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Created February 10, 2013 14:25
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Coursera Data Analysis -- in Python
{
"metadata": {
"name": "svd_pca"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Principal components analysis and singular value decomposition -- in Python"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pandas as pd\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# a simple function to compute hierarchical cluster on both rows and columns, and plot heatmaps\n",
"def heatmap(dm):\n",
" from scipy.cluster.hierarchy import linkage, dendrogram\n",
" from scipy.spatial.distance import pdist, squareform\n",
" \n",
" D1 = squareform(pdist(dm, metric='euclidean'))\n",
" D2 = squareform(pdist(dm.T, metric='euclidean'))\n",
" \n",
" f = figure(figsize=(8, 8))\n",
"\n",
" # add first dendrogram\n",
" ax1 = f.add_axes([0.09, 0.1, 0.2, 0.6])\n",
" Y = linkage(D1, method='complete')\n",
" Z1 = dendrogram(Y, orientation='right')\n",
" ax1.set_xticks([])\n",
" ax1.set_yticks([])\n",
"\n",
" # add second dendrogram\n",
" ax2 = f.add_axes([0.3, 0.71, 0.6, 0.2])\n",
" Y = linkage(D2, method='complete')\n",
" Z2 = dendrogram(Y)\n",
" ax2.set_xticks([])\n",
" ax2.set_yticks([])\n",
"\n",
" # add matrix plot\n",
" axmatrix = f.add_axes([0.3, 0.1, 0.6, 0.6])\n",
" idx1 = Z1['leaves']\n",
" idx2 = Z2['leaves']\n",
" D = dm[idx1, :]\n",
" D = D[:, idx2]\n",
" im = axmatrix.matshow(D, aspect='auto', cmap='hot')\n",
" axmatrix.set_xticks([])\n",
" axmatrix.set_yticks([])\n",
" \n",
" return {'ordered' : D, 'rorder' : Z1['leaves'], 'corder' : Z2['leaves']}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%load_ext rmagic"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%R -o dataMatrix\n",
"set.seed(12345); par(mar=rep(0.2,4))\n",
"dataMatrix <- matrix(rnorm(400),nrow=40)\n",
"\n",
"set.seed(678910)\n",
"for(i in 1:40){\n",
" coinFlip <- rbinom(1,size=1,prob=0.5)\n",
" if(coinFlip){\n",
" dataMatrix[i,] <- dataMatrix[i,] + rep(c(0,3),each=5)\n",
" }\n",
"}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# dataMatrix is generated and pattern-added using the same R commands as in the video\n",
"f, ax = subplots(ncols=1)\n",
"\n",
"ax.matshow(dataMatrix, aspect='auto', cmap='hot');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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kA9iekQ4A4AbpALYHvXdLRwDwF+kAtnrpALYD0gGA8pGip1fTg9jAIDY2FqmpqQCAiIgI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\n"
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# the heatmap after a pattern is added\n",
"# note: the resulting cluster pattern is somehow mirrored compared to the one in the video\n",
"hh = heatmap(dataMatrix)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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EUMCBapNqo5cmvhTLWKnJvAwCAELDGjAAAAYUMAAABhQwAAAGrAG3clv/4k4Q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\nRU5ErkJggg==\n"
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# patterns in rows and columns; compute and plot column and row means\n",
"f, (ax1, ax2, ax3) = subplots(ncols=3)\n",
"\n",
"dataMatrixOrdered = hh['ordered']\n",
"\n",
"ax1.matshow(dataMatrixOrdered, cmap='hot')\n",
"\n",
"ax2.plot(np.mean(dataMatrixOrdered, axis=1), range(39, -1, -1), 'ok')\n",
"ax2.set_xlabel('Row Mean')\n",
"ax2.set_ylabel('Row')\n",
"\n",
"ax3.plot(np.mean(dataMatrixOrdered, axis=0), 'ok')\n",
"ax3.set_xlabel('Column')\n",
"ax3.set_ylabel('Column Mean')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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6+qJPnz6yOHVGRB0KOyPaAzYPWVlZcHR0VLm8s7MznJ2dAQADBgyAj48PKisr\nkZGRgZMnTwIAEhISIBKJqDNSgzFl0nWWnp6OX3/9lXm+ixBVKOyMaA/YPPTt2xdvvvkmTp06BQAQ\niURYv369StcalZWVoaioCGFhYaipqYGTkxMAwMnJCTU1NYLPSUpKkv0tEokgEol6/BpMgS4z6SQS\nic5SsT09PdHc3EydEekRhZ1Rz/aAX2fUeo0RZ8xl9RGjOC+QOTeHUZbxvzyXkU0nvS0cd2VUb+wW\nLFgAf39//Otf/wLP8/jqq68wf/58fPPNNwqfV19fj+nTpyM1NRW2trZdHuM4jpmV17kzIo/oMpOu\ne6efnJzc4zo79OvXD0FBQRg/frzsNXAcJ5s9ghBVqHzOSJM9YGIcSktLu3Q8SUlJCAwMVPiclpYW\nTJ8+HfPmzcPUqVMBtH8Xqqur4ezsjKqqKrWG/ojxzk8XFxeHuLi4LjG6PICoS6XOSJM94KSkR1Nc\ni0R/gEg0pIdN1b+C/95MTb9+/ZCXlye70PX06dOwsbFhlud5HgsXLoSvry9WrFghi8fFxSEtLQ1r\n1qxBWlqarJMiqlG2AJ8q9LFa7CuvvKLT+ol54HihZRo7aWlpweTJkxETEyP74fH29oZEIpHtAY8b\nNw6//PLLo0o5Djw/jVHjl4w4Y5iO36XsNTzyCiPOGKYrPSgcd2dUU97tvgcguMqlsSkuLkZ8fDzq\n6uoAAA4ODkhLS2MeHZ0+fRpjx45FQECAbEdk06ZNeOqppzBz5kxcv36dmdjCWhmU9JxQNp6npydS\nU1PlOiRtfg7fffcd1q9fj7KyMrS2tsrq1/dKr/RdMwyqfg4KOyOe55GQkIDBgwdj69atsvjq1asx\nePBgrFmzBikpKaitre1yzog6I+NUV1cHjuNga2uLgwcPYtasWVrfBv1A6I5YLBacsFQsFiM7O7tL\nTJufg6enJ9LT0zFq1ChYWBjOdfT0XTMMqn4OCofp8vPzsXfvXgQEBCA4OBhA+x7w2rVrMXPmTOze\nvVu2ByznXrpwpQ5PKm99Z5sY8f8n/+KGfSk8Tu3PqGIdI85a/s/UpgOqr6/Hzp07UVpailGjRuG1\n117Dt99+i7fffhteXl466YyI7uhrXjs3Nzf4+fkZVEdEjI/Czig8PBxtbW2Cjx0/flwnDSK9Jz4+\nHnZ2dnjmmWeQk5ODL774AtbW1vjnP/+JoKAgfTePqElf89pt3rwZMTExGDduHPr27QugfW+YVnsl\n6qAZGMznsePDAAAgAElEQVTYlStXcPHiRQDAokWL4OLigmvXrqFfv356bpnx0UfiQHf6ysZ79913\nYWtri6amJjQ3N+t0W8R0UWdkxjpP3dKnTx+4urpSR6QBocQBfSyIp41sPE1UVVXh2LFjOt0GMX3U\nGZmxixcvdknVb2xslN03hGwoY2FI0/jExsb2+jYnTZqE77//HmKxuFe3S0wLdUZmTCqV6rsJJsHc\nF8T729/+hr/+9a/o27cvrKysANDODFGf7joj5jnTROHwG2uF4ztGCsfvy2fOLWds8X98hOONPwvH\nuU+E4y92z9n4mrFBYlbMfUG8+vp6fTeBmAA6MiKkh4x1Gh9t6ZhgtztaQoKogzojQnpI14kDhpCp\np8gHH3wgm4mjqakJhYWFGD16NE6cOKHnlhFjQp0RIVqgq8QBQ8nUU+TIkSNd7peXl2P5ctagOSHC\n6JJpQgyYokw9Q+Xm5oaff2ackCWEgY6MCDFgxpCp1/ncWFtbG4qLizF69Gg9togYI911Rv0CGA+s\nEQ7vYCzE9bffhOPPy4f+h7EwqYSxk8aas67fDcYD3bdJ2XREx4whU69zx2NpaYk5c+YgPDxcjy0i\nxoiOjAgxYMaQqUfrGRFtoM6IEAOmSqaevrLt/P1ZYwvtF712zHuoiezsbKxYsQJSqRSLFi3CmjVd\nR1QkEgmef/55PPFE+xz706dPxzvvvKPx9oj+UWdEiIFTlKmnz2y77777Tif1SqVSvPHGGzh+/Dhc\nXV0xZswYxMXFwcen69XrkZGRyMjI0EkbSO+jbDpCjJg+s+3c3d1lt379+qGkpASXLl2CjY0N3N3d\nNa63sLAQXl5ecHd3h5WVFWbPno1vv/1WrhwtnGda6MiIECNmCNl2Bw8exFtvvYXIyEgAwBtvvIEt\nW7bgxRdf1Ki+yspKDBs2THbfzc0NP/zwQ5cyHMfhzJkzCAwMhKurK/7617/C19dXrq6kpCTZ3yKR\nCCKRSKM2EdVJJBJIJBK1n6ezzug7Tni8+BqEV2N9w0a4nuIG4XjQB/Kxb+qEy+4TDuNfPwjH/xkm\nHL/LqIcQfTGEbLs///nP+PHHH+Ho6AgAuHXrFsaPH69xZ9Qxm4MiISEhKC8vh42NDY4ePYqpU6fi\nt9/kM287d0akd3Tv9JOTk1V6Hg3TEWLEEhMT4enp2SXW29l2PM9jyJAhsvuDBw/u0RCaq6srysvL\nZffLy8vh5ubWpYytrS1sbNr3YGNiYtDS0oK7d2l30ZjRMB3RyIIFC5CZmQlHR0eUlJQAaN8L/eyz\nz2Q/TJs2bcLEiRNVrtPQ52AzRPpaUK+ziRMnQiwW46WXXgLP8zhw4ABiYmI0ri80NBSXL19GWVkZ\nhg4digMHDmDfvq7jGzU1NXB0dATHcSgsLATP8xg0aFBPXwrRI+qMiEbmz5+PZcuWIT4+XhbjOA4r\nV67EypUr1a7PGOZgM1T6WFCvsy1btuDrr79Gfn4+AGDJkiWYNm2axvVZWlpix44dEIvFkEqlWLhw\nIXx8fLBz505Z/YcOHcInn3wCS0tL2NjYYP/+/Vp5LUR/OF7B8XR5eTni4+Nx8+ZNcByHxYsXIzEx\nUekeMMdxYCVcXmPE1T5nNFw+9g2jcl2dM1oG887oKSsrw5QpU2RHRsnJyRgwYABWrVrFfA7HcYLv\nmVgsRk5OjmA8Oztbe40mANifgzouX76MmpoaudkWTp8+DRcXF7nhw96mjddIek7Vz0HhkZGVlRW2\nbt2KoKAg1NfXY/To0YiKiurRHjAxbdu3b8eXX36J0NBQfPjhh7C3t5crI5ThZAhZYaZM0wwnRVas\nWIFNmzbJxe3s7LBixQqdXYdETJPCzsjZ2RnOzs4AgAEDBsDHxweVlZUAlB8RsBa0vsyI32QcATEX\nxi6XDz1gFP0TI17AOAKSv6Kh3YGu51CxrIJR0EwtXboU69evBwC8++67WLVqFXbv3i1XTijDyRCy\nwkyZphlOitTU1CAgQH4OyoCAAFy9erXH9RPzonI2XVlZGYqKivD0008DaN8DDgwMxMKFC1FbW6uz\nBhLj0XFCmeM4LFq0CIWFhSo/1xCywoh6FP3f0xEtUZdKnVF9fT1mzJiB1NRUDBgwAEuXLsXVq1dR\nXFwMFxcXwXME+zvdLmm3zXojeQgk3X90I11VVVXJ/k5PT2fOXSYSiSAWi5GZmSmLxcbGIjU1FWKx\nGJGRkRCLxUhNTaXkBQMWGhqKTz/9VC6+a9cuWkKCqE1hAgMAtLS0YPLkyYiJicGKFSvkHu9+Ehto\nP2GVzqgvlxF/mxEXGI0DAIwW6EbT2oTLCuQ6AABYA0BbGfHuw3RchfkmMMyZMwcnT57E7du34eTk\nhOTkZEgkEhQXF4PjOHh4eGDnzp1wcnLq8rzOFzR6enpSh6Mn2ji5X11djWnTpqFv376yzufcuXN4\n+PAh0tPT4eLioo2maowSGAyDqp+Dws6I53kkJCRg8ODB2Lr10U90VVWV7Iu2detW/Pjjj/jnP//Z\nZePUGREh3a+up2w5/dDWDzXP88jNzcWlS5fAcRz8/Pzw3HPPaaGFPUedkWHQSmd0+vRpjB07FgEB\nAbIfkY0bN2Lfvn0K94A5jgPPyBr48WPhuIjRhtVKX8IjG/4gHP/ltnDcO5RRUbVwWNItYWEcqDNS\nV/fOKDIyUutZXkQ5c/ihNofXaAy0ktodHh6Otjb5w42eXF1NSGeULUcIAWhuOqJH3bPlMjMzIRaL\nBRMcCCGmjaYDIr0uMjJSbg41mg6IEPNGnRHpdULniBQtEkedESGmj4bpiEGg6YAIMW86OzKSMrLm\nxjByuNf/RTh+gFH/34SCu4TLek8XjqedFY4nMOb5FN3oFmDNwErURtMBEWLe6MiIGASaDogQ80bn\njIhB0OYicbRIHyHGhzojYjC0sUgcZeURoju63NGjzoiYFMrKI0Q31N3R6+i4VEXnjIhJoaw8QnRD\n0Y5edx0dl9DqzSw6OzJKY8T7M7Lm1gxixH0ZFYULxP7DKDtHOJzwK6O8/OKkAIDPP2SUJwaDsvII\n0Q11dvSEOi5l6MiImBTKyiNEN9TZ0WN1XIrQOSNiUjTJyqPsO0KUS0xMRGlpaZcjHtaOHqvjUoQ6\nI2Jy1MnKo+w7QlSjzo6eUMelDHVGxKxR9h0xJvo+ild1R69zx/X999+rVDd1RsSsUfYdMRbqHMXr\nu9PqaFNsbKzcgposOuuMFjDW+v7mGuMJvwuHy04Lx92fEQh+IFz2nRrh+J8ZawQWvyscDxQOEyNG\n2XfEWKh6FG+sQ8+UTUfMGmXfEWOh6lG8OtcDGRIapiMaWbBgATIzM+Ho6IiSkhIAwN27dzFr1ixc\nu3YN7u7uOHjwIOztGRdtaVFPhiS0OSceIbqk6lG8sQ49U2dENDJ//nwsW7YM8fHxslhKSgqioqKw\nevVqbN68GSkpKUhJSdFpO7QxJKGNOfEI0TVVU6uNdehZ4TBdU1MTwsLCEBQUBF9fX6xbtw5A+x5w\nVFQURo4ciejoaNTW1vZKY4nhiIiIgIODQ5dYRkYGEhISAAAJCQk4fPiwztthrEMShKgrNjYWqamp\nEIvFiIyMhFgsRmpqqtyOlLEOPSs8MrK2tkZubi5sbGzQ2tqK8PBwnD59GhkZGb2+B0wMX01NDZyc\nnAAATk5OqKkRzhxJSkqS/S0SiSASiTTeprEOSfQ2iUQiuNw7MS6qHMUb69Cz0mE6GxsbAEBzczOk\nUikcHByQkZGBkydPAmjfAxaJRPKd0TDh+oawsukY88ed/EI43rxFPsaamo6xuCzAmPfO9qhwnBEm\nAjiOY6Z0du6MespYhyR6W/dOPzk5WX+NITpnjEPPSrPp2traEBQUBCcnJ4wbNw5+fn4q7wET8+Lk\n5ITq6moAQFVVFRwdHXW+TWMdkiCEdKX0yMjCwgLFxcWoq6uDWCxGbm5ul8dZe8BJ1x/9LRrYfjN2\nl/97I8Li4uKQlpaGNWvWIC0tDVOnTtXp9jqy6GxsbDB48GA4OzvDzc3NKIYkCCFdqZxNN3DgQMTG\nxuLcuXOyPWBnZ2fmHnDS41ptp0EY8d9bB3MetpszZw5OnjyJ27dvY9iwYXjvvfewdu1azJw5E7t3\n75alduuKUBadvb09dUSEGCmFndHt27dhaWkJe3t7NDY24tixY9iwYUOv7wETw7Nv3z7B+PHjx3tl\n+zSnHCGmRWFnVFVVhYSEBLS1taGtrQ3z5s3D+PHjERwc3Gt7wIQIoSw6QkyLws7I398f58+fl4sP\nGjRI+R6wlXA4YgWj/B7h8C1G8TaB2MSnhMueKBSOP8f43SpnbPONbivoLotmFCQ6R1l0hJgWmpuO\nGKWeZtFlZmZCLBZDJBJBLBYjMzNTF80kGsrOzoa3tzdGjBiBzZs3C5ZJTEzEiBEjEBgYiKKiol5u\nIdE2mg6IGKWeXNhnrLMamwupVIo33ngDx48fh6urK8aMGYO4uDj4+PjIymRlZeHKlSu4fPkyfvjh\nByxduhQFBQV6bDXpKeqMiNHS9MI+Sn4wbIWFhfDy8oK7uzsAYPbs2fj222+7dEadp54KCwtDbW1t\nl+sfifGhzoiYHUp+MGyVlZUYNuzRFC5ubm744YcflJapqKiQ64y0OfUUUY2mU0/prDO6lyscd2As\nlodg4fD/PGCUbxCI+QsXHcRIYPjzx8LxM4xNiuRzOYgRouQHw6bqyqA8zyt9njanniKq0XTqKUpg\nIGaHphAybK6urigvf5TTWl5eDjc3N4VlKioq4Orq2mttJNpHw3TEpKiy0J6xzmpsLkJDQ3H58mWU\nlZVh6NChOHDggNxF1nFxcdixYwdmz56NgoIC2Nvb0/kiI0edETEZ6mTJGeOsxubC0tISO3bsgFgs\nhlQqxcKFC+Hj44OdO3cCAJYsWYJJkyYhKysLXl5e6N+/P/bsYVyoSJTqyUrJ2sTx3QdetVEpx+Eu\n4zEHxsWwrHNGUOec0QThosW7heNHGFWzzhlldVslg1srP25NFOM4TmfvmVgsRk5OjmA8OztbJ9s0\nVrr8HAyFObzGnhLagfP09BRctE9Tqn4OdM6ImAzKkiNEPYa0UrLOhumEfxYUYK2M18KI/10g9oNA\nDECQcPIUgrwZdd9hxFnzBBGDQFlyhKjHkHbg6MiImAzKkiNEPYa0A0cJDMRkaDtLzlBO7BKiK4mJ\niSgtLZU7Z6SPHTjqjIhJ0VaWHM1fR8yBIV3moLNsuirGY86sbDrWsuRaOGeETxhxdc8ZPd/1Lvcx\nZdOpy1gynEw9M89YPoeeMIfXaAwom46QHjCkE7uEmAOdDdO9zojvZhzpOLCOgE4x4gLXJS0XWnEP\nQKqbcHzSBeF4FqM8shhxYnIM6cQuIeaAjowIEUCZeYT0LkpgIFrn7u4OOzs79OnTB1ZWVigsZEyb\nroHeynAzpBO7hJgD6oyI1nEcB4lEgkGDBmm13t7OcKP56wjpPQqH6ZqamhAWFoagoCD4+vpi3bp1\nANrXCHFzc0NwcDCCg4NNIruIaJcuspgMaeoSQoh2KTwysra2Rm5uLmxsbNDa2orw8HCcPn0aHMdh\n5cqVWLlyZW+1kxgRjuMwYcIE9OnTB0uWLMGrr77a5XFNV9+kDDfNabr6JiG9RekwnY2NDQCgubkZ\nUqkUDg4OAJTv+TIS1Zhz1p2rE46Pfk84XiqQOce6hOl6hXA8kFEeYuHwnxmzf5Ou8vPz4eLiglu3\nbiEqKgre3t6IiIiQPa7p6puU4aY5TVffJKS3KM2ma2trQ1BQEJycnDBu3Dj4+fkBaD+xGxgYiIUL\nF6K2tlbnDSXGw8XFBQAwZMgQTJs2TWsJDJThRojpUtoZWVhYoLi4GBUVFTh16hQkEgmWLl2Kq1ev\nori4GC4uLli1apXc8+51ujVqv916cRXAiU43Iq+hoQEPHrQvQvX7778jJycH/v7+cuUyMzMhFosh\nEokgFouRmZmptO7Y2FikpqZCLBYjMjISYrFYq+uuEEL0R+VsuoEDByI2NhZnz57tcri/aNEiTJky\nRa68g1aaZ1g8/nvrkKuvhhiwmpoaTJs2DQDQ2tqKl19+GdHR0V3K9CQrjjLcCDFNCjuj27dvw9LS\nEvb29mhsbMSxY8ewYcMGVFdXw9nZGQCQnp4uuOdLzJOHhweKi4sVllGUFUcdDSHmSWFnVFVVhYSE\nBLS1taGtrQ3z5s3D+PHjER8fj+LiYnAcBw8PD9na9ISogrLiCCHd6WzWbp6VqsbIdfC7JhzPYFTT\nXyDmLDBfHQCkFgnHQxh1RwxlPDC8613u/2jWbnVxHIfo6GiTnhHbGJjDjNbm8BqNAc3aTQyWpllx\nmiQ9EEKMA00HRHqdJvO+0WJ3hJg26oyIXqibFUdJD4SYNhqmI0aBkh4IMW3UGRGjQFMBEWLadDZM\nJ2VMTneAUT6REfccKBx/U2Auu622wmVnMeo+w4jfvCEcb2DEie4lJiaitLS0y1AdTQVEiOmgc0bE\noLAWz6PF7ggxbdQZEYOhLGOOpgIixHTROSNiMGjxPELMF3VGxGBQxhwh5ktnw3R9GN3cNIFF8QCg\nn3CyFGAvHA4RSGDgTwmXdWYkQZQxFvR7YRSjLb93u3+VUY5ohDLmCDFfdGREDAYtnkeI+aIEBmIw\nNM2YY2XgEUKMB3VGxKComzFHc9YRYhpomI4YNcrAI8Q0UGdEjBpl4BFiGnQ2TPdvRtacX5xwPJmx\nit5SxqJ780LVaAxjob9Lu4XjJy4JxxlJeUSPKAOPENOg8yOjH9UsX6ZmeckDNcpWqVd3sXrFSS+R\nSCSyvzXJwOv8/J5uX191aKMN5BF13k9jKqvv7auDOiMFGHO9EiWys7Ph7e2NESNGYPPmzVqvf9eu\nXbIVX7dt24a5c+dCLBYjMjISYrEYqampCpMXDKEjMIQ2GKK7d+8iKioKI0eORHR0NGprawXLubu7\nIyAgAMHBwXjqqad6vF1D+NE2986IsumIVkmlUrzxxhs4fvw4XF1dMWbMGMTFxcHHx0cr9WdmZuLo\n0aO4d++eLFZaWqq0AyLGISUlBVFRUVi9ejU2b96MlJQUpKSkyJXjOA4SiQSDBg3SQyuJLlACA9Gq\nwsJCeHl5wd3dHVZWVpg9eza+/fZbrdW/bdu2Lh0RQNlzpiQjIwMJCQkAgISEBBw+fJhZluf53moW\n6QUcr4NPlOM4bVdpsOgfoqtDhw7h+++/x65duwAAe/fuxQ8//CDrLMzpu2HoDPG76+DgINvZ4Hke\ngwYNktv5AIAnnngCAwcORJ8+fbBkyRK8+uqrcmXou2Y4VPmu6WSYzhC/5KR3KPsBoO8GiYqKQnV1\ntVz8L3/5S5f7HMcxv0/5+flwcXHBrVu3EBUVBW9vb0RERHQpQ98140LnjIhWubq6ory8XHa/vLwc\nbm5uemwRMTTHjh1jPubk5ITq6mo4OzujqqoKjo6OguVcXFwAAEOGDMG0adNQWFgo1xkR40LnjIhW\nhYaG4vLlyygrK0NzczMOHDiAuDjGxWWEdBMXF4e0tDQAQFpaGqZOnSpXpqGhAQ8etKfR/v7778jJ\nyYG/v3+vtpNoH3VGRKssLS2xY8cOiMVi+Pr6YtasWVrLpCOmb+3atTh27BhGjhyJEydOYO3atQCA\nGzduyLIlq6urERERgaCgIISFhWHy5MmIjo7WZ7OJNvCE6NCdO3f4CRMm8CNGjOCjoqL4e/fuCZYb\nPnw47+/vzwcFBfFjxozheZ7njx49yj/55JO8l5cXn5KSIvi8ZcuW8V5eXnxAQAB//vz5Lo8pe35u\nbi5vZ2fHBwUF8UFBQfz777/f5fH58+fzjo6O/KhRo5ivT9H2lT1f2favX7/Oi0Qi3tfXl/fz8+NT\nU1PVboMqdShrhzFS5bvD86p9xh1U/Tx4nucbGxv5p556ig8MDOR9fHz4tWvXKqy7tbWVDwoK4idP\nnqy0HUL/K0Lu3bvHT58+nff29uZ9fHz4//u//2OW/eWXX2Sff1BQEG9nZ8d8fRs3buR9fX35UaNG\n8XPmzOGbmpqY9X700Uf8qFGjeD8/P/6jjz5S+LqoMyI69dZbb/GbN2/meZ7nU1JS+DVr1giWc3d3\n5+/cuSO739raynt6evJXr17lm5ub+cDAQP6nn37q8pzMzEw+JiaG53meLygo4MPCwtR6fm5uLj9l\nyhRm20+dOsWfP3+e+UOlaPuqPF/Z9quqqviioiKe53n+wYMH/MiRI9V6D1StQ1k7jI0qn30HZZ9R\nZ6q8l539/vvvPM/zfEtLCx8WFsbn5eUxy3744Yf8Sy+9pNLn0P1/hSU+Pp7fvXu3rA21tbVKn8Pz\nPC+VSnlnZ2f++vXrco9dvXqV9/DwkHVAM2fO5L/44gvBekpKSvhRo0bxjY2NfGtrKz9hwgT+ypUr\nzO3SMB3RKU2vG1HleqXOdYeFhaG2thY1NTUqP7/7NruLiIiAg4ODSq+t+/ZVeb6y7Ts7OyMoKAgA\nMGDAAPj4+ODGjRtqtUGVOpS1w9ioc62bKp9RB1Xfyw42NjYAgObmZkilUuYFuhUVFcjKysKiRYtU\n/hyUlaurq0NeXh4WLFgAoH34fOBA1WbXPH78ODw9PTFs2DC5x+zs7GBlZYWGhga0traioaEBrq6u\ngvX88ssvCAsLg7W1Nfr06YPIyEh88803zO1SZ0R0qqamBk5OTgDaM6U6/1B2xnEcJkyYgNDQUOza\ntQuVlZVd/hnc3NxQWVnZ5TlCZSoqKpiPdX8+x3E4c+YMAgMDMWnSJPz0009qvTZF21eFOtsvKytD\nUVERwsLCNG4Dq46evg+GRpXPvqdY72VnbW1tCAoKgpOTE8aNGwdfX1/Bcm+++Sa2bNkCCwvVfo67\n/68IuXr1KoYMGYL58+cjJCQEr776KhoaGlSqf//+/XjppZcEHxs0aBBWrVqFxx9/HEOHDoW9vT0m\nTJggWHbUqFHIy8vD3bt30dDQgMzMTIX/H9QZkR6LioqCv7+/3C0jo+tU7MquGykqKsLRo0fx8ccf\n45dfflFp2933EDvqV+WCx5CQEJSXl+PChQtYtmyZYOaWpttXharbr6+vx4wZM5CamooBAwZo1AZF\ndWjjfTAkur7YVdnn0cHCwgLFxcWoqKjAqVOnBOdzO3LkCBwdHREcHKzyUVH3/5W8vDy5Mq2trTh/\n/jxef/11nD9/Hv379xecVqm75uZmfPfdd3jxxRcFHy8tLcVHH32EsrIy3LhxA/X19fjHP/4hWNbb\n2xtr1qxBdHQ0YmJiEBwcrLDDpc6I9NixY8dQUlIid4uLi5NdNwJAretGbt68qfR6pe7XNFVUVMiG\nDFS53snW1lY2lBITE4OWlhbcvXtX5detaPuqUGX7LS0tmD59OubOnSvYSajSBmV19PR9MDS6vNZN\n2XspZODAgYiNjcXZs2flHjtz5gwyMjLg4eGBOXPm4MSJE4iPj1dYn9A1Vt25ubnBzc0NY8aMAQDM\nmDED58+fV9rWo0ePYvTo0RgyZIjg42fPnsWzzz6LwYMHw9LSEi+88ALOnDnDrG/BggU4e/YsTp48\nCXt7ezz55JPMstQZEZ3S9LqRmJgYpdcrxcXF4csvvwQAFBQUwN7eXjYkqMr1TjU1NbK90cLCQtn0\nM+q8Ntb2VaFs+zzPY+HChfD19cWKFSs0aoMqdfT0fTA0urrWTZX3ssPt27dlM443Njbi2LFjCA4O\nliu3ceNGlJeX4+rVq9i/fz+ee+452ecpRNVrrJydnTFs2DD89ttvANrPA/n5+Sl9jfv27cOcOXOY\nj3t7e6OgoACNjY3geR7Hjx9nDj8CwM2bNwEA169fR3p6OnP4DwCldhPdunPnDj9+/Hi51O7Kykp+\n0qRJPM/zfGlpKR8YGMgHBgbyfn5+/MaNG3me5/msrCx+5MiRvKenpyz297//nf/73/8uq/9Pf/oT\n7+npyQcEBPDnzp3rsm1lz9+xYwfv5+fHBwYG8s8884xc6uvs2bN5FxcX3srKindzc+N3796t1vaV\nPV/Z9vPy8niO4/jAwEBZym1WVpZabVClDmXtMEZCn72Qjs+ob9++vJubG//5558zywq9l0ePHhUs\ne/HiRT44OJgPDAzk/f39+Q8++EBpmyUSidJsuv/85z+C/ytCiouL+dDQUD4gIICfNm2a0my6+vp6\nfvDgwfz9+/cVltu8ebMstTs+Pp5vbm5mlo2IiOB9fX35wMBA/sSJEwrr1clEqYQQQog6aJiOEEKI\n3lFnRAghRO+oMyKEEKJ31BkRQgjRO+qMiEnq06cPgoODERAQgBdeeAH19fVaq/uLL76AhYUF/vd/\n/1cWO3z4MCwsLBROd0LMS3V1NWbPng0vLy+EhoYiNjYWly9fFixbVlZm9stgUGdETJKNjQ2Kiopw\n8eJF2NnZYefOnVqrm+M4+Pv7Y//+/bLYvn37ZPOWEcLzPKZNm4bnnnsOV65cwdmzZ7Fp0ybmdFiE\nOiNiBp555hmUlpYCAIqLi/H0008jMDAQL7zwAmpra3Hz5k2EhoYCAC5cuAALCwvZHFqenp5oamqS\nqzMiIgKFhYVobW1FfX09SktLERgYKLt49Ny5cxCJRAgNDcXEiRNls1Ds2rULTz31FIKCgjBjxgw0\nNjYCAF555RUsX74cf/zjH+Hp6Ymvv/5a5+8L0Z3c3Fz07dsXixcvlsUCAgIQHh6Ot956C/7+/ggI\nCMDBgwflnvvFF19g2bJlsvuTJ0/GqVOnALRP0Lp69WqMGjUKUVFRKCgoQGRkJDw9PfHdd9/Jnv/C\nCy8gJiYGI0eOxJo1a3T8arWDOiNi0qRSKXJycjBq1CgAQHx8PLZs2YILFy7A398fycnJcHR0RFNT\nEx48eIC8vDyMGTMGp06dwrVr1+Dk5ARra2u5ejmOQ1RUFL7//ntkZGTIrvDnOA4tLS1YtmwZvv76\na5w9exbz58/H22+/DQCYPn06CgsLUVxcDB8fH+zevVtWZ3V1NfLz83HkyBHZonLEOF26dAmjR4+W\ni5SjqKQAAANeSURBVH/99de4cOECLl68iOPHj+Ott95SerTUea69hoYGjB8/HpcuXYKtrS3Wr1+P\nEydOID09HevXr5eVu3DhAg4ePIiSkhIcOHBA6xPF6oKlvhtAiC40NjYiODgYlZWVcHd3x2uvvYa6\nujrU1dUhIiICQPuSFh0TQj777LPIz89HXl4e1q1bh+zsbPA8LysrZNasWUhNTcX9+/fx4YcfYuPG\njeB5Hr/++iv+/e9/y2YzlkqlGDp0KACgpKQE77zzDurq6lBfX4+JEycCaP/B6ZgqycfHh4ZzjJyi\nCYFfeuklcBwHR0dHREZGorCwUOXzRX379oVYLAYA+Pv7y5ZnGDVqFMrKymTlxo8fD1tbWwCAr68v\nysrK1Jo3UR+oMyImqV+/figqKkJjYyPEYjG+/fZbjB8/vkuZzpOPjB07FqdOncL169fx/PPPIyUl\nBRzHYfLkycxtjBkzBpcuXUL//v0xYsSILo/5+fkJTiD5yiuvICMjA/7+/khLS+syk3Pfvn0F20aM\nj5+fHw4dOiT4WPfPtnvHZWlpiba2Ntn9zsPEVlZWsr8tLCxk3xkLCwu0trbKHnvsscdkf/fp0wdS\nqVSDV9G7aJiOmLR+/fph27ZtePvtt2FrawsHBwecPn0aAPDVV19BJBIBaD8HtHfvXowYMQIcx2HQ\noEHIyspCeHi4XJ2df0xSUlKwceNG2X2O4/Dkk0/i1q1bKCgoANA+03PHGkH19fVwdnZGS0sL9u7d\nq/PlDoh+PPfcc3j48GGX9YYuXrwIe3t7HDhwAG1tbbh16xZOnTqFp556qstz3d3dUVxcDJ7nUV5e\nLjgrt7qMYeeGjoyISer8Ix8UFAQvLy8cPHgQaWlpeO2119DQ0ABPT0/s2bMHADB8+HAA7UdIQHvn\ndOPGDcHVMTuvy9QxzNaZlZUVDh06hMTERNTV1aG1tRVvvvkmfH198f777yMsLAxDhgxBWFhYl5Tz\nzm2mTsr4paenY8WKFdi8eTOsra3h4eGBrVu3or6+HoGBgeA4Dlu2bIGjoyPKyspkn3l4eDg8PDzg\n6+sLHx+fLueeun8vhL4zQuuGGcP3iSZKJYQQonc0TEcIIUTvqDMihBCid9QZEUII0TvqjAghhOgd\ndUaEEEL0jjojQgghevf/AcVR7pe63S+xAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# a simple scale function to normalize a matrix\n",
"def scale(matrix):\n",
" from numpy import mean, std\n",
" return (matrix - mean(matrix, axis=0)) / std(matrix, axis=0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# compute SVD\n",
"# note: the U and V matrices computed in numpy are different from R\n",
"# the resulting plots below aren't thus the same as the ones in video\n",
"U, D, V = np.linalg.svd(scale(dataMatrixOrdered))\n",
"\n",
"f, (ax1, ax2, ax3) = subplots(ncols=3)\n",
"\n",
"ax1.matshow(dataMatrixOrdered, cmap='hot')\n",
"\n",
"ax2.plot(U[:,0], range(39, -1, -1), 'ok')\n",
"ax2.set_xlabel('First left singular vector')\n",
"ax2.set_ylabel('Row')\n",
"ax2.set_xticks([-0.2, 0.0, 0.2])\n",
"\n",
"ax3.plot(V[:,0], 'ok')\n",
"ax3.set_xlabel('Column')\n",
"ax3.set_ylabel('First right singular vector')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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SvSICAFjz1S/rAk/8BZ74Nb6Kzit+TEJUoY/r3gGtIyuEqEJupxQTE4OjR4/i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\n5jIGlF32AAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# the D matrix, however, is the same\n",
"f, (ax1, ax2) = subplots(ncols=2)\n",
"\n",
"ax1.plot(D, 'ok')\n",
"ax1.set_xlabel('Column')\n",
"ax1.set_ylabel('Singular value')\n",
"\n",
"ax2.plot(D**2 / np.sum(D**2), 'ok')\n",
"ax2.set_xlabel('Column')\n",
"ax2.set_ylabel('Percent of variance explained')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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J7JPZVpx4/vnn8fTTT2PIkCFwcnLSVe7I7t27V+P7jy4WStQY8TI4WVu9Saq8\nvBxLliyxRiyS4ebmVuP7DweMENXk22+/xYsvvogLFy5I6j6UudR0GfzhayYqspR6R/eNGDECGRkZ\n1ohFMpKTk+Hn56f3np+fH5KSkmwUEdmDRYsWAQDGjh1r40gsY9myZXoJCniQpJYvX26jiKgxqPdM\naunSpVi0aBFcXV0hl8sBPLjcd+fOHYsHZysPfxUuX74cFRUVcHd3R1JSEn8tUp3atm2LIUOGoKCg\nQG9hZuBBn9m0aVO9dahUKsyZMwdarRYJCQmYN2+e3udnzpxBfHw8cnNz8e677+qtrenj4wMPDw84\nOztDLpcjOzvbPAf2/3gZnGyh3iRVUlJijTgkZ/jw4UxKZJQtW7YgJycHf/zjH/Ff//VfejeFDbmP\nq9VqMWvWLGzfvh1eXl6IiorCqFGjEBgYqNunbdu2WL58OX744Ydq5WUyGbKystCmTRvzHNBjeBmc\nbKHWJHX69GkEBgYiJyenxs979eplsaAcDW82Nw6urq7o3bs39u/fD09PT90PvObNmxtUPjs7G/7+\n/vDx8QEAxMXFIT09XS9JeXp6wtPTs9ZL8JYcuZecnIz8/PxqUzN4GZwsqdYk9Y9//AOffvopXn31\n1Rp/Be7cudOigTkK3mxufK5cuYKhQ4fixo0bAB4kli+++ALBwcF1lisqKtJ7DI5CocDBgwcN/l6Z\nTIbBgwfD2dkZiYmJtT4eZMGCBbrXMTExiImJMah+XganhsjKyjJtrVchMRIMqUGGDh0qAFT7UyqV\ntg6N6mFqW+zdu7fYsWOHbnvnzp2iT58+9ZbbsGGDSEhI0G1/9dVXYtasWTXuu2DBAvH3v/9d773f\nfvtNCCHEtWvXRFhYmNi9e3e1co7Wv8h+GdoWax3dd+jQIVy+fFm3/cUXX2DUqFFITk7GzZs3jc+G\njRRvNjc+ZWVlGDhwoG47JiYGpaWl9Zbz8vJCYWGhbruwsBAKhcLg7+3YsSOAB2duY8aMMfvACSJb\nqDVJzZgxQ3ejdPfu3Zg/fz6mTJkCDw8PzJgxw2oB2jvebG58fH198fbbb0OtVqOgoADvvPOOQfOm\nIiMjkZeXB7VajcrKSqSlpWHUqFE17iseu/dUVlaGu3fvAgBKS0uRmZmJkJCQhh8MkY3Vek+qqqpK\nN0ooLS0NiYmJGDt2LMaOHYuwsDCrBWjveLO58Vm9ejXefPNNxMbGAgD69+9v0DJiLi4uSE1NhVKp\nhFarxbS+KUzYAAAWqUlEQVRp0xAYGIiVK1cCABITE3HlyhVERUXhzp07cHJyQkpKCk6dOoVr167p\nvk+j0WDSpEkYOnSo5Q6SyEpqXbsvODgYubm5kMvl6N69Oz755BMMGDAAABAUFISTJ09aJiAHXFss\nIyODN5vtkCO2RUc8JrJPDV67b8KECRgwYACeeOIJNG3aFP379wfw4CFufBy2cTjniojINHWugr5/\n/37dcNpmzZoBAM6dO4eSkpIGzZMqLi5GQkICTp48qVtRvXfv3g8C4i89kghHbIuOeExknyT9PKkp\nU6ZgwIABmDp1KjQaDUpLS9GyZcsHAbET1YqTgq3L1Lb4888/V3sY6N69e/GHP/zBXKGZjP2LpEKy\nSer27dsIDw/HhQsXag6InahGfBCj9ZnaFsPDw5Gbm1vve7bA/kVSYbbnSZlbQUEBPD09ER8fj2PH\njiEiIgIpKSlo2rSpbh9TZ8Q7srpWoGaSMg+TZ8T/v/3792Pfvn24fv06/vGPf+g64N27d1FVVWWm\nKIkaF6snKY1Gg5ycHKSmpiIqKgpz5szB4sWL8dZbb+n2eTRJ0QOcFGx5j/8gWrhwoVHlKysrcffu\nXWi1Wt2cJQDw8PDAhg0bzBUmUaNi9SSlUCigUCgQFRUFAHjhhRewePFia4dhdzgpWPoGDBiAAQMG\n4E9/+pNukVgiahirJ6kOHTrA29sb586dQ7du3bB9+3YEBQVZOwy7w0nB9uPevXuYPn061Go1NBoN\ngAfX33fs2GHjyIjsj01G9x07dgwJCQmorKyEn58f1qxZw9F9BuCkYOsytS2GhoZi5syZ6NWrF5yd\nnXV1RUREmDtEo7F/kVRIdnRffdiJSCpMbYsRERE4cuSIBSJqOPYvkgpD22KtC8wSkWlGjhyJFStW\n4PLly7h586buj4iMxzMpolqY2hZ9fHxqfFBoQUGBOcJqEKn0L05MJ8nOkyJydGq12tYhSBqfVk3G\n4OU+IjMrLS3F22+/rXt8e15eHjZv3mzjqKSjronpRI9jkiIys/j4eLi6umLfvn0AgE6dOuG///u/\nbRyVdHBiOhmDSYrIzPLz8zFv3jy4uroCgO4JAvQAJ6aTMZikiMzMzc0N5eXluu38/Pxa/8fcGCUn\nJ8PPz0/vPU5Mp9pw4ASRmS1YsADPPvssLl26hIkTJ2Lv3r34/PPPbR2WZDwcHMGJ6WQIDkEnqkVD\n2uLvv/+OAwcOAAB69+6NJ554wpyhmYz9i6SCk3mJbOS7776Di4sLRowYgREjRsDFxQU//PCDrcMi\nsks8kyKqhaltMSwsDMeOHdN7r2fPnjh69Ki5QjOZo/UvTgq2XzyTIrKRmjqeVqs1qKxKpUJAQAC6\ndu2KJUuWVPv8zJkz6NOnD9zd3fHhhx8aVdbRPJwUnJmZiV27diEzMxOzZ89GRkaGrUMjM+KZFFEt\nTG2L8fHxaN26Nf7zP/8TQgisWLECt27dqnfwhFarRffu3bF9+3Z4eXkhKioK69atQ2BgoG6f69ev\n49dff8UPP/yA1q1bY+7cuQaXbcgxSZFSqURmZmaN76tUKhtERMbgmRSRjaSmpkIul2P8+PGIi4uD\nu7s7VqxYUW+57Oxs+Pv7w8fHB3K5HHFxcUhPT9fbx9PTE5GRkZDL5UaXdTScFNw4cAg6kRlpNBqM\nGDECO3fuNLpsUVERvL29ddsKhQIHDx40e9kFCxboXsfExCAmJsboWKWAk4LtS1ZWFrKysowuxyRF\nZEYuLi5wcnJCcXExWrVqZVTZmlZOt0TZR5OUPePTqu3L4z+IFi5caFA5JikiM2vWrBlCQkIwZMgQ\n3ZJIMpkMy5Ytq7Ocl5cXCgsLdduFhYVQKBQGfWdDytorTgpuHJikiMwsNjYWsbGxurMbIYRBZzqR\nkZHIy8uDWq1Gp06dkJaWhnXr1tW47+M3nI0p60iGDx/OpOTgOLqPqBYNaYtlZWW4ePEiAgICjCq3\ndetWzJkzB1qtFtOmTcMbb7yBlStXAgASExNx5coVREVF4c6dO3ByckKLFi1w6tQpNG/evMay5jwm\nR8b5VtZnaFtkkiKqhaltcdOmTXjttddw7949qNVq5Obm4s0338SmTZssEKVx2L+qq+khjH5+fkhJ\nSWGisiAOQadaZWRkQKlUIiYmBkqlkpMfzWzBggU4ePAgWrduDQAIDw/HhQsXbBwV1YYPYZQ23pNq\nZPjobsuTy+XVRvY5OfH3oFRxvpW0sec0MvzVaHlBQUFYu3YtNBoN8vLykJSUhL59+9o6LKoF51tJ\nG5NUI8NfjZaXmpqKkydPws3NDRMmTICHhweWLl1q67CoFnwIo7Txcl8jw1+NllNeXo6PP/4Y58+f\nR2hoKPbv319t+SKSHs63kjaO7mtkOJLJcMa2xXHjxsHV1RX9+vWDSqVCly5dkJKSYsEIjcf+RVLB\nIehUq4yMDP5qNICxbTEkJAQnTpwA8GANv6ioKOTm5loqPJOwf5FUGNoWebmvEeIsfctwcXGp8TUR\nmY5nUkS1MLYtOjs7o2nTprrt8vJyNGnSRFfXnTt3zB6jsdi/SCp4JkVkZYY+fZeIDMch6EREJFk2\nSVJarRbh4eEYOXKkLb6ezITLKxGRpdnkcl9KSgp69OiBu3fv2uLryQy4vBIRWYPVz6QuXbqELVu2\nICEhgTdw7RiXVyIia7D6mdQrr7yCDz74oM6RTo8+3vrxRw6TNDji8kpZWVnIysqydRhE9AirJqnN\nmzejXbt2CA8Pr/N/Bo8mKZImR1xe6fEfRAsXLrRdMEQEwMqX+/bt24dNmzbB19cXEyZMwI4dOzB5\n8mRrhkBmwkU5icgabDaZd9euXfj73/+OH3/8UT8gTja0G46+vJIjtkVHPCayT3YxmVcmk9ny66mB\nuLwSEVkal0UiqoUjtkVHPCayT4a2Ra44QURkJpzgbn5cu49IQlQqFebMmQOtVouEhATMmzev2j7J\nycnYunUrmjZtis8//xzh4eEAAB8fH3h4eMDZ2RlyuRzZ2dnWDr9R4wR3CxESI8GQqJGydlvUaDTC\nz89PFBQUiMrKShEWFiZOnTqlt09GRoZ47rnnhBBCHDhwQERHR+s+8/HxETdu3KjzO9i/LGfo0KEC\nQLU/pVJp69AkydC2yMt9RBKRnZ0Nf39/+Pj4QC6XIy4uDunp6Xr7bNq0CVOmTAEAREdHo7i4GFev\nXtV9Lni/yWYccYK7FPByH5FEFBUVwdvbW7etUChw8ODBevcpKipC+/btIZPJMHjwYDg7OyMxMRHT\np0+v8Xu4ootlOOIEd3MydUUXJikiiTB0SkZtZ0s///wzOnXqhOvXr2PIkCEICAhA//79q+3HFV0s\nIzk5Gfn5+Xr3pDjB/d9MXdGFSYpIIry8vFBYWKjbLiwshEKhqHOfS5cuwcvLCwDQqVMnAICnpyfG\njBmD7OzsGpMUWcbDwRGOPMHdFnhPikgiIiMjkZeXB7VajcrKSqSlpWHUqFF6+4waNQpffvklAODA\ngQNo1aoV2rdvj7KyMt2jb0pLS5GZmYmQkBCrH0NjN3z4cKhUKmRlZUGlUpmcoDiU/d94JkUkES4u\nLkhNTYVSqYRWq8W0adMQGBiIlStXAgASExMxbNgwbNmyBf7+/mjWrBnWrFkDALhy5QpiY2MBABqN\nBpMmTcLQoUNtdixkOg5l18cVJ4hq4Yht0RGPydEolUpkZmbW+L5KpbJBRJbBFSeIiOwQh7LrY5Ii\nm+P1d6J/41B2fbwnRTbF6+9E+jiUXR/vSZFNSfn6uyO2RUc8Jkfk6M9qA+zkeVJEvP5OVB2f1fZv\nvCdFNsXr70RUFyYpsqnk5GT4+fnpvdeYr78TkT5e7iOb4lIyRJaVkZGBZcuW4d69e3Bzc0NycrJd\n9S8OnCCqhSO2RUc8JqpdTaNn/fz8kJKSYvNExcm8RESN3LJly/QSFPBgisfy5cttFJHxmKSIiByU\nI4yeZZIiInJQjjB6lkmKHAaXVyLSZ87Rs7bqXxzdRw6ByysRVWeu0bO27F8c3UcOwRLLKzliW3TE\nYyLLM2f/ejgkPjMzk8siUePhCDeIiaTKXP2rpjOy+vCeFDkER7hBTCRV5upfNQ2Jrw+TFDkES9wg\nJqIHzNW/ajsjqwsv95FDsOQNYqLGzlz9q7Yzsrpw4ATRIx6/QexobZH9i2zp8R+BjXpZpKysLEnV\nY866WI/l6jHlckRjJIV/K9Zjm7oaUs/w4cORkpJi1OV0qyepwsJCDBw4EEFBQQgODsayZcss8j1S\n+AexVF2sx3L1mHI5wpxUKhUCAgLQtWtXLFmypMZ9kpOT0bVrV4SFhSE3N9eosuYihX8r1mObuhpa\nz/Dhw40atm71JCWXy/HPf/4TJ0+exIEDB7BixQqcPn3a2mEQ1aimG8TWotVqMWvWLKhUKpw6dQrr\n1q2r1je2bNmC8+fPIy8vD5988glmzpxpcFkie2T1JNWhQwf07NkTANC8eXMEBgbit99+s3YYRDUy\n5XKEuWRnZ8Pf3x8+Pj6Qy+WIi4tDenq63j6bNm3ClClTAADR0dEoLi7GlStXDCpLZJeEDRUUFIjO\nnTuLu3fv6t4DwD/+SebPmr799luRkJCg2/7qq6/ErFmz9PYZMWKE2Lt3r2570KBB4vDhw2LDhg31\nlhWC/Yt/0vozhM2GoJeUlOCFF15ASkoKmjdvrntfcOQRNVIymcyg/RrSR9i/yN7YJEndv38fY8eO\nxR//+EeMHj3aFiEQSY6XlxcKCwt124WFhVAoFHXuc+nSJSgUCty/f7/eskT2yOr3pIQQmDZtGnr0\n6IE5c+ZY++uJJCsyMhJ5eXlQq9WorKxEWloaRo0apbfPqFGj8OWXXwIADhw4gFatWqF9+/YGlSWy\nR1Y/k9q7dy++/vprhIaGIjw8HADw3nvv4dlnn7V2KESS4uLigtTUVCiVSmi1WkybNg2BgYFYuXIl\nACAxMRHDhg3Dli1b4O/vj2bNmmHNmjV1liWye8bc2LW0rVu3iu7duwt/f3+xePFik+uJj48X7dq1\nE8HBwQ2K5+LFiyImJkb06NFDBAUFiZSUFJPqKS8vF0899ZQICwsTgYGBYv78+Q2KS6PRiJ49e4oR\nI0aYXEeXLl1ESEiI6Nmzp4iKijK5nlu3bomxY8eKgIAAERgYKPbv3290HWfOnBE9e/bU/Xl4eJj8\n33rRokWiR48eIjg4WEyYMEFUVFSYVM/SpUtFcHCwCAoKEkuXLjWpDqkxR/9i3zKMOfqXOfqWEPbf\nvySTpDQajfDz8xMFBQWisrJShIWFiVOnTplU1+7du0VOTk6DO9Lly5dFbm6uEEKIu3fvim7dupkc\nU2lpqRBCiPv374vo6GixZ88ek+P68MMPxcSJE8XIkSNNrsPHx0fcuHHD5PIPTZ48WaxatUoI8eDY\niouLG1SfVqsVHTp0EBcvXjS6bEFBgfD19dV1nHHjxonPP//c6HpOnDghgoODRXl5udBoNGLw4MHi\n/PnzRtcjJebqX+xbhjFH/zJ33xLCPvuXZJZFMuc8j/79+6N169YNjsmcc7qaNm0KAKisrIRWq0Wb\nNm1MqufSpUvYsmULEhISGjxSq6Hlb9++jT179mDq1KkAHlxyatmyZYPq3L59O/z8/ODt7W10WQ8P\nD8jlcpSVlUGj0aCsrAxeXl5G13PmzBlER0fD3d0dzs7OGDBgAL777juj65ESc/Uv9i3DNaQOS/Qt\nwD77l2SSVFFRkd5/OIVCgaKiIhtGpE+tViM3NxfR0dEmla+qqkLPnj3Rvn17DBw4ED169DCpnlde\neQUffPABnJwa9k8nk8kwePBgREZG4tNPPzWpjoKCAnh6eiI+Ph69evXC9OnTUVZW1qC41q9fj4kT\nJ5pUtk2bNpg7dy46d+6MTp06oVWrVhg8eLDR9QQHB2PPnj24efMmysrKkJGRgUuXLpkUk1RIuX85\nWt8CGt6/LNG3APvsX5JJUobOEbGF2uZ0GcPJyQlHjx7FpUuXsHv3bpPWv9q8eTPatWuH8PDwBv/S\n27t3L3Jzc7F161asWLECe/bsMboOjUaDnJwc/Md//AdycnLQrFkzLF682OSYKisr8eOPP+LFF180\nqXx+fj6WLl0KtVqN3377DSUlJVi7dq3R9QQEBGDevHkYOnQonnvuOYSHh5vlf1y2JNX+5Yh9C2h4\n/zJ33wLst39JpucZMkfEFsw9p6tly5YYPnw4Dh8+bHTZffv2YdOmTfD19cWECROwY8cOTJ482aQ4\nOnbsCADw9PTEmDFjkJ2dbXQdCoUCCoUCUVFRAIAXXngBOTk5JsUDAFu3bkVERAQ8PT1NKn/48GH0\n7dsXbdu2hYuLC2JjY7Fv3z6T6po6dSoOHz6MXbt2oVWrVujevbtJ9UiFFPuXo/YtoOH9y9x9C7Df\n/iWZJCXFeR7CTHO6fv/9dxQXFwMAysvLsW3bNt3we2MsWrQIhYWFKCgowPr16/HMM8/o5swYo6ys\nDHfv3gUAlJaWIjMzEyEhIUbX06FDB3h7e+PcuXMAHlzvDgoKMrqeh9atW4cJEyaYXD4gIAAHDhxA\neXk5hBDYvn27yZd+rl27BgC4ePEivv/+e5MvkUiF1PqXo/YtwDz9y9x9C7Dj/mX00AwL2rJli+jW\nrZvw8/MTixYtMrmeuLg40bFjR+Hq6ioUCoVYvXq1SfXs2bNHyGQyERYWphu+uXXrVqPrOX78uAgP\nDxdhYWEiJCREvP/++ybF86isrCyTRyBduHBBhIWFibCwMBEUFNSg/9ZHjx4VkZGRIjQ0VIwZM8bk\nEUglJSWibdu24s6dOybHIoQQS5Ys0Q2RnTx5sqisrDSpnv79+4sePXqIsLAwsWPHjgbFJBXm6F/s\nW/UzV/8yV98Swr77l+SezEtERPSQZC73ERERPY5JioiIJItJioiIJItJioiIJItJSoKuXLmCuLg4\n+Pv7IzIyEsOHD0deXl6N+6rVapOGjxM1Ruxb9sdmT+almgkhMGbMGMTHx2P9+vUAgOPHj+Pq1avo\n2rWrjaMjsl/sW/aJZ1ISs3PnTri6umLGjBm690JDQ9GvXz+89tprCAkJQWhoKL755ptqZT///HMk\nJSXptkeMGIHdu3cDeLCI5+uvv47g4GAMGTIEBw4cwIABA+Dn54cff/xRVz42NhbPPfccunXrhnnz\n5ln4aImsh33LPjFJScwvv/yCiIiIau9v3LgRx44dw/Hjx7F9+3a89tpruHr1ap11PbpeW1lZGQYN\nGoRffvkFLVq0wN/+9jfs2LED33//Pf72t7/p9jt27Bi++eYbnDhxAmlpaZJZhJSoodi37BOTlMTU\nthDo3r17MXHiRMhkMrRr1w4DBgwwaj0wV1dXKJVKAEBISAgGDhwIZ2dnBAcHQ61W6/YbNGgQWrRo\nATc3N/To0UPvMyJ7xr5ln5ikJCYoKAhHjhyp8bPHFwd5vNO5uLigqqpKt11RUaF7LZfLda+dnJzg\n6uqqe63RaHSfubm56V47OztDq9WacBRE0sO+ZZ+YpCTmmWeewb179/SeQXP8+HG0atUKaWlpqKqq\nwvXr17F792489dRTemV9fHxw9OhRCCFQWFho0srmj+OqWeQo2LfsE0f3SdD333+POXPmYMmSJXB3\nd4evry/++c9/oqSkBGFhYZDJZPjggw/Qrl07qNVq3a++fv36wdfXFz169EBgYKDe9ffHfxk+uv3w\ntUwmq3M/InvHvmV/uMAsERFJFi/3ERGRZDFJERGRZDFJERGRZDFJERGRZDFJERGRZDFJERGRZP0f\nKoDmlweJJi8AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## relation between SVD and PCA\n",
"# There is no 'dedicated' or built-in 'PCA' in Python (numpy, scikit.learn, ..)\n",
"# PCA is achieved through SVD"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# components of the SVD - variance explained\n",
"constantMatrix = dataMatrixOrdered * 0\n",
"constantMatrix[:,5:] = 1\n",
"\n",
"U1, D1, V1 = np.linalg.svd(constantMatrix)\n",
"\n",
"f, (ax1, ax2, ax3) = subplots(ncols=3)\n",
"\n",
"ax1.matshow(constantMatrix, cmap='autumn')\n",
"\n",
"ax2.plot(D1, 'ok')\n",
"ax2.set_xlabel('Column')\n",
"ax2.set_ylabel('Singular value')\n",
"\n",
"ax3.plot(D1**2 / np.sum(D1**2), 'ok')\n",
"ax3.set_xlabel('Column')\n",
"ax3.set_ylabel('Percent of variance explained')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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rJZg8VOlFRt5Z7kpMlCqShgkPD8fVq1cxZcoUhIWFoW3btnjssceMri8oKAgT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\ngg==\n"
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# again generate a new dataMatrix with R"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%R -o dataMatrix\n",
"set.seed(12345); par(mar=rep(0.2,4))\n",
"dataMatrix <- matrix(rnorm(400),nrow=40)\n",
"\n",
"set.seed(678910)\n",
"for(i in 1:40){\n",
" coinFlip1 <- rbinom(1,size=1,prob=0.5)\n",
" coinFlip2 <- rbinom(1,size=1,prob=0.5)\n",
" \n",
" if(coinFlip1){\n",
" dataMatrix[i,] <- dataMatrix[i,] + rep(c(0,5),each=5)\n",
" }\n",
" if(coinFlip2){\n",
" dataMatrix[i,] <- dataMatrix[i,] + rep(c(0,5),5)\n",
" }\n",
"}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# cluster the dataMatrix\n",
"from scipy.cluster.hierarchy import linkage, dendrogram\n",
"from scipy.spatial.distance import pdist, squareform\n",
"\n",
"hh = dendrogram(linkage(pdist(dataMatrix)))\n",
"\n",
"dataMatrixOrdered = dataMatrix[hh['leaves'], :]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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WfyvLXXQFuuK2vPJtji0doXa4/8cXMZwNmLV7Fg5cPADn6sa/Ft6Y/KJ8AMDx1OP3PG1W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\nHPw5ycgAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# SVD - true pattern that was added to the dataMatrix\n",
"f, (ax1, ax2, ax3) = subplots(ncols=3)\n",
"\n",
"ax1.matshow(dataMatrixOrdered, cmap='hot', origin='lower')\n",
"\n",
"x = np.array([0, 1])\n",
"\n",
"ax2.plot(np.repeat(x, 5), 'ok')\n",
"ax2.set_xlabel('Column')\n",
"ax2.set_ylabel('Pattern 1')\n",
"\n",
"ax3.plot(np.tile(x, 5), 'ok')\n",
"ax3.set_xlabel('Column')\n",
"ax3.set_ylabel('Pattern 2')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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Ggbpzf4iIiFqDl9chIiLVsfkQEZHq2HyIiEh1Nruw6A3RgjPK4Q8F6cObnr8K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\n1bH5EBGR6v4XUSYAvoIVDrgAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# V and patterns of variance in rows\n",
"# again, the SVD results here are not comparable to the video\n",
"U, D, V = np.linalg.svd(scale(dataMatrixOrdered))\n",
"\n",
"f, (ax1, ax2, ax3) = subplots(ncols=3)\n",
"\n",
"ax1.matshow(dataMatrixOrdered, cmap='hot')\n",
"\n",
"ax2.plot(V[:,0], 'ok')\n",
"ax2.set_xlabel('Column')\n",
"ax2.set_ylabel('First right singular vector')\n",
"ax2.set_ylim([-0.8, 0.6])\n",
"\n",
"ax3.plot(V[:,1], 'ok')\n",
"ax3.set_xlabel('Column')\n",
"ax3.set_ylabel('Second right singular vector')\n",
"ax3.set_ylim([-0.8, 0.6])\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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Cp0WMHBUjkag7xb+pqSleeOGFehcIEmGJ5XqVxMRELFmyBLa2tmjT5tml7Rcv\nXhQwKyIGVIxEwphnMmgNDOV6ldpBFNpas2YNrl69ii5dGOdbCdESFSORsLKyUolZW1ujX79+WLVq\nFXr06CFAVqSWIVyvwjeIQlPdu3dHhw4dmjErQmrorRiVsZ5Q/c4EAFxltWccaSrhfQH/jHUoYG2c\nsewsc2gfcwY9wc2dOxdOTk6YOHEigJplyHNycuDn54dp06bp/eJY0jihr1fhG0ShKRcXFwQFBSE0\nNFQ5xFsikWD+/PnNkSJpxWjPSCR27dqFrKws5eOZM2fC19cXK1aswPLlywXMjBgK1iAKTXTv3h3d\nu3dHZWUlKisrwXFck+eVI0QdKkYiYWFhgeTkZIwbNw5AzWJ7tSfH6cuCAOxBFJoQ20S3xHBQMRKJ\nzZs3Y+7cufi///s/AMBLL72En376CY8fP6ar1gkA/kEUTTV37lzEx8fXu4SglkQiwa5du5ojRdKK\nqS1GeXl5iIqKwp9//gmJRIKZM2ciJiYGRUVFiIyMxM2bN5XrmXTsyDj/QlqEq6srdu/ezfvcwIED\nWzgbYojqDqL473//q9Fra6eVqnsJQS3a8ybNQW0xMjMzw+rVq+Hr64vS0lL4+/sjJCQEGzduREhI\nCD744AOsWLECcXFxiIuLa6mcCY8///wT69evR25uLqqqqgDUfEl8//33AmdGDEntIApNC4i/vz+A\n+pcQFBUV4fbt2+jTp09zpkhaKbXFyN7eHvb29gCA9u3bw93dHXfu3MGuXbtw5MgRAMCUKVMglUpV\nihFzQBpjcdVAVnvGADa+33UvwZK/MXNU823+8Cz+MLCd9YTgRo0ahX/84x8ICQmBiYkJAPrFSpqf\nVCrFrl27UFVVBX9/f9jY2OCVV17B6tWrhU6NGLkmnzPKzc3FuXPnEBgYWG/deTs7OxQWMoZUkxbz\n+PFjrFixQug0iMgVFxejQ4cO+O677xAVFYUlS5bA29tb6LSICDSpGJWWliI8PBzx8fEqF1dKJBLe\nX+C/17lvA8BWlywNRHr6LaSn5zXeUACvvfYa5HK5UU26SYyPQqFAfn4+UlJS8MknnwCgPXCiSpuZ\nPhotRk+fPkV4eDjeeOMNjB49GkDN3lBBQQHs7e2Rn58PW1vVUuOpURrGQSrtDqn02YSQS5acEDCb\n+tasWYNly5ahbdu2MDMzA1DzJfHo0SOBMyNi8tFHH0Emk+GVV15B//79kZOTg169egmdFjEg2s70\nYaLuSY5GNcoLAAAgAElEQVTjMH36dHh4eGDevHnKeFhYGJKSkgDUrDBaW6SIcEpLS1FdXY2KigqU\nlJSgpKSEChFpduPGjUNWVha+/vprADWjOH/55ReBsxI/uVwOmUwGqVQKmUwGuVwudEpM2s70oXbP\n6Pjx4/jpp5/Qp08f+Pn5AQCWL1+ORYsWYfz48diwYYNyaHdDg1gbHcwf7nuO0X4sf7jNKb7oQ/7G\njAX9gEP8YeaROH/WE4K5fPky3N3dkZmZyft83759WzgjQkhzMraFGbWd6UNtMRo4cCCqq6t5nztw\n4IBWb0ia1xdffIH169dj/vz5vMfuDx8+LEBWhJDmYmwLM2o70wfNwGDk1q9fDwA0ESppEdevX1eZ\nAZ4vRpqPsS3MqO1MH2rPGRHjsW3bNuU5oqVLl2Ls2LHMQ3eEaCs8PFwlVjsfItEPY1uYMTQ0FPHx\n8ZDJZBq9jvaMROLjjz/GuHHj8Ouvv+LgwYN477338NZbb+HUKd6Ta4Ro5PLly7h06RIePnyI7du3\nK2frfvTokcH+QhcLQ1mYURPazPRBxUgkapeA3r17N6Kjo/Haa69h8eLFAmdFxCI7Oxupqal4+PAh\nUlNTlXErKyvloWKiH4awMGNL0FsxsmE9wZixh3XFjuseTbbPuLqJuTdrx3qCIVnD9i3HwcEBM2fO\nxP79+7Fo0SJUVFQwB58QoqlRo0Zh1KhROHHiBAYMGCB0Oq2O0AsztgQ6ZyQSKSkpkMlk2LdvHzp2\n7IgHDx5g5cqVOm+3qKgIISEh6N27N4YOHYri4mKVNnl5eQgKCoKnpye8vLw0vvKaGI+ePXvi008/\nRXR0NKZOnYqpU6di2rRpOm+X+hmhYiQSlpaWCA8PV14N37VrVwwdOlTn7cbFxSEkJATZ2dkIDg7m\nnZ29dnb333//HRkZGfjyyy9x+fJlnd+bGJ5Ro0bh0aNHCAkJUf5ab45f7NTPCJ0zImo1ZYZ2vtnd\n7969C3d39xbPl+iXvibkpX5GqBgRtTSdob3u7O586i5bLZVK662PQ/QnPT29Wa5F09eEvNTPxEGX\nfkbFSCQWLlyo8ouVL8YnJCQEBQUFKvFPP/203mPWDO21SktLERERgfj4eLRv3563Td0vCdJyGn4h\nL1myRKPXt2/fXvnZazshL/Uz8dOln+mtGF1jPdGTP3yd1b4Lf5h/8T7G9Q7MyyAO8od/ZbX/nfWE\n4Pbt26dSePbs2dOkYrR//37mc02ZoR14Nrv766+/ThPnilBpaanO26B+RtShAQxG7uuvv4a3tzeu\nXr0Kb29v5c3Z2blZloNuygztrNndifhkZmaq3HJycpRL3WuL+hmhYmTkJk2ahNTUVISFhWH37t1I\nTU1Famoqzp49i82bN+u8/UWLFmH//v3o3bs3Dh06hEWLFgEA7t69qzxvUDu7++HDh+Hn5wc/Pz+k\npaXp/N7E8Lz99tsIDAxEdHQ0oqOj8dJLLyEiIgK9e/fGf//7X623S/2M0DkjI2dtbQ1ra2ts3boV\nCoUChYWFqKqqQllZGcrKytC9e/fGN6JG586deWdo79atm3JNFXWzuxNx6datGzZs2ABPz5oLzC9d\nuoTFixfjs88+w9ixYzWej6wW9TNCxUgkEhMTsWTJEtja2iqnBgKAixcvCpgVEZurV68qCxEAeHh4\n4MqVK3B1daXlx4lOqBiJxJo1a3D16lV06cIY8UFIM/D09MTs2bMxYcIEcByHlJQUeHh44MmTJ8rR\ndYRoQ8JxHNfsG5VIEMV4LimMPz5uF398G/+wOfTlmZwucwx/24U7+OMrgvjjXzHWo3t7Vf3HkgU1\nJ1UNQVBQEPbt22fQXwgSicRg/n+1dtp+FuXl5fjqq69w/PhxAMArr7yCt99+G+bm5igrK4OVlVVz\np6ox6meGQ5PPgvaMjNyqVTUVskePHpBKpXjttdfQtm1bADUdYf78+UKmR0TGwsIC7733Ht577z2V\n5wyhEBHjRcXIyJWUlEAikaB79+5wcnJCZWUlKisrlevNENIcxo0bh23btsHLy0ulX0kkEmRlZQmU\nGRELKkZGjq40Jy0hPj4eACCXy+kQGNELtcUoLy8PUVFR+PPPPyGRSDBz5kzExMQgNjYW3333HWxs\nak7cLF++HMOGDWuRhAm/kSNH1js+K5FIYG1tjYCAAMyaNctglygmxqFbt26oqqrCm2++icOHGSdV\nCdGB2mJUO2W7r68vSktL4e/vj5CQEOW5CDofYThcXFxw//59TJw4ERzHITk5Ge3bt0d2djaio6Px\n448/Cp0iMXKmpqYwMTFBcXExOnbsKHQ6RGTUFiO+Kdvv3LkDoPFRZD6sJ2bwhz0Yo+nAWDn7C74g\nY/keO8ZoOiTyh529GO2LGHEDcOLECZw5c0b5OCwsDAEBAThz5ky960II0YWlpSW8vb0xdOhQWFhY\nAKjZC6eF7oiumnzOqHbK9pdeegnHjx9HYmIifvjhBwQEBGDVqlX0S0lgZWVluHnzJl544QUAwM2b\nN1FWVgYAytF1hOhq7NixGDt2rHIQAw2UIc2lScWo4ZTts2fPxkcffQQAWLx4MRYsWIANGzbUe03d\nWapcwZys26ik36y5GaJVq1Zh0KBB6NGjBwDg+vXr+Oqrr1BWVoYpU6YInB0RizfffFPoFIhINVqM\n+KZsrzu9+4wZMzBy5EiV12k3Q5Vhk75Qc6u15JhwuTQ0YsQIZGdn48qVK5BIJHjxxReVgxZohmNC\niKFTW4xYU7bn5+eja9euAIAdO3bA29tbv1kSpoMHDyI4OBi//PJLvdF0OTk5AGoOqxBCiKFTW4xq\np2zv06cP/Pz8ANSs8rhlyxacP38eEokELi4uWLduncprHVgbZexNWLPaX+APf80TkzI2Yc/a9m7+\nMHPwBXMFQOEcPXoUwcHBSE1N5T12T8WIEGIM1BYj1pTtw4cP11tCRDNLlixBdXU1hg8fjsjISKHT\nISJV91B8w/nGJBIJdu1iDYclpGloBgYRMDExwWeffUbFiOjNggULANQcli8oKMDrr78OjuOwZcsW\n2NnZCZwdEQMqRiIREhKCzz//HJGRkbC0tFTGO3fuLGBWRCykUimAmqJ09uxZZTwsLAz+/v4CZUXE\nhIqRSGzduhUSiQRffvmlMiaRSHD9ugGe6CJGq7y8HDk5OXB1dQVQcwlBeXm5wFkRMaBiJBK5ublC\np0BagdWrVyMoKAguLi4Aavrdt99+K3BWRAz0VoxYi11Hqi5zDwBgzhEwkD9s8z+e4B/8bQ8xNj0p\ngD/+K6N9pAnjCUJaiWHDhtW7ns3NzQ3t2rUTOi0iArRnRAjRSGZmJm7cuIGqqipcuFBz7UVUFGtt\nZ0KahooRIaTJXn/9dVy/fh2+vr5o06aNMk7FiOiKipFIBAcH4+DBg43GCNHF2bNncenSJZoclTQ7\nKkZG7vHjxygvL8e9e/dQVPRsjYtHjx4pl/sgpLl4eXkhPz8f3bp1EzoVIjJUjIzcunXrEB8fj7t3\n79a73sPKygrvvPOOTtsuKipCZGQkbt68CWdnZ6SkpDCXClEoFAgICICjoyNSU1N1el9iuO7duwcP\nDw/0799fOXBB1xkYxNTP5HI5EhIS8OTJE7Rr1w4xMTEIDQ0VOi2jIOH0sKC9RCLBb4znWCPVxjDi\n3zHihTyx+FWMxow56PANI/5z095UktD4IoMtJTExEXPmzGnWbX7wwQd4/vnn8cEHH2DFihV48OAB\n4uLieNt+8cUXOHv2LEpKSphfTA2nkSHC0fazSE9PV74eeLae0eDBg7XORSz9TC6XY+7cucpJigHA\n1dUV8fHxrbYgafJZ0GBlkbCzs0NJSQkAYOnSpRg7diwyMzN12uauXbuUayFNmTIF//nPf3jb3b59\nG3v27MGMGTOo2IicVCqFm5sbHj16hJKSEnh4eOhUiADx9LOEhIR6hQiomT0/MZGxpDSph4qRSCxd\nuhRWVlb49ddfcfDgQUybNg1vvfWWTtssLCxUzjtmZ2eHwkK+/VHg3XffxcqVK2FiQt1J7FJSUhAY\nGIht27YhJSUF/fv3x7Zt23Taplj62ZMnT3jjFRUVLZyJcaJzRiJRO8x29+7diI6OxmuvvYbFixc3\n+rqQkBAUFBSoxD/99NN6jyUSCe8Iqt27d8PW1hZ+fn7KQzjqxMbGKu9LpVLlnGdEv9LT05v0+TTm\nk08+wenTp5ULbN67dw/BwcEYN26c2te1hn7Guvi3dpHL1kCXfkbnjPgY4Tmj0NBQODg4YP/+/Th3\n7hzMzc0RGBiovChRG25ubkhPT4e9vT3y8/MRFBSEK1eu1Gvz4Ycf4scff4SpqSkqKirw6NEjhIeH\n44cfflDZHp0zMhzafhbe3t7IyspSFozq6mr4+Pjg4kXWnCuNE0s/o3NGquicUSu0bds2yGQy7Nu3\nDx07dsSDBw+wcuVKnbYZFhaGpKQkAEBSUpJy2fm6li1bhry8PNy4cQNbt27Fq6++yvsFQcRh2LBh\nkMlk2LRpEzZu3IgRI0bovL6ZWPpZaGgo4uPjIZPJMHjwYMhkslZdiDSltz0jVjeZx4hvYsStGHG+\n3/tzWbtXrJLbgxG3YcTX1H8ouWsYe0ZVVVXw8vJS+TWpq6KiIowfPx63bt2qN+T27t27iI6Ohlwu\nr9f+yJEjWLVqlcGNciKqdPksfvnlFxw/fhwAMGjQIIwZw/rDaxrqZ+KlyWdBxYiPkRUjABg1ahQS\nEhLwwgsvCJ0KE31JGA5tP4sbN27A3t4ezz33HICai64LCwvh7OzczBlqj/qZ4dDks6ABDCJRVFQE\nT09P9O/fX7m4Hi0HTZpbREQE/ve/Z1Pmm5iYICIiAmfOnBEwKyIGVIxEYunSpUKnQFoBhUKBtm2f\nLfjSrl07PH36VMCMiFioLUYVFRUYPHgwnjx5gsrKSowaNQrLly/XaPoO0jJoiDRpCc8//zx27tyJ\nUaNGAQB27tyJ559/XuCsiBioHU1nbm6Ow4cP4/z588jKysLhw4fx66+/Ii4uDiEhIcjOzkZwcDBz\n6g6if6+88goAoH379rCysqp369Chg8DZEbH55ptvsGzZMjg5OcHJyQlxcXFYt26d0GkREWjyAIby\n8nIMHjwYmzZtQnh4OI4cOQI7OzsUFBRAKpXWG8klkUgwkbEd1iDQk4w4/7XY4B0g8RzrOiPWrDg7\nGHEnRvyj+g8lk4UfwHDz5k2DHrRQF51YNhy6fhalpaXgOA5WVqwhRsKhfmY4mvU6o+rqavj6+sLO\nzg5BQUHw9PRs8vQdRP/qDqsNDw8XMBPSGhQUFGD69OmIiIiAlZUVLl26hA0bNgidFhGBRgcwmJiY\n4Pz583j48CFkMhkOHz5c73nW9B11r8e2BWCna6YGIP0SkH5Z6Czqq/ur4/r16wJmQlqDN998E1On\nTlVO49OrVy+MHz8e06dPFzgzYuyaPJrO2toaoaGhOHv2rPLwXO30HbXzVNXl3axpGgapR82t1pLt\nwuVCiBDu37+PyMhI5XliMzMzmJrSoFyiO7WH6e7fv4/i4mIANRe37d+/H35+fk2avoO0jKysLOWA\nhYsXL9IABqJX7du3x19//aV8nJGRAWtrawEzImKh9idNfn4+pkyZgurqalRXV+ONN95AcHAw/Pz8\nMH78eGzYsEE5tJsIQ6FQCJ0CaUVWrVqFkSNH4vr16xgwYADu3buHn39mzSxMSNPpbTqgNYznPmXE\nX2PEWWN1DvHELi5gND6h4ZuyRNR/KHlR+NF0xoRGORkOXT6Lp0+f4urVqwCAF198EWZmZs2Zms6o\nnxkOmrWbENKsTp06hfz8fAA154nOnj2LDz/8EAsWLEBRUZHA2RExoGJECGnUrFmzlIvHHT16FIsW\nLcKUKVPQoUMHzJw5U+DsiBjQMBhCSKOqq6vRuXNnAEBycjJmzZqF8PBwhIeHw8fHR+DsiBjQnhEh\npFEKhUI5IeqBAwcQFBSkfK6qqkqotIiI6G3PKJkR38uIL2LEKxhx3jVMixmNWdP7sNYzusmIL2bE\nCRG5iRMnYvDgwXj++edhYWGBQYMGAQCuXbtGkySTZkGH6QghjfrXv/6FV199FQUFBRg6dChMTGoO\nqnAch8TERIGzI2JAxYgQ0iQvv/yySqx3794CZELEiM4ZEUIIERwVI0IIIYKjYkRIA3K5HDKZDFKp\nFDKZDHK5XOiUCBE9vZ0zesqIr2bEX2fELzLifKPyhrEuBGfN48iam2gII/4iI05EQy6XY+7cucjJ\nyVHGau+HhoYKlRYhokd7RoTUkZCQUK8QATXFiEaMEaJfVIwIqePJkye88YoK1hVvhJDmQMWIMBUV\nFSEkJAS9e/fG0KFDlWtbNVRcXIyIiAi4u7vDw8MDGRkZLZxp86mdf60hc3PzFs6k9WiN/YyoomJE\nmOLi4hASEoLs7GwEBwcrV/dsaO7cuRgxYgQuX76MrKwsuLu7t3CmzScmJgaurq71Yq6urpgzZ45A\nGYlfa+xnRJXe1jMKYDzHGgMQwoizBjDwDZCIH8NozBrAcIYRZw1gaLC4kmSpuNczcnNzw5EjR5TL\nzEulUly5cqVem4cPH8LPzw/Xr19vdHvGss6MXC5HYmIiKioqYG5ujjlz5ohu8IIhfRattZ+1Bpp8\nFnorRoWM595nxO8y4hMZ8Uye2NrhjMastb9Yc9axdKv/UPIvcRejTp064cGDBwBq/p2dO3dWPq51\n/vx5zJo1Cx4eHrhw4QL8/f0RHx8PCwsLle3Rl4ThMKTPgvqZeGnyWdB0QK1cSEgICgoKVOKfflp/\n3LtEIoFEIlFpV1VVhczMTKxduxb9+vXDvHnzEBcXh48//pj3/WJjY5X3pVIppFKpTvmTpklPT0d6\nerpg70/9rHXQpZ/RnpEmWtmekZubG9LT02Fvb4/8/HwEBQWpHD4pKCjAyy+/jBs3bgAAfv31V8TF\nxWH37t0q26NfrIbDkD4L6mfiRcuOk2YRFhaGpKQkAEBSUhJGjx6t0sbe3h5OTk7Izs4GULPWjaen\nZ4vmSYwb9TMCNFKMKioqEBgYCF9fX3h4eOCf//wngJpdYEdHR/j5+cHPzw9paWktkixpWYsWLcL+\n/fvRu3dvHDp0CIsW1aw6dffu3Xon9BMTEzF58mT4+PggKysLH374oVApEyNE/YwATThMV15eDgsL\nC1RVVWHgwIH4/PPPcfDgQVhZWWH+/Pn8G6XDdIQHHT4xHGL+LMT8bzM2zTqAoXa0SmVlJRQKBTp1\n6gSg8S/hMEbchxFnjaZmFalBfEHWcrEljLjq4eYabRhxQgghetHoOaPq6mr4+vrCzs4OQUFByuO0\niYmJ8PHxwfTp05lXTBNCCCFN0eTRdA8fPoRMJkNcXBw8PDxgY2MDAFi8eDHy8/OxYcOGZxuVSOBQ\n57Ud/r4B7D2jHow4a/bvXjyxyCOMxs20Z5ReAaTfePZ4ySE6TKcJOnxiOMT8WYj532Zs9HKdkbW1\nNUJDQ3HmzJl6Y/ZnzJiBkSNHqrR3bOqGjYi0R82t1pJDwuVCCCFiovYw3f3795WH4B4/foz9+/fD\nz8+v3sVrO3bsgLe3t36zJIQQImpq94zy8/MxZcoUVFdXo7q6Gm+88QaCg4MRFRWF8+fPQyKRwMXF\nBevWrWupfAkhhIiQ3mZg4FuJFQB8GfF/M+Ksc0l8o7Xnq05TVWMwI87aLxzAiDecKDWGzhlpgo7l\nGw4xfxZi/rcZG5qBgRBCiFGhYkQIISIil8shk8kglUohk8kgl8uFTqlJaNZuQggRCblcjrlz5yIn\nJ0cZq71v6Gty0Z4RIYSIREJCQr1CBNQUo8TERIEyajoqRoQQIhJPnjzhjVdUVLRwJprT22G6PEac\n9b+ENZdpESPely84itH4NUZ8PyN+lRHXdGJVQghpQe3ateONm5ubt3AmmqM9I0IIEYmYmBi4urrW\ni7m6umLOnDkCZdR0NICBEEJEonaQQmJiIioqKmBubo45c+YY/OAFgIoRIYSISmhoqFEUn4boMB0h\nhBDB6W3P6DYjfo4Rv8eI/4sRP8AXZK3Q9xMj3pkRj2TE9zDihBBCdEJ7RsRoGeuV5oQQVXTOiBgl\nY77SnBCiivaMiFEy5ivNCSGqqBgRo2TMV5oTQlRRMSJGyZivNCeEqNLbOaMyRjyIEb/EiLdhxF/Q\n5E1fZMRZcxZlMuK9GHHS4mJiYpCTk1PvUJ2xXGlOCFGl9z0j1vc9S66G7X/XoG06a7w5q32uZu3F\nqKioCCEhIejduzeGDh2K4uJi3nbLly+Hp6cnvL29MWnSJOZhtKZKT09X+3xoaCji4+Mhk8ng4+MD\nmUyG+Pj4RgcvNLbd1tLW0BhqP6O2urXVhNEXI9YeFR8qRpqLi4tDSEgIsrOzERwcjLi4OJU2ubm5\nWL9+PTIzM3Hx4kUoFAps3bpVp/dtSocPDQ1FWloaRo8ejbS0tCaNojOEP1BDaGtoDLmfUVvt22qC\nzhkRtXbt2oUpU6YAAKZMmYL//Oc/Km06dOgAMzMzlJeXo6qqCuXl5XBwcGjpVIkRo35GqBgRtQoL\nC2FnZwcAsLOzQ2FhoUqbzp07Y8GCBejevTu6deuGjh07YsgQ1nQYhKiifkbA6QGAVnMTgyFDhnBe\nXl4qt507d3IdO3as17ZTp04qr//jjz84d3d37v79+9zTp0+50aNHcz/99JNKO6E/K7oJ23epn7XO\nW1PpZTRdTX8gxmL/ftYqgzW/UgsKCmBvb4/8/HzY2tqqtDlz5gwGDBiALl26AADGjh2LEydOYPLk\nyfXaUb9o3aifEXXoMB1RKywsDElJSQCApKQkjB49WqWNm5sbMjIy8PjxY3AchwMHDsDDw6OlUyVG\njPoZkXD0M4KoUVRUhPHjx+PWrVtwdnZGSkoKOnbsiLt37yI6Olo5Oelnn32GpKQkmJiYoG/fvvju\nu+9gZsZaTJ6Q+qifESpGhBBCBEeH6UiLSEtLg5ubG3r16oUVK1Yw202bNg12dnbw9vZudJt5eXkI\nCgqCp6cnvLy8kJCQwGxbUVGBwMBA+Pr6wsPDA//85z8b3b5CoYCfnx9Gjhyptp2zszP69OkDPz8/\n9O/fX23b4uJiREREwN3dHR4eHsjIyOBtd/XqVfj5+Slv1tbWav99mlwMGh8fD29vb3h5eSE+Pl5t\nvsaG+lkNo+xnTR7qQIiWqqqqOFdXV+7GjRtcZWUl5+Pjw126dIm37dGjR7nMzEzOy8ur0e3m5+dz\n586d4ziO40pKSrjevXszt8txHFdWVsZxHMc9ffqUCwwM5I4dO6Z2+6tWreImTZrEjRw5Um07Z2dn\n7q+//mo0X47juKioKG7Dhg3KPIqLixt9jUKh4Ozt7blbt27xPn/jxg3OxcWFq6io4DiO48aPH89t\n2rSJt+3Fixc5Ly8v7vHjx1xVVRU3ZMgQ7o8//mhS7oaO+tkzxtjPaM+I6N2pU6fQs2dPODs7w8zM\nDBMmTMDOnTt52w4aNAidOnVq0nbt7e3h6+sLAGjfvj3c3d1x9+5dZnsLCwsAQGVlJRQKBTp3Zi31\nC9y+fRt79uzBjBkzmjQ6qyltHj58iGPHjmHatGkAAFNTU1hbWzf6ugMHDsDV1RVOTk68z2tyMeiV\nK1cQGBgIc3NztGnTBoMHD8b27dsbzcEYUD+rYaz9jIoR0bs7d+7U6+COjo64c+dOs75Hbm4uzp07\nh8DAQGab6upq+Pr6ws7ODkFBQWpHYr377rtYuXIlTEwa/xORSCQYMmQIAgICsH79ema7GzduwMbG\nBlOnTkXfvn0RHR2N8vLyRre/detWTJo0ifm8JheDenl54dixYygqKkJ5eTnkcjlu39ZwniwDRf2s\nhrH2MypGRO8kEolet19aWoqIiAjEx8ejffv2zHYmJiY4f/48bt++jaNHjzLn2Nq9ezdsbW3h5+fX\npF+ix48fx7lz57B37158+eWXOHbsGG+7qqoqZGZm4u2330ZmZiYsLS1552Crq7KyEqmpqRg3bhyz\nTU5ODtasWYPc3FzcvXsXpaWl2Lx5M29bNzc3LFy4EEOHDsXw4cPh5+fXpC9CY0D9rIax9jNx9EJi\n0BwcHJCX92zK3Ly8PDg6OjbLtp8+fYrw8HC8/vrrvNem8LG2tkZoaCjOnDnD+/yJEyewa9cuuLi4\nYOLEiTh06BCioqKY2+vatSsAwMbGBmPGjMGpU6d42zk6OsLR0RH9+vUDAERERCAzk7VeSY29e/fC\n398fNjY2zDZ1LwY1NTVVXgzKMm3aNJw5cwZHjhxBx44d8eKLrDVWjAv1sxrG2s+oGBG9CwgIwLVr\n15Cbm4vKykokJycjLCxM5+1yHIfp06fDw8MD8+bNU9v2/v37ymUJHj9+jP3798PPz4+37bJly5CX\nl4cbN25g69atePXVV/HDDz/wti0vL0dJSQkAoKysDPv27WOO0LK3t4eTkxOys7MB1Byj9/T0VJv3\nli1bMHHiRLVtNL0Y9M8//wQA3Lp1Czt27FB7aMaYUD+rYbT9rNEhFoQ0gz179nC9e/fmXF1duWXL\nljHbTZgwgevatSvXtm1bztHRkfv++++ZbY8dO8ZJJBLOx8eH8/X15Xx9fbm9e/fyts3KyuL8/Pw4\nHx8fztvbm/vss8+alHd6erraUU7Xr1/nfHx8OB8fH87T01Ptv43jOO78+fNcQEAA16dPH27MmDFq\nRzmVlpZyXbp04R49etRonitWrOA8PDw4Ly8vLioqiqusrGS2HTRoEOfh4cH5+Phwhw4danTbxoT6\nWQ1j7Gd00SshhBDB0WE6QgghgqNiRAghRHBUjAghhAiOihEhhBDBUTEirUpBQQEmTJiAnj17IiAg\nAKGhobh27Rpv29zc3CZNpElIQ9TPNKeXlV4JMUQcx2HMmDGYOnUqtm7dCgDIyspCYWEhevXqJXB2\nRCyon2mH9oxIq3H48GG0bdsWM2fOVMb69OmDgQMH4v3334e3tzf69OmDlJQUlddu2rQJc+bMUT5+\n7TgMRYIAAAH+SURBVLXXcPToUQA1k2d+8MEH8PLyQkhICDIyMjB48GC4uroiNTVV+fqxY8di+PDh\n6N27NxYuXKjnfy0RCvUz7VAxIq3Gb7/9Bn9/f5X4L7/8ggsXLiArKwsHDhzA+++/j8LCQrXbqjsP\nWnl5OYKDg/Hbb7/BysoKH330EQ4dOoQdO3bgo48+Ura7cOECUlJScPHiRSQnJzf7JJ7EMFA/0w4V\nI9JqsCbSPH78OCZNmgSJRAJbW1sMHjyYOe8Xn7Zt20ImkwEAvL29ERQUhDZt2sDLywu5ubnKdsHB\nwbCyskK7du3g4eFR7zkiHtTPtEPFiLQanp6eOHv2LO9zDSciafiFYmpqiurqauXjiooK5X0zMzPl\nfRMTE7Rt21Z5v6qqSvlcu3btlPfbtGkDhUKhxb+CGDrqZ9qhYkRajVdffRVPnjyptxZMVlYWOnbs\niOTkZFRXV+PevXs4evSoyrLOzs7OOH/+PDiOQ15enka/aFloJi5xon6mHRpNR1qVHTt2YN68eVix\nYgXMzc3h4uKC1atXo7S0FD4+PpBIJFi5ciVsbW2Rm5ur/OU6cOBAuLi4wMPDA+7u7vXOCTT8dVv3\nce19iUSith0RF+pnmqOJUgkhhAiODtMRQggRHBUjQgghgqNiRAghRHBUjAghhAiOihEhhBDBUTEi\nhBAiuP8fibsW9JPEGM8AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# D and variance explained\n",
"f, (ax1, ax2) = subplots(ncols=2)\n",
"\n",
"ax1.plot(D, 'ok')\n",
"ax1.set_xlabel('Column')\n",
"ax1.set_ylabel('Singular value')\n",
"\n",
"ax2.plot(D**2 / np.sum(D**2), 'ok')\n",
"ax2.set_xlabel('Column')\n",
"ax2.set_ylabel('Percent of variance explained')\n",
"\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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1+s0vJyfHrA8sLi6Gu7s7pkyZgiNHjiAsLAwpKSlo166dcZ/k5GTj4+joaERH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\nioiIZOv/AHeboDVJAm0dAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# SVD performance\n",
"bigMatrix = np.reshape(np.random.normal(size=1e4*40), (1e4, -1))\n",
"\n",
"# this computes full U matrix; warning: slow\n",
"print 'timing for computing full SVD matrices:'\n",
"%timeit numpy.linalg.svd(scale(bigMatrix))\n",
"print '-----------------------'\n",
"\n",
"# this won't produce complete U and V matrices, but way faster\n",
"# I believe this is the comparable result compared to R\n",
"# by looking at the dimension of the U matrix from R's SVD, \n",
"# R by default doesn't compute full U matrix\n",
"print 'timing for computing incomplete SVD matrices:'\n",
"%timeit numpy.linalg.svd(scale(bigMatrix), full_matrices=False)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"timing for computing full SVD matrices:\n",
"1 loops, best of 3: 30.7 s per loop"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"-----------------------\n",
"timing for computing incomplete SVD matrices:\n",
"10 loops, best of 3: 86.5 ms per loop"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# for comparison, this is how R performs on my machine\n",
"from IPython.core.display import Image\n",
"Image('https://dl.dropbox.com/u/12210898/Rscreenshot.png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"png": 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kCKQIpAikCLx0I5AO1kPn7hV9OE6H36EnRuKkCKQIpAikCKQIpAi8ciPwSj48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"prompt_number": 35,
"text": [
"<IPython.core.display.Image at 0x1104cf290>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# SVD and NaN values\n",
"import random\n",
"\n",
"dataMatrix2 = dataMatrixOrdered.ravel()\n",
"dataMatrix2[random.sample(range(100), 40)] = NaN\n",
"dataMatrix2 = dataMatrix2.reshape(dataMatrixOrdered.shape)\n",
"\n",
"# ERROR\n",
"np.linalg.svd(scale(dataMatrix2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"ename": "LinAlgError",
"evalue": "SVD did not converge",
"output_type": "pyerr",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mLinAlgError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-27-e1d0ccd9dff7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;31m# error\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msvd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdataMatrix2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/linalg/linalg.pyc\u001b[0m in \u001b[0;36msvd\u001b[0;34m(a, full_matrices, compute_uv)\u001b[0m\n\u001b[1;32m 1319\u001b[0m work, lwork, iwork, 0)\n\u001b[1;32m 1320\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mresults\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'info'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1321\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'SVD did not converge'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1322\u001b[0m \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_realType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1323\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcompute_uv\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mLinAlgError\u001b[0m: SVD did not converge"
]
}
],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# interpolate NaN values and compare the SVD results\n",
"def nan_helper(y):\n",
" return np.isnan(y), lambda z: z.nonzero()[0]\n",
" \n",
"idnan, x = nan_helper(dataMatrix2)\n",
"dataMatrix2[idnan] = np.interp(x(idnan), x(~idnan), dataMatrix2[~idnan])\n",
"\n",
"U1, D1, V1 = np.linalg.svd(scale(dataMatrixOrdered))\n",
"U2, D2, V2 = np.linalg.svd(scale(dataMatrix2))\n",
"\n",
"f, (ax1, ax2) = subplots(ncols=2)\n",
"ax1.plot(V1[:,0], 'ok')\n",
"ax1.set_ylim([-0.8, 0.8])\n",
"ax2.plot(V2[:,0], 'ok')\n",
"ax2.set_ylim([-0.8, 0.8])\n",
"f.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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1efJkPf/8847mqKqq0ogRI3Tffffp2muv1fz583X27FlP6nv11Vc1e/ZsR88d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\nAMBK/wcPplE517vcVQAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%R -o faceData\n",
"download.file(\"https://spark-public.s3.amazonaws.com/dataanalysis/face.rda\",destfile=\"./data/face.rda\", method=\"curl\")\n",
"load(\"./data/face.rda\")"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# face example\n",
"matshow(faceData, cmap='hot');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAPwAAAD5CAYAAAADZljUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngBfCIhTwQliEAl4Ii/hf/BXE43y9pQYAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# face example - variance explained\n",
"U, D, V = np.linalg.svd(scale(faceData))\n",
"\n",
"plot(D**2 / np.sum(D**2), 'ok')\n",
"xlabel('Singular vector')\n",
"ylabel('Variance explained');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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IiYlxui4TRddyZr7j5nLDhw9vt5yzCcDZhOJMOXf0iFzdlrPlumui665tuesz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\n"
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# face example - create approximation\n",
"# note: the V matrix from numpy SVD is transposed compared to R\n",
"# therefore there's no need to transpose it again for the reconstruction\n",
"approx1 = np.dot(U[:,:1], np.dot(np.diag(D)[:1,:1], V[:1,:]))\n",
"approx5 = np.dot(U[:,:5], np.dot(np.diag(D)[:5,:5], V[:5,:]))\n",
"approx10 = np.dot(U[:,:10], np.dot(np.diag(D)[:10,:10], V[:10,:]))\n",
"\n",
"f, (ax1, ax2, ax3, ax4) = subplots(ncols=4)\n",
"\n",
"ax1.matshow(faceData, cmap='hot')\n",
"ax2.matshow(approx10, cmap='hot')\n",
"ax3.matshow(approx5, cmap='hot')\n",
"ax4.matshow(approx1, cmap='hot');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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WuQkaEkm7V1QeY1dQFNQaoWzbmlGcp5FF35d9JuqDUVr0pNjKR6G2SfcraUj3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\n7GDZwzjaJg6IDYkcX/8ZZ70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}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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