnXfMJlUct8MgNNMOA3jjntUs9nl/o0Rvl1MPqV3dSaLQxNEOfwlhqkWJvp8be6RrNmk8gVQD1FIhQBWypsoGE6qO1VTBdGedMsoJ+mrM4SqsVdyDNLaeWJ4Qi1AOv2vVUlAzzkmAjm6ARKVYmOZO8JCtK6mGVBzvdCAg8j5l6yNIgZZSWZIWhWw+50k8pjWGYFLxwfp3FQcajuzrMtWMu9CZ8d2GdcuN1fVdlWR3BUhP+AAAgAElEQVRcd/RotQg1N1d9fOGF6jHntnA9UOd9ebdD426UUD9ICo5d7LN/qs7F9YSD0zWMNjzxaJej59a43E/JSkvsCbHvMco09dijnypGScGlfsIbl3ukpUEb8ERYGVXHEpcaIr86gE6JYrlXVEWRrWWYGhChFlTzqIO0RBuLBxS66skCYCEQyEtYTwvamc9sM2KzwOjaOKMVK5phQGwtvUlBaT2sMezuxJxfSygKaMcBO9sxq6OC5WFGLfDY0Y54YL7JWpJzZnWEQlgcZByY0Sipzn56eHebYVZQjz06tRCABM04L+klOd1a+PZSgFuH6Zs7k4ZDOHECPv3pKni6HNHbzr2qzvvybofG3SjADrOcNy4PGWQGYy072zFP7u8yXQ8JfcWDO5rsn2ry3PlVklLjUQ21jbU0Qo+VQUpuoBaFFGVJUhjKjR6kCHgbR3dorSk0iBhCvxq+Q9XD7NR8Qt9D65J++laPTG8E0sJC5EFZWi6vT5jr1Ag9jyhQrA4TwsCnnxZVTmdeYCx4vuLc6phcW3Jj6NQCaoFHPTI8ONfEAB/f16UThbx8YZ3I9+hPqkT908tDDs40iEKPbi2gUw9ZGeXkpQGpNgScXalewzBQ18wzXzNMVwomk6rH2WzC+fPw8svwzDNv5Yy6HNHbxg3hnfdt89C4Tx2a5pnr5uk2A2xaatbGGeO8xBOPQapphh6NwOPYxR4vX+xjBZ7aN83hnW08BbPNjV07kU/sK/Z0azyyq8uje6tg6wtVxSNbxY3Ah0BBkhuUtbTqAaFXBcNxAYmuepXaVnOs983WqUcBsR8QBx5KqjlaTTUvmmqqOU0DWWm5NEhZGqQo5THXiGhEHmujksJCpqsAPc41WhtWRlkV7EcF042Qdj3k8I4Wl3ope6Zirgxy5psxU42IWujz5uqEmWbIk3uniEOfJ/dOsWeqxuooY3mQUmjDI7vbzLViYt/j2KVqlf+aIiNzc9ULceLEW6vyH/94FVAvX66qPz300B37Pfle4Hqgzrbc7NC4zQA7yUsmuebF8+vs6dZZTzIu9hOUCPum6rTigAu9hMf3dLBYSmNQSjg42+CNK0NOLQ4xWPZ0Y1696HN5MKIoq55n6FV//TcXqdISWiJXb2/SQBwoZhoBa0lBpjXNyGN5XOJ7HsnG2fObLFWvtJ9mZIVF4dGNA9bHeVXtKYJGHJLlmmFeFXmGqkjzOCvYO1Xnwfk2SWm40k8YZRpB2DdTo1sL+bjfIcmrPy6fPTx39Y9Ppx7w2QfneGJvl9IY3rgyYqZR9RyvyaUtrisy0mpVXezRqLovDOGTn4QHH6xOAb1R4WbnlnEB1LktqhMr+2SF4ezqGGuF3d0ak1wTKkWnHtKpheyfqrM6ylhYT8gKXRVW1nD/fJOpRsgL59b50zdWiEPh8HyT82sp1lS7l6worLG042qle5KXKKkCrN3SlnGuMQa8oMrvTHJDP6nmQ6+/FsD3hEh5eKFQjxSrSUlRWgqtiXyFARS2WnzKS4yVjfs92nHAxX5KK/LxPOHAbJ3L/ZT755pcGaTo3GKwPLqnS3tjvhPeXgqwMObG88zquiIjZQkPP1xF/eXl6rGnnqqG8Tcr3OzcEu7VdG65ralOzTDggdkWL19cJ8lLkrxk52yLw/MtSmNoxD5GWx7bHRL5HsZa1kcZuTXs7dYx+wwnlwdMUs1MM2LvVMwgKchKzSjTtGs+Nd8nDBSTPMdTQs23GARrbLUDKYBektFfN6RFFUwBYh9CBbnZmE8FSiAvLTq0zDZDBpOCNNNoYykNgEGJIdXV1+nEEAVCUhh2dGNmWhGXegmzzTq+Lzyyq4M2lqf2T3HyypCk1FdzYzd78O9UCnCclzeYZ1ZvbeXs9aof5DOfqXqXm4tK7oTPD817fjVF5EeA/wz4qrX2JRH5GWvtr9yKRojI54Bfpsp3/j+ttb903eMR8GvAJ4FV4Cesteduxfd2br3NlfjcGk6sDBkkOVeGGU/t63L/jgaR710tbXd4vsUL59dYGRdkhWaUFpxZGTHJddVj04bFYY4vsKsb058YwsDnqQNdXr5Q9XDroWK2GZGbmLlGwNm1SbXTyBpybWn4PiujAlHVaHdzcUlvTH4qqsAJ1edRoAh9YZQUTHTVK/Y8IbAwzA1+9WXUAqEoqyfLS80o0eSlZroekhuNMj7HrwzY263TCD2ePjSNgbft3rq+OpWl2lX11L4qaL7tQL6pKXj8cfiLv6hW0V5++e1DdFdw5EPxfv4c/W3g7wJfFpFp4Mlb0QAR8YCvAj8CXACeE5GvWWtf23LZTwPr1toHRORLwD8EfuJWfH/nvXu3EzY3hZ4CgROLA2LfZz3JaUYepbbs7tTICsOT+7vUQ59SG16/MmRlnCNiOX55SCP0mOSaQVKgRGhFiuVRzktv9lAIc+0IXzw+fWiW75xeYZQZCpPz2J4p9k3VmG/XePVSn0FWVD1IrSmqxW0KU6UsFXZzBV8oi7cG8QbQ2lAaoSirsnb10EMpGExKQkC8KhBjLc3Iw/eEuVZMrjXffGOF+XbMTDMiDn3yQrM6zPBVVVv0yX1d6k2fNC8Z5SXN0L+aubA6yljoTUhzjbaWJ/d1addu8F+0LOHYsSpg3miI7gqOfGjezys6tNb2gP9JRH4J+NQtasPTwClr7RkAEfkN4EeBrQH0R4Ff2Pj8d4B/JiJirb1++sq5TW62ffN6vqc4PN/ilYt9klzTmxQ8uruDBZQSLG8tQl3uJ5xcHrI8yCm0ZZgVeEoYpgWjTIOF0hpqgU/gSZWgHnhEoaLUmvlWiEWYaobkpebi+oS9U3XiA8Jz59bR2rI4yNjMR7dAvvFbk2oIsfhelU+6qTTQn2jasUehNYO03NgdVQ35rRJagbeRl2qoBQHjJKewggIKM8EKfHq2wYVexvmVCe26T6Cqs5ieOTTFs2fXKUpD4Cu+8NhuHt7Z5refX8AToRb47J2ucfzKgGcOzQBc+4frvQzRXcGRD8X7SWP6vc1PrLU/RzWkvhX2AAtbbl/YuO+G11hrS6APzFz/RCLyMyJyVESOLi8v36LmOVvn6KYb0bVpNe9grhUx3wo4tzZidZTz7dOrDJKqgMfmgkipDa9c7JMVlv0zDQ7O1gmUsDxIsRZCX4j8apmnNIbAE3Z2IiaZrp5HPFq1kMxYVkYZF9cmLA5T6qFidVxQC3xqQYDvVUd1bG2twNUjQNJrF+IpgdJW+aW6qveMEouvqueIver44kasAMFiGWQFpS4RqarjL6xM+LcvX+TbZ1Z48UKPvzizjiDo0vCv/vw8ke+xd6pBM/L5vVcuIWI5PN/iyX1TPLanw0wjQmvL0jDl2bOrPHd2jWfPrtKfFNdWq4d3HqL7/tvL4Tm31LsGUBH55Y3e3r/Zer+19p/evmZtj7X2V6y1R6y1R+Y2ays6H9i7bd+8kVIbLvYyGoHPvqka1lrOrIwYJgX3zzWvPi8WZlsRhTYYY5lqBoSe0KkFtKMAlJBtDLGjjYDYqYXs6daYafisTnJCJUSeMMgKTi8P+c2jb/LKhX6Vg6oMZcnVxPtNwcZ86DivdiZdT9mqfQYIA1UlzivITLUdNC81e9p1ZhshgacwVhhlmlGhGSSa9UnGyjgnKzWtjYWhPzu1xNnVMUv9lIvrEyZ5SSOsCqvkpSUMVDWtoKqNCAicWhy9/Q+XbCwkpWm18p6mboh+h7yXV3wIfE1EfsJaOxGR/wT4eWvtZ25RGy4C+7bc3rtx342uuSAiPtChWkxyPgQ3275ZasMkr5Zg6qF/dW50lJd4Ijy2Z4rSGB7Z3eXU8pBhVnJsoUcUejy2u0M99plvhpxaHpHraqj+/Q+06daqxPU/O7XEYi2pCpH4itNLQ+Y7MRf6CUVhiX0PaywX1xO0teSFxRPD8ijHB5KyygWFjbzRjc+teevzUCC5bjLIAqESxkChDb4ofEW1UwiLtVXAnm1HTNcjzq6OuNJPMMbSiDyyotouWg8USaZZ0ikGODzXYJAGYC0X1hN2dSICX9GtBW+rYnV4R4s3FofX/OG6mg/qhuh3hXd91a21XxaRnwT+g4jkwAj4uVvYhueAB0XkEFWg/BLwk9dd8zXgvwa+DfwY8A03//nheaftm6Os5DtnVzm1NEKscP+OBs8cmqVTD2iGPoGvSMuqlzVMc1aGKcvNkL5f1e9MC82T+7o8f26NZhTgK2HPVJ0drQiD5dzyCG3gofk2C+sJG7U9eObgDKW1vLLaY5QVNHwfEUVWFNXxyb7H5m5NnypwGq4dwlvZCKgbu5p8s7FCD0Q+GA2NUDFMq0CYiaE0UAs2SuspocqSqvbhF9oSKI/MVEcoR75HaQy1yKdb81kd5kS+MEgNnz08x+tXRqxNEuqR4q8/sZc49EnL/JoqVqF/87oDribonSfvFodE5K8AX6YaAe0Cvmitff2WNkLkrwL/hCqN6V9aa39RRL4CHLXWfk1EYuD/Ap4C1oAvbS46vZMjR47Yo0eP3spmfs/bugoP8OenVji1MqIR+mCFcV5w/3yTz9w/i+8pFlYn/N4rlyjKqmTcOCu4f65N6Cvy0rA6yvjhR+b5969eqRaVROg2fL5zbp35ZoxSlsGkYKGX0AwDSmM4szwi9Dx8X+hPCuaaEXHo8cbikEle0IlCeknGILNY3qoD+k58qYbzua6uCzyQKlOehq9oxgFJUZDkhqSERiS0Ip9mXNUDzUpDP81Ic4snQrdRnRevpJowGGUlcejhYenEEamphv47OxG7p2p8/tGdNGshpTY8e3a1ygX1N3NB9dUTTN/L4p1zS8m7X/LehvD/APhfrLXfFJHHgd8UkZ+11n7jAzVvC2vt14GvX3ffz2/5PAV+/FZ9P2d7tm7fnOQlSalRCKFXDTGTQshyffX4jn0zdX7q+w4yykuMMfz28xevVjhCLMYaTi+PqEd+NReoNf/u2CJ7p2MOzTZJy5LlQcZiL6UflYitih+vTwp8JSgFy6OUpw9NMU4iTi0X9NKcTNurvc53C6ChXwVRkSpDwFMKbQxGWyyWTJeMsrf6rklmMaYgjnxCT4hQhL5PIxCS0lDa6mymR3e3eXxfl8vrKaW1LPZTCmsZJjlRoFgZ5Ty4s0W8cfTJjapYjbOSWujxzKGZ95Q+5nz43ssQ/oe2fH5MRD4P/C7w/bezYc7dLfQUNd/DYMm1BisYa4lC760hJhBvzItO8pJDsw2uDFISdLXHfboGFg7Ptzm3OmZtXDApSvZM1SmtJvQUWWl4cEeLOPC40ks4eWWEUhDGYVWcuajSpKpTMmv0JgU1r2SlNCggf5efIy2gHSnqUTXsLoxlnGpKC0VuSTZyQYONHylQoA0MJgVQzftqbZlphkx71SJQK/Z4aHebi72UrKxyOmuRjxSGZ+6bI/RVVeVe5Oofm8155mo7avVabg7Xb1Z3wLmz3vcEirX28saw3vke5nuKJ/ZNkZaGk0vDq3OgT+6duuY/+zX5o0rY2Y7xlKC1QRBOL4/wfcW+bo21YVoNZc+ssqMVo41FW/iRh3fwm8+d59zKmHFhaEWKpChJCphkmhffXKceerTiiFJnlEbRDKsV9ElRpSS9EwEmuUEKw/RMQG5gklTzobVQGG5MBWgDjUDhe4I2lqIs2TvVZFKUpEXJxb4l9BSt2GNXt8bOVo3D820GScEgyxEjXB6mRIECK4hwzR8b31Ps79b5+quXr8kPdYHz7ratGWhrbXKrG+Lcezr1gB/62DzP3DcNXLsKDzfe4z1ICx6ab/L6UlVcOAw8ziyN+JPXF9nbrjPViDi5NOD00oR2zWN3p4a2Bk8U7XpIkmtKYxklJbFXLbSMUkMvKWllVbGP/ign8BSRL+SlvmkA1UA9qJLnJ5mmFnk0Ih9VWkpjURtr9Zbq6I6aUsSBotBV1RJrQETQxuCHPlHggViUgmFacn59Qm+cc2Cmzkw94tIgueEfm1Ib3uxNeGpft1qgMpbz62N2dWMXRO9ibgnP+UB8T11TVWir6+f18sJw4tKQUVpwfi0h8hWdWsCjuztc7E3wfEEVwq52td3ziQNdBknJ8+erqvVJWTLVjOiNM8irOct66FcBNTXVMRtjyCwoDHE9qk7kTDWFfXvVJagKiihR+ErY0YlIcoPngTKWVuCBNchGLmrgQSDVvnhPCY/v7rA4yrDLQrvmM9sISQrN+qjg+XPrrCcFe7o1puoRO9o10lLz2YeqBbbr/9hsvlad+K3Xcm2cXR3iO3cnF0Cd22Zr/qivVLU3PlLsaMWcX51wZnnEkQMzGGuIfQ+f6jA5Y4Uw9AhEEWzMDx6ab3B6eVSdU6SERuThKaE0VZm5vNr1SWbB96o0oEFakhWa2K92Pt5IUYKIpREqLvbS6lC6TBMFHklpmG5WPcBmKGTa0I5CAh+mGzEGKEuDr8Bqy8J6wiTTzLVjxkXJKC05vzLhhx7egRJBa0sc+tUpnDd5rW6YsuTclVwAdW4b31M8vLPNiwvrG6daag7PtXhjeYQS4VIv5XxrxGwj5mO721zqpaRZVYWpHXusjHIMhrwQ9nRrnF0eM0gKfF/Y14250EuZpCVhqKgHoO3GFk2BQAmxL4yzqnhII4DRDYKoUmCN3QicJXHgEShF4Hl0a4pWLeTAVJ0o8tjZjrHWEnge2hoiz8NX8NrlPiNPEXiCtpbFQcp3z68TeB7tesA3jl9hvhMT+oon9nVvGEDf7agU5+7kAqhz2/QmOcevDBAEz1McmKqz0J/QCH1mmzFPH5qmKDUzjYDpZkBvnGFUdQpnVmjOrgz5gQfmMBZeuzxguukzyX08UUwKQ7cesGIMWW4oLUR+VQvUCmTaYguD70EjDphkGsFUBU2oTuo0ttqyGYeKLC9JcihNSSsOKUrD0Fp2dz2O3D+FsoqXLvSYqgVXj0LWIVzoJ3TrEWlREns+eVHg+7A6KaiH1XHH3XrA2jjnBx+Yv1og5EaBcbOSv0tZune4AOrcFpsLSIFSRLFHoQ2XkpxRUqIQfKWqrYpXBhgsHsIg0Ty6q4NCOLM6YmF1wiQrWRzmrIyq85W0sZS2RItiPcmo+8J0I2JlmCFY6rHPJNcoBdMNn/64xBMQZfGpFo2qIiKQFFUQ9UTwI5/SlJS22udugVawkYvp+aDg0wenuNTPyEvN2dVxtQ9ePEJfkRZVePa8atnJl6pKvacUB2aaKIFWzWeSlzed13QpS/cWF0Cd2yLXhv44Z31SMkwLlgZVCk8t9JhvVcd5HL88oB757J9usjSYsDbJ2T1dY2mYVVWSCsNLF6rjjH2BduSBhbTI6Sd5tXvIWHJyio3CyIWG6WZMoCDyPPK4OnSuKKvxfeht1AUtq6G+51VHeNR9DxsrRkmORSh0yTAVdnUVbywOOLMyodRgrcX3ql1Qp5eG7Gg32Dtd58zyiKVBijaGHa2IyPeohT7DpOTsypA48Ll/tkUYunnNjxIXQJ3bQgELvYR64DFIS3xfSEvDQztb/OnJFWYbIYujjP/44V14Sphp1phpRqyPM9ZGGRfWEwpdcH6tJNsYirdrIcOkRBuIAw+LpigtWW4JBJqxz1QjwlrLobkGvUlBbjS7miH/f3v39mPXed53/Pus0z6f5jxDDsnhSaIk69SRT02copYStU1jX6RJAySRARf5A9obA7ookLZo2lw0QNGLGL6RgxYNbDS1kaBGIyWw3dZqRcuKZIYUKYoiOeScT/u8115rvb1Ym6MhOUMOF8nZnOHzAQbce/bCnvedDf5mvet91vuutEKW6y2a/qdbd+Q8sHqFSoGBUtbGtT38bkgnAFsi2n7ISr3L7FqbkaJHaOitUxqxWA+odap4jsVgxsEhRSkbz6J3wojVhs/hwRye4zCQ8zi/WOWf/J3Ju55h7nThatV/GqDqoYiAQ5Uc16tNam2ffMalnHVYaXaZGsrzxGiBjxZqXF1rMFzwMBi+dHKIK8sNLs7XaPtdcmkvnjTqTc60u/F6m5ExhCZe8q7a6tIODI5tUcmlKKZd6n7IcD6NZ9uUMx5XVhp0gpCmz6f7xccZSCYTLy/fCUO8yMYgWI5FwbLI9bY+nq22KGYcIhGa3RBbDI1uxHDewQ/irT3max1OTRR56fAQ19ZbrDXa+CH86rPjDBcyRMZQa3fJeFstnvepe1m4WvWf/nlTD4VnWxSzDqfGikwN55kopkm7FkEQkfMcylmPpyfKtDsR87U27SDky0+O8ZXnJzg5VsKSeBm4jOuQ7YVO1nM4PJQj41kYDJVcmpPjBTKuRTFtk3IcRODIYIbf+uxhvnB8kJVGh04Qh64IOFY8dPdcIQJGC+l4BfhyjlefGaOSdTGhoRuE1Dpd5qsdFmttSlmHFw+UKaccjIFmN8Sx41KqSiYNlsVKo8u1apOJYobJwRxPjBao5Dw8J77F03OtOw7f237A6csruJa144WrVX9pgKqH4kZZjgHGixma3fis0AgcHMhgW4LrCE9OFHjuYJnpQxVyKZurK20OlDNMDecpZlwMhoznUEx5HBkq8MxEmZeODJBzHWwxrDcDxktZBrJpulFcAtX2I/7738xw5vo6ay2fbjckCEIsAWMEIb52agHrbZ8ogmzKoZxzGc6lEVuwJF5YBDHx/e6RcGmpgedZFDIOlZxLuxvvCjpba3GonOHQQI7laocfXVwgiOBgJctaq8tKo0M7CO9YlrRUa/NXH87z85l1LszXqbeDHS1crfpLh/DqodlclmMxTAS0/JCzc1VWGh1a3QBLLD6cq2HbwrGhPAZ49mCFmbUWAlyvtqB3X7ofBKQcC8+2GS+nGMyncCwhn/ZYbfjxIskCURhxdraGZ1nYCO0wiq+jWuCHhrRjYaKIUsalnHbJpz2Gch5vX1ymEwbxdiKuFc+yOzYp1+L4cJ4XDlUIo4gzvf3uT19ZITLxffMjxTRPjBRohxFRFPG5o3GpUrMTbGygt2141tt8990ZBFhrdcl5LhcX65wYzWsx/SNOA1Q9VLeW5WQ9h89PDdL0A967skY25WzceXN+oRbvdeQafvnpUX5+bZ3CvMvx4RyHh3LMrjZ5/9o6pYzH54+OMLfepNbpEoSGjGszV23hB4ZuFC8pN1HMEiE4NohlUUo7hJFhopwh69g8OVHkyFCe2bUmZ2arrDS6QMRgLkXatRgtpekGEQu1Dov1DjNrLY4N5eOdQrMu/+gzE5yfrzNbbREZQ90Pma+2SHs2QW9l+kYnuGNpUhBGvHd1DVuEoXyalGPzyXKDcsZlrJzipcNb14yqR4MGqNp1NwLFwE3bVcxX2wRRxLXZNkYMB8pZxoppDlZypF2boVyac/N1nhwrYlsW9XaX9XZAIW3zwUyNpbq/cStmuxuvVZpyLNqBTT4NhbQbr+LkB0wN5xgppgmiiNVGwEQ5w7GRPGXP4SeXllltdbm63MQApYzL8ZE8FsK5uXWOjuSZWW4RRIYTIwVOjRV49+oqng1pz+ZAKcul5QYnR+SuZ5Dx2Xm8E6cfRJQyHuOlkMmBDL9wbGhjvVD1aNJPR+26IIwIwgiBjXu/m36Xq6tNnj1QZrSQiVduavrM1nxWm/EOmwM5d2Obi4vzNRbrHYIoIu/ZFDMpbISra23CCLqRYaXuY9tCKedRTrvMVdt4ts1IIc1oMc1yvcNy3acTRHSjiCfzRRphRGQMjiUcGshSawdMDeY4P1/tbW0cD8+fnyzzzqVlLi42uL7eIojAiPCFo4Ms1nxWGx3qnZDpwwO3rVC1uUTJsy081+LgQIaZlRbVtk8YwbMH9DbOveCuW3rsVbqlx8OVtFZxc5lOOwiR3lmiH4TMr7cJEYwxCMJyo83TEyUW6h3afrzv0Eg+xUK9zU8vx2uADuVTDGRc/vyD6ziWRdUPKKfiPeI9x6KSc+mGJl74IzQ8MVYgZVuMFlLUuwHPHSxzZbWF3w352dU1immHjxbqPDNRxnOEpXqLD67VGCt6+BEMZT1KuRRfPDrI1ZUm7SBiKO9xeblJhOHYUJ4To3ma3fC2M8itSpRyKZvFeocLczWCyFDr+Hh2XHmgZUx99cC29FDqJklrFbdaH7ThBxwdzPHhXI2/ub5OzrU5MVqkE8Qz6l86OcxoMU03iqi2Ap4aL/LTy8ucubZOOeMykk/z3rU1BKHe6UIEzW7ASCFNPmVzYiTPK8+O8oP351itB2CgayLOLawTGYvpIwM8NVbizNwaTm8dznzaoe4H4Ed8ONeg1uri2ULec1lqdBkqpPl4sc719Rbz1Q7FtEsx7bJU78T7vQ9keenw4E3heWvfm36XH55fIJ92sCVeW/TEaJ5Li42brgt/cH1t23vnVf/pp6LuyeYguNdaxe32lz+/UCft2RwbLOA48ay8AcaKGdpBhG1Z8Zmqa+E6N3bDFC6vNPk/Hy/RDkJeOFRhajiP4wgY0zv7TPHMZJnxfIZSxqOQsTg3v86FuXUuLbbohiE/ODNLJwh4YrhANmXz9IESJ0aLLNfa/O8LS8yttwgRqu2Aeidgpd6mG0Ys1bu9xZwDEEMrCBgquFjAcwcLt/1B2dz3WrvLudkaPzy/wPm5Gp5tk/McPpyv0Y1u//1sV8Z0Y0tprRPtHw1QdU+2C8Gd1CpuXvMS4uufEYYwMjhWfJ/8saE8BwcynBjO8/SBIlFoWGl0aHYCjgxkeX9mnaW6z/TUAEeGcvH1ShGOjxb48pPjPHOgxNRwnqnBLJ87OsCzB8p8uBBPPHXC+P74lUZAIeWwuN7h6lKT779/naVGh89PDZJyHAayLuvtgLRjU86myKfiPZ0W6x3aQcT1tRaNTpcohK4xLFZ9ZlabXFtrM7PS5Ns/ucKlxfqWfW/6XS4u1QkxZD2XYtqLtzWxLKzeqHHz72e7Sai1ps/bl5Z559IKb19aZr25zYKn6qHSAFX3ZKsQ3Gmt4o3i+nYQbhSXHx3M8fFSnQ+ureEHISsNn24vjD8/NStl+h4AABGLSURBVMQXjw9xcrSAETgzW+X9K+v4XUM+5XBypMBkJcuTY0WC0HB1tUajHWILzFXb/PjCIj/8cJEzM1XEgqGchx8ajIH1dgi2kMu4HK5kSbs2g7kUk4MZTo7kmRrMMVrOcGIsj2NZiGXj2MKLhwawEK6vNxHL8NyBMsdGMvihYbycxrItVho+f/yji8xXW7f1vd4JWWv42CJMDmSwbQiiiHqni+daPD958+9nq+L7+xkFqAdLr4Gqe3K/C//eXFwPp6+scmq0xJW1Bm0/RET4x8+NM17K4NgWQRhxsbf3fCntcjnV4OxslbmagyUWEYZqy+fSQo2Plxq0gpCpoTxZL97R89xslcnBDOfnaszX2hTTLg2/SzvwiYxNZThHPh1PNPlhl2srbbpRiGUJhwdzBGFIJethjOELx4Y4NJDl8nKThVqb+XWfQsZlve3jiFBtBRwsZymkXa6vNfnpJ6v88tOpjd9NKevyd48NYjAUUi5RBGfn12l3IkJjeP5AZUdrgm63BbJu/7H7NEDVPbvfhX9v1IE2/YAwNAzkU5SyzsZE0WD+09DZHBa1VpfIwFy1xXLDYryU4UA5w8cLDXJZh8nBLNdWWyzVOhQyLqPFFH4UMVHOcHauSsaxMSZiKJdivtpGRIgimBzI8PFSgxcmKxweyFPvxHsZXVlpcnW5yXAxxUgxxWgxzXytw+GBHCsNn4OVNJZl8dRonh9dXKSccTZqTdOejWNbN4VaEMY7hb4wWeHsXJUwNBwfynN0OEcx427c83+3NUF1+49HhwaoSuRBLPx7855JQieIcK2bg8Cz4yuDK80Onyw18FyLYyMFjg3lCaOIqeEcFxfqZF2Pbgpsu0MQRHTDeIY/7dhcW2vh2TZ2Sjg1XqLVDThYyTJXbTGUSwHCoUp2Y6uNUsbDDyKemihwYb6OZQlihHYQxG1yLU6NF/EDQ7XTxfEsXj41xgcz61xeqZNNuXzhyCDZ1KfbFt9auXBqrEjGs2n6AefmavdU0aDbfzw6NEBV39wIgrcvLfHRQn1ju99GJ6SUjcOg3gloBSFnr8VL350YKXCwnMFxBBPEky5pz8YAI4UU1ZbPJ8sNithkHZtCxsG1LZ49UKHW6vLmh3OcHCmABa88M0qjHfD8wRLnF+sbZ3RL9Tbn5qqcmYVcyubUaAnXEWqtLoWMRyHl8vFig9BEDEUep8YK1DoBlZzHhfkanmNjO2yE2lblW2fnqkwfqnBurnbT93datqTbfzwaNEBVX+VSNmnX5rmDZfIplyCKNkIE4OfX1xnMpfjFk2ne+cSiG0ZYlvD+lTUMhvFShq99YYr/eXaOmZUmA7kUf//JUT47NUA55/De5XVGihkAROBAOcvUcA7PtriwWKfdiTibrXF0MM/l1XjTuvMLNY4PFbhebZHxbD5aqvHUWJFuGPHURJHLK00Gci5XVpscquQIwvhmlIOVLEcGc9T9gCiM74WH7a9Z1nuXMJJey9TtP/pPA1T1lR9GYNhYyR0smu0OTT9ehGNzwDwzUeI7P71CyolDdzAfL8R8cqzA0eEca20fz4r3qb9x5pdNN1htdri22qbVDTAYWn7IuZUaGdfmhUMVXEe4vNpg+lCFuh9ggMFcioV6B4xQa3Z55/IKYWRIu3GtaMazsaB3h1PEz66sbZR2ldLeTXu6b3fNMu85ei1zj9NPSvXV5nCptbq8e2WFC4t13ruyRssPbyqZCom3FH56osxzkxXGS1k+WWzS9APSnsNYMbuxj/sNhwez/O1MlfWWj+tYvHBwANexmBrM8eKhAfJpZ6OWNQLKGY+UaxFEEceG89TaPpdWGjgivDg5QDblcHauimdbG3u8ZzcFIdxe2rVV+dZnJsqkPWfL7+tZ5d6hZ6Cqr26Ey3szq5yZqZJOWbw4OYDrCGfnqpwaK3J2rhoPbbsh4+U0ac/CtoTQRBjZei2HG5M2C2stLq3WOVTJIoDnWITGwrHi+kvbuvnMb/METacbMVpMU8l6HBvJxwssw8YwG9i4Bnm3SZ3trlnqtcy9TQNU9V0p6/LCZJl2N2S0kL4pqDKefVPdqBFhZq1Ji/guphMjhY3Z8xtuTNqYCGarPmnbYqXZZTCf4uzcOsdG8jwzUdoI5lsDr5R1eXKswHtX10i7NtfWWww10wzkvY2wbfoB794ye36nILzT4it6LXPv0gBVj4Ss55BLOQSRwba47azwRsB8bmqQ9FWLVhCScWyem6zcFj5+GHF9pcH7M1U+WY5XTPLs+D2H8ilOjhQYzKe2DbwgjDg3V4uH846N61icnVvnhCmQcq2Ns+JPFwYJeOfyMr9wbOi2MAfdKG4/0wBVj4Sd1jaWsi5fPD50xyFvFEa8e3WdjGdhAZ4tBFHEoUoWjFDphdd2Z363zpoP5uLQfXayRDnj3Vbc//FSPFElCNOHB24Kx61KmHSFpf1DA1Q9MnZ6PfBuW2SstrqUMi6tbhjXi0ZgWw6IcHgwy93uGLeAIDI0/S5Zz6UThHiuRTnjbfwMBJp+wMdLDRBDOeeRT9m3haPedrm/aYCqR8r9XA+8MVReXG/z4XyNwVw8oz6W9RARnp4oYll3LhO68R6dbsiFhRqHKjmKWae3EEiwMRTvBBHrTZ/VZodyzuP4UHwtdnP5Euhtl/udfopqX7gxVHYti4Yf8eKhCrXe1sDX19s8e6CMZd35lsfNw+3JgRwvTFbwXNnYcnnzCkgDufiOpCfHCpwcyZNPO1uG43YlTHr2uT/oGajaE+62hcjGULl3vXOykiPj2BwZzhKGMD1VodwrsN/OrcPtrOfQ7oZEW7yWcmwaVsAzE2UuLtZZaXTueN1WS5X2Jw1QtauS7KW0k1nsG0PleEM4i4bfJZ2yKaZdupG5a3hufo/thttbvTacTzGcT93XdVu1d+knqnZNklXUd7p48I2hcjeKGMi51DsBg9kU3cjseMh8p+H23V7Leo4G5GNIz0DVrkhaznMvs9i3LtYcwcZZ4U7PfO803C5l3Y375fOec8c925PuWqr2Fg1QtSuSlvPc6yz2VkPley1k3264vdP30cL5x4f+aVS7IuleSvc7i/2g9g/a6fvofkWPFz0DVbviflZRv59Z7AdVyL7T99HC+ceLBqjaNfcThElnsR9UIftO30cL5x8v+qmqXbXbM9YPqpB9p++jhfOPFzFm6/UUd+WHiwwAfwocAT4BfsMYs7rFcT8APg/8L2PMr+7kvaenp83p06cfXGPVnvagZsV3+j46C7/nyU4O6vcn+w3gLWPMCeCt3vOt/CHwO7vWKrXvPKgz352+j9aGPh76/el+BXij9/gN4KtbHWSMeQuo7VajlFJqJ/odoKPGmNne4zlg9H7eTER+T0ROi8jpxcXF+2+dUkrdwUOfhReRN4GxLV56ffMTY4wR2WaDmx0yxnwT+CbE10Dv572UUupuHnqAGmNe3u41EZkXkXFjzKyIjAMLD7s9Sin1oPR7CP994LXe49eA7/WxLUopdU/6HaB/ALwiIheAl3vPEZFpEfnWjYNE5MfAd4Avi8iMiPxKX1qrlFKb9PVOJGPMMvDlLb5/Gvhnm57/4m62SymldqLfZ6BKKbVnaYAqpVRCGqBKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCWmAKqVUQhqgSimVkAaoUkolpAGqlFIJaYAqpVRCGqBKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCWmAKqVUQhqgSimVkAaoUkolpAGqlFIJaYAqpVRCGqBKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCWmAKqVUQhqgSimVkAaoUkolpAGqlFIJaYAqpVRCGqBKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCWmAKqVUQn0NUBEZEJG/FJELvX8rWxzzvIj8RETOiMj7IvKb/WirUkrdqt9noN8A3jLGnADe6j2/VRP4XWPM08CrwB+JSHkX26iUUlvqd4B+BXij9/gN4Ku3HmCMOW+MudB7fB1YAIZ3rYVKKbWNfgfoqDFmtvd4Dhi908Ei8lnAAy5u8/rvichpETm9uLj4YFuqlFK3cB72DxCRN4GxLV56ffMTY4wREXOH9xkH/gR4zRgTbXWMMeabwDcBpqent30vpZR6EB56gBpjXt7uNRGZF5FxY8xsLyAXtjmuCPwF8Lox5u2H1FSllLon/R7Cfx94rff4NeB7tx4gIh7wZ8C3jTHf3cW2KaXUHfU7QP8AeEVELgAv954jItMi8q3eMb8BfAn4moi81/t6vj/NVUqpT4kx+/NS4fT0tDl9+nS/m6GU2ptkJwf1+wxUKaX2LA1QpZRKSANUKaUS0gBVSqmENECVUiohDVCllEpIA1QppRLSAFVKqYQ0QJVSKiENUKWUSkgDVCmlEtIAVUqphDRAlVIqIQ1QpZRKSANUKaUS0gBVSqmENECVUiohDVCllEpIA1QppRLSAFVKqYQ0QJVSKqF9uyuniCwCl3fpxw0BS7v0s3bbfu3bfu0X7N++7Wa/lowxr97toH0boLtJRE4bY6b73Y6HYb/2bb/2C/Zv3x7FfukQXimlEtIAVUqphDRAH4xv9rsBD9F+7dt+7Rfs3749cv3Sa6BKKZWQnoEqpVRCGqBKKZWQBmgCIjIgIn8pIhd6/1a2OOZ5EfmJiJwRkfdF5Df70dZ7tZO+9Y77gYisicif73Yb74WIvCoiH4rIRyLyjS1eT4nIn/Ze/78icmT3W3nvdtCvL4nIuyISiMiv96ONSe2gb/9cRP629//qLRE53I92ggZoUt8A3jLGnADe6j2/VRP4XWPM08CrwB+JSHkX25jUTvoG8IfA7+xaqxIQERv4T8A/AJ4CfktEnrrlsK8Dq8aY48B/AP7d7rby3u2wX1eArwH/ZXdbd3922LefAdPGmGeB7wL/fndb+SkN0GS+ArzRe/wG8NVbDzDGnDfGXOg9vg4sAMO71sLk7to3AGPMW0BttxqV0GeBj4wxHxtjfOC/Evdvs839/S7wZRGRXWxjEnftlzHmE2PM+0DUjwbeh5307a+NMc3e07eBg7vcxg0aoMmMGmNme4/ngNE7HSwinwU84OLDbtgDcE99e8QdAK5uej7T+96WxxhjAmAdGNyV1iW3k37tVffat68D/+OhtugOnH794EediLwJjG3x0uubnxhjjIhsWwsmIuPAnwCvGWMeibOBB9U3pfpJRH4bmAZ+qV9t0ADdhjHm5e1eE5F5ERk3xsz2AnJhm+OKwF8Arxtj3n5ITb1nD6Jve8Q1YHLT84O97211zIyIOEAJWN6d5iW2k37tVTvqm4i8TPwH/5eMMZ1datttdAifzPeB13qPXwO+d+sBIuIBfwZ82xjz3V1s2/26a9/2kHeAEyIy1fs8/ilx/zbb3N9fB/7KPPp3l+ykX3vVXfsmIi8Afwz8mjGmv3/gjTH6dY9fxNfI3gIuAG8CA73vTwPf6j3+baALvLfp6/l+t/1B9K33/MfAItAivk71K/1u+zb9+YfAeeLrz6/3vvf7xP/5ANLAd4CPgP8HHO13mx9Qv17qfS4N4jPqM/1u8wPs25vA/Kb/V9/vV1v1Vk6llEpIh/BKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCWmAqseCiPy1iLzSe/yvReQ/9rtNau/Te+HV4+JfAr8vIiPAC8Cv9bk9ah/QO5HUY0NEfgjkgb9njKmJyFHiBSlKxpg9tWq7ejToEF49FkTkM8A44BtjagAmXrT36/1tmdrLNEDVvtdblu8/E69sXheRV/vcJLVPaICqfU1EssB/A/6FMeYs8K+Ir4cqdd/0Gqh6bInIIPBvgFeIl+r7t31uktpjNECVUiohHcIrpVRCGqBKKZWQBqhSSiWkAaqUUglpgCqlVEIaoEoplZAGqFJKJaQBqpRSCf1/VQhTPmiKb2cAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_unrotate = unrotate(x_scaled, V_trans)\n", "plot(x_unrotate, set1, set2, [-0.25, 0.25], [-0.25, 0.25], 'Unrotated')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have successfully decorrelate the different feature dimension of the data. Note that this means that after the whitening process it is as if we are sampling data from a multivariate gaussian with covriance identity matrix!" ] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }