{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %load ../../preconfig.py\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set(color_codes=True)\n", "plt.rcParams['axes.grid'] = False\n", "\n", "#import numpy as np\n", "#import pandas as pd\n", "\n", "#import sklearn\n", "\n", "#import itertools\n", "\n", "import logging\n", "logger = logging.getLogger()\n", "\n", "def show_image(filename, figsize=None, res_dir=True):\n", " if figsize:\n", " plt.figure(figsize=figsize)\n", "\n", " if res_dir:\n", " filename = './res/{}'.format(filename)\n", "\n", " plt.imshow(plt.imread(filename))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "11 Dimensionality Reduction\n", "========================" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 11.1 Eigenvalues and Eigenvectors of Symmetric Matrices\n", "\n", "#### 11.1.1 Definitions\n", "$M e = \\lambda e$, where $\\lambda$ is an *eigenvalue* and $e$ is the corresponding *eigenvector*.\n", "\n", "to make the eigenvector unique, we require that:\n", "\n", "1. every eigenvector is a *unit vector*.\n", "\n", "2. the first nonzero component of an eigenvector is positive." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.1.2 Computing Eigenvalues and Eigenvectors\n", "To find *principal* eigenvector, we use **power iteration** method: \n", "start with any unit vector $v$, and compute $M^i v$ iteratively until it converges. When $M$ is a stochastic matrix, the limiting vector is the *principal* eigenvector, and its corresponding eigenvalue is 1.\n", "\n", "Another method $O(n^3)$: algebra solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.1.3 Finding Eigenpairs by Power Iteration\n", "idea: \n", "Start by computing the pricipal eigenvector, then modify the matrix to, in effect, remove the principal eigenvector.\n", "\n", "1. To find the pricipal eigenpair\n", "\n", " power iteration: \n", " Start with any nonzero vector $x_0$ and then iterate:\n", " $$x_{k+1} := \\frac{M x_k}{\\| M x_k\\|}$$\n", "\n", " $x$ is the pricipal eigenvector when it reaches convergence, and $\\lambda_1 = x^T M x$.\n", "\n", " Attention: Since power iteration will introduce small errors, inaccuracies accumulate when we try to compute all eigenpairs.\n", "\n", "2. To find the second eigenpair\n", "\n", " we create $M^* = M - \\lambda_1 x x^T$, then use power iteration again.\n", " \n", " proof: the second eigenpair of $M^*$ is also that of $M$. \n", " 略" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.1.4 The Matrix of Eigenvectors\n", "the eigenvectors of a symmetric matrix are orthonormal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.1.5 Exercises for Section 11.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 11.2 Pricipal-Component Analysis\n", "idea: \n", "treat the set of tuples as a matrix $M$ and find the eigenvectors for $M M^T$ or $M^T M$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AJETexv8Gj0bl8jYgEjF3bD84OFbHmVfpJdlke/wn4/NWrdCqVSt88c1yVChj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\n6e8VM+hT7/kkElH8y5tUq3o1uvcqhoj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(plt.imread('./res/fig11_2.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.2.2 Using Eigenvectors for Dimensionality Reduction\n", "Since $M^T M e = \\lambda e = e \\lambda$, \n", "Let $E$ be the matrix whose columns are the eigenvectors, ordered as largest eigenvalue first. Define the matrix $L$ to have the eigenvalues of $M^T M$ along the diagonal, largest first, and 0's in all other entries.\n", "\n", "$M^T M E = E L$\n", "\n", "Let $E_k$ be the first $k$ columns of $E$. Then $M E_k$ is a $k$-dimensional representation of $M$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.2.3 The Matrix of Distances\n", "\\begin{align}\n", " M^T M e &= \\lambda e \\\\\n", " M M^T (M e) &= M \\lambda e = \\lambda (M e)\n", "\\end{align}\n", "\n", "the eigenvalues of $M M^T$ are the eigenvalues of $M^T M$ plus additional 0's, and their eigenvectors are shared." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.2.4 Exercises for Section 11.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 11.3 Singular-Value Decomposition\n", "#### 11.3.1 Definition of SVD\n", "Let $M$ be an $m \\times n$ matrix, and let the rank of $M$ be $r$.\n", "\n", "$$M = U \\Sigma V^T$$\n", "\n", "+ $U$ is an $m \\times r$ *column-orthnormal matrix* (each of its columns is a **unit vector** and the dot product of any two columns is 0).\n", "\n", "+ $V$ is an $n \\times r$ column-orthnormal maxtrix.\n", "\n", "+ $\\Sigma$ is a diagonal matrix. The elements of $\\Sigma$ are called the *singular values* of $M$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LDIOq1cDN6Pz3vvbT1diMTakf4FU2LHffBq55eAEeLlCfEMJ1SSBXIfmHttNu\nXBTN90SzevdxNFsJ9909gHUbNhHS4G2+/u6+K7sHZk3nlhu7Yj7HU8u/3kqnsGqXvaS/e+Olz+g9\n+Rk8zto1vfq1d5n/5KIr+7MRQvxnEshVyNerVhMxYDrHVnZm51u7eW/WaIbMX03BH59itxvoHOzj\n7BIrlTLWZte+fRWG63Q617hRhSphZ04B795/+1+DlJ2PN/3OA7P9nViYEKIqkECuQv73zme8OG4+\nbo2bwaHZzPu2Hz/HdiSqW2+8rh+Gp5vB2SVWqsXzZ/DBJ99XGB7SujNvLZnn9JPZ7Dm7MZn96NA0\nuGxYSfZJclv2xtv9yv5shBD/nQRylaCwmfPYFtgafw8D9RuF4OZuYP1Xr6LTTCzenskT8/o6u8hK\n98hjT9FvyJMVhrt5eKN3gTPLDf7BeBjyOHwqi2DfOthtxSSMG0hExPuyu1oIcVFVKpCVUihAd/qx\nXq8vHXb68RXLXsTD99+NW76V5Zv/4N6GTXjx02/xN2cx+rHR1KnXkO1fvMnhkT25xs/xv0DiKnwC\ngvAJCHJ2GednbMCaVxYyrMcdXN+lJVnH9nHP2Bju6RTi7MqEEFVAlQnk33Zu58tPV+PV/D4a8xtR\n81ex+ftPWPvWImYu+ZzN29fidaWexWrwJfmLzeUGPXJ6Hf/68o+dUJA4nx4jIzgyMsLZZQghqqAq\nk2DNWrciOn4BmVs+4KBfSw7+vJY3Zo2mpH4L9uxcT7b5yvw5OCGEEFeHi/aQNU0jOjqaw4cPo9fr\niY+Px93dnenTp6PX6wkPDyc2NhaAlStXsmLFCtzc3BgzZgzdu3d3WKG2k99T3WbFvXU/hrbxYLy/\nncB7Z3Fd0XrMOl9qeVaZzr4QQghRwUVTbP369eh0OpYvX862bdtYuHAhSikmTZpEp06diI2NZd26\ndbRr147k5GTWrFmDyWRi0KBBdOnSxWE/U7V8ThLWxh2YMvwGNi0dTv2WDzGwY30WT/6UFiMXc0Xf\nD0MIIcQV76IxdvvttzNr1iwAUlJSCAgIYM+ePXTq1AmAbt26sWXLFnbt2kXHjh0xGo34+voSGhrK\nvnNcM/pvvfrdHzw+7y2Meh0zZq7i8Qnj0SvFF6s/Z8Gkm5i94EfOcQMnIYQQokq4pH6lXq9n+vTp\nJCYm0rt3b9RZ9y708fGhsLCQoqIi/Pz8yoZ7e3tTUFDgsEKPp9sYf1czdNg47uHPwNuao5TGoWIv\nYidOY3qubqpsAAAgAElEQVTE9XJpiRBCiCrrkg+8zp07l6ysLPr374/Z/NfNC4uKivD398fX15fC\nwsIKwx3leEZG2eOU1L9+6eiPk6fQGwyucacmIYQQ4l+6aA/5o48+4pVXXgHAw8MDvV5Pq1at2LZt\nGwCbNm2iY8eOtG7dmh07dmCxWCgoKODQoUOEh4dXbvWAwWiUMBZCCFHlXbSH3LNnTyIjIxk6dCg2\nm43o6GiuueYaoqOjsVqtNGrUiF69eqHT6Rg2bBiDBw8uO+nL3f3KvUmFEEII4UgXDWQvLy+ee+65\nCsOTk5MrDBswYAADBgxwTGVCCCHEVUQuFhJCCCFcgASyEEII4QIkkIUQQggXIIEshBBCuIAqF8ia\nppW7MYkQQghxJahygXzgwAGKioqcXYYQQgjhUFUukG02G5qmObsMIYQQwqGqXCALIYQQVyIJZCGE\nEMIFSCALIYQQLkACWQghhHABEshCCCGEC5BAFkIIIVyABLIQQgjhAiSQhRBCCBcggSyEEEK4AAlk\nIYQQwgVIIAshhBAuQAJZCCGEcAESyEIIIYQLkEAWQgghXIAEshBCCOECJJCFEEIIFyCBLIQQQrgA\nCWQhhBDCBUggCyGEEC5AAlkIIYRwARLIQgghhAuQQBZCCCFcgASyEEII4QIkkIUQQggXIIEshBBC\nuAAJZCGEEMIFXFIgZ2Vl0b17dw4fPsyxY8cYPHgwQ4cOJT4+vmyclStX0q9fPx588EE2btxYWfUK\nIYQQV6SLBrLNZiM2NhZPT08AkpKSmDRpEu+88w6aprFu3ToyMzNJTk5mxYoVLFu2jAULFmC1Wiu9\neCGEEOJKcdFAfvrppxk0aBC1atVCKcWePXvo1KkTAN26dWPLli3s2rWLjh07YjQa8fX1JTQ0lH37\n9lV68UIIIcSV4oKBvHr1aqpXr06XLl1QSgGgaVrZ8z4+PhQWFlJUVISfn1/ZcG9vbwoKCiqpZCGE\nEOLKY7zQk6tXr0an07F582b27dvHtGnTyMnJKXu+qKgIf39/fH19KSwsrDBcCCGEEJfmgj3kd955\nh+TkZJKTk2nWrBnz5s2ja9eubN++HYBNmzbRsWNHWrduzY4dO7BYLBQUFHDo0CHCw8MvyxsQQggh\nrgQX7CGfy7Rp04iJicFqtdKoUSN69eqFTqdj2LBhDB48GKUUkyZNwt3dvTLqFUIIIa5IlxzIb7/9\ndtnj5OTkCs8PGDCAAQMGOKYqIYQQ4iojNwYRQgghXIAEshBCCOECJJCFEEIIFyCBLIQQQrgACWQh\nhBDCBUggCyGEEC5AAlkIIYRwARLIQgghhAuQQBZCCCFcgASyEEII4QIkkIUQQggXIIEshBBCuAAJ\nZCGEEMIFSCALIYQQLkACWQghhHABEshCCCGEC5BAFkIIIVyABLIQQgjhAqpMICul0DSt7H9N05xd\nkhBCCOEwRmcXcKkOHTpEz549sVqtGI1GlFJs3bqVWrVqObs0IYQQ4j+rMoHcqFEjjh8/jtVqBcBg\nMBAYGOjkqoQQQgjHqDK7rAH8/f3LHtetWxd3d3cnViOEEEI4TpUK5LFjx5Y9HjhwoBMrEUIIIRyr\nSgXyoEGDyh736tXLiZUIIYQQjlWlAjkkJAQ3Nzf0ej2dO3d2djlCCCGEw1SZk7oAfHx8aNKkCVlZ\nWXh5eTm7HCGEEMJhqlQgA9x4443k5eVhMBicXYoQQgjhMFUukPv27UtISIizyxBCCCEcqsoFcq9e\nvbDZbJU6DU9PTxYvXoxeX6UOsVdZzpzPO3bsYPHixU6bvjPIci2Ea9IppZSzi3A1RUVFzi7hquPt\n7Y1Op7vs071aP2tnzW8hxPlJIAshhBAuQPZdCSGEEC7gko4h9+3bF19fXwDq16/PmDFjmD59Onq9\nnvDwcGJjYwFYuXIlK1aswM3NjTFjxtC9e/dKK1wIIYS4klw0kC0WCwBvv/122bCxY8cyadIkOnXq\nRGxsLOvWraNdu3YkJyezZs0aTCYTgwYNokuXLri5uVVe9UIIIcQV4qKBvHfvXoqLi3nkkUew2+1E\nRESwZ88eOnXqBEC3bt3YvHkzer2ejh07YjQa8fX1JTQ0lH379tGqVatKfxNCCCFEVXfRQPb09OSR\nRx5hwIABHDlyhNGjR3P2eWA+Pj4UFhZSVFSEn59f2XBvb28KCgoqp2ohhBDiCnPRQA4NDS27EUdo\naCiBgYHs2bOn7PmioiL8/f3x9fWlsLCwwnAhhBBCXNxFz7JetWoVc+fOBSAtLY3CwkK6dOnCtm3b\nANi0aRMdO3akdevW7NixA4vFQkFBAYcOHSI8PLxyqxdCCCGuEBe9DtlqtRIZGUlKSgp6vZ6pU6cS\nGBhIdHQ0VquVRo0akZiYiE6n44MPPmDFihUopRg7diy333775XofQgghRJUmNwYRQgghXIDcGEQI\nIYRwARLIQgghhAuQQBZCCCFcgASyEEII4QIkkIUQQggXIIEshBBCuAAJZCGEEMIFSCALIYQQLkAC\nWQghhHABF/1xCfHf2O12zn8zNB1GowEATdPQ611k+0gpFKDT6f7Zc2WjqHLP//3vC09aoWnaBccx\nGAxYzGYsFgtePr4Y9JfW9oWU5OdwKiuXOvUa4u1u+M/tOYpmt5FyMgW9hw/Btapd8ny8ZEqhAXpH\nt3sWm8WC2WrB4OaBp7vzfh/dbCrBYrXh7aBlpiKF2WzGYrbi5euD0VW+zw6h0NTFlpNLGUdcyJW0\nxLikWdMfp0ubcEIaNmTQkCEMGTyYwQ8OpEPrZoQ0vA27UmT+/jHDHx5Pie3CQVTZNLsNk6mYTZ+9\nx9pfDpZ7zm63YSop4rP3X2JXWv6FWuGF2fF8vf57du/+lQ9WvEXy179yqfdn/eHd52nUOJwed9xF\nnz73EdawAc07dKbP/fdz07UdCQlrQkaRhUlPjqBl86YcTCu8eKMXkbr3G67r0pf5c6bSskcsmovc\nTFYpxePD+/Dauh1069ia/RnFDp/GgZ0bGDT8CUqsdoe3fcbi5+ZwfZtWLF31XaVN41JMHvMALZs1\n5XCm4+cjAJqJ8WMepmXzNvx5we9I1XP8j60MGT6G7GLb6SEKq8VSbpz9P29g0LCx5JXYKjYgLon0\nkCtZ3PyX6d01ifvGfMTy5Sswnt4EshTn0rl9B+yaIvvwPvbuOYDFrvBy4ieydd37PPfeD/yyfg0R\nSz6EDn89t+adF1i5/k92fLOapd/0o22d87fz/ZfLWZK8HL3RnRvuHs5zia251G3mUwWZLFvzDbe3\nCwOgbctwhkyey1PDbwM0nh19CzkmG0tefZ/DzcJxREdn7txnmPH627T3OMVtJ9wvudZKZ0/lhxM+\n7HjoPpq6F1LH393hk8g6fJBDf/yEza6gkjqvEU/FUbfkT1Jw7p6HJa+9y69N22LQVVI/RO/Fy28s\n5+YObdG7zlLkELkpxzj0x8+YLDbwNoKyMT36eRbMm1I2TubhQxze+zNmmx2Jln9H5tplUNrhMnJm\nT05hXh4+/oE80z8Es10j/O4pbL97CvxtN+9Zf2DXFAbDXysSnU531jg6dLq/XlP6+K/hoNA0hVKg\n1+vOu9vzhjuGcsMdQ+nf+PMKz/UfMZ7+wxU9r/nkou+35o3D2PN0VFmdZ88JpS68u7sgz0DPlg3L\nDftrbD0PR0azM6eIJtW9MZ5+5u/zoWxqp3d/6/X6805TKYWloJA61b1pGnYtzdqUzjylnd79dtb8\nqnjoQQeX2Pe/2C5+pWkodH9NTymUJRMPXx/06HhgyDDO3cSZz1Zd8H2emY6maaArjQudTsd1fUax\nrc+ov6Z5kdr/Pg/sdjsGg6H8uGe1c+a1ur/tvlVKoZSGQo9ed2Y8xbmO7pzrPZ1dR/nvwunnNQ10\nOnT68tFYbmks+77oKrRXrkalu+D35u/1/P2DOvP5otOj0+vKajjTfulyW3450zTt9DB9WXNl9UK5\n+Xu+2is69/dDd3q50Z1ruAKdXkerWwfw4/YBcHp6hWmH+TU9p1xNnfs+wta+j1RYj51pS1+htvLf\nH4cfjqmCJJAvI3V6RTX4xs6s3r2HGya8gFFvIuapSDJyYeELi/Bx02MzF/HGc0kcLVAEN76WjF+/\n5ecDR0l66lFeXP4R9Zt0Y9qEQbyZGMm2EzkMjZxHl1Bvpk2ZSm6+iRlPPsizryznpqHTGNA5jGP7\ntrPgxXcxGHTUb9+LCUPuqKRjaKXsdiuH9u3iZEY+14S3oF7t6uh0YCnM5oWX3mLUuPH4epx70evc\nszc+hvP3YHzrXUsbm1fZ34W5x4l/8X0KcrO5Z+REbm7TGJ0OSvJTmTlzLna9nhKTL08viMbfq2IP\n8+v3lrHvRAZr3n2VnbXDmDB6IKmHfuO5pW9g1IF3/ZZMGDscP0/FjKeeIivHxPiRfXg5eTU9Rseg\n/30Vn37/O/ePnsSutR+Qk5NHi5vv5662NVnyyrvkF+QzaMwUOjWtf873o5SdzR+vYM3G7ej1Ojrf\nOYD7b+2MNesIz897gexTB1iyZAm39BtB63r+FV6/d/s3vLXyK0pMZtr37M/Qu7ue+7NVNj5+fQk7\nThRiNRWQmuPDqy/GEDNtMpnZ+Tz3wstYDm4ievFK6l97F+19U/j+16MUuAeTNH0s3u5GlLLz07o1\nrPrmZ0rcA+kUrPHl+m08kfgsq19eSKHJznOLFpH/22ckvPIFlno9eDm67zn6ihrrP3qDL7/fg6XE\nQr+R4+jaIRxlyiJyegI5xkAeuaMFb33wDYPGRdG1TWj5l1vTePm1VdjtCv8azRky8FY+fnMZaRYb\n13S6Hbdjm/l8825MJWZ6P/Qkt3dqWvG4pj2P6Igo0os9eP6VBZz8aS2L3vqQ2o1aMyNiDDoUu7//\njNf+9w0GncYNdw2lX49rz3l8tDg/g1eXvEhGsYXQFjdgO+uYh91q4oOXk9h6MB+b2cRj02bRMqQG\naHZ2bPyIt9d8i6enB6263MmQe7ujx87a99/my+27Mejg5vuHcedN7TFoucyYFEOmqQ4THuvCBx99\nQ05eIZOiY9m7YTmbfz2OzqcB0yY/ho+HnYQZ0zmZWcjohwfwyecbKCw08dCTk2jTuHQ51KwmVry5\nlG17MtEbNfqNGMMNrcLQLCW8Nv8ZTtm8MBWlYajWgIRp45gdG8nxU1kkLlxK0fGdTH9iFEdLglmy\nZAk1GrbiwXu6EhcTSUpaDnMXvUh1HzfMhdksfv45UjJsaG5Gxk6YQJN61fli6UI+2b2PQWOm8vvG\n9zmRmkej6+9kRJ9bMVztoaxEpdv20RxVN7iNWr1qtVr2bIxq0KChstq1s8awqdD6LVS2yaaU0tTk\noXepu5M+V0op9WiXVmryok/U5yuWK5tdU18l3aP6DE1U2umXD7nrevXq9pNKKaXs1hIV2qC+unHq\ncvVS5AB13aClKvvQT6p+vUaq0GxTSinV59rm6q11f1yw3n6NQtULH26t+ISmqR6hDdUXe9Mu8Gq7\nGnRdc/XFryeUMmWqVg3rq4+3HlFKKXXyl69VaIN6amdK/qXMNqWUUm1aNFbz3lp3zufubRqu2lw/\nQVntSqn8XapJ25tVicWm7LYS1attmPr6j9I6t704WvV/bKbSNO2c7Tze/ya16WimUkopU+4x1axF\nJ5VXYlVKKbVj5Ux10x3DlcWuKUvBKRUW0kDdn/A/NefJ+1X3ka8rTSnV6/p2qlHTW1S+yaaUJVO1\nathA9Rg4Stnsmso8+KNq2Kqvsp1z0pr6ZOEj6q6h05TNrimlNDWhbxe14KNflaZpym7+Q13be5Sy\nn6dupUyqWUiw+ua3FKU0u+rdsZn6YveJc4556sdk1Wnmx0rTNKVpdjXo9hHKqmnKXnRShdevp3KL\nLaXv9/MXVN3gYLXlUK5SSqnB7VuqRWt+UZpSat+Gd1W9sNbKbNPUwXVLVdsbeqiDu7aq9EKzMqft\nUKHXNFFFp5ez799+RtXtEqvsp6e/ImGIWvjeRqWUUpaTP6q6DRurlEKT0uw21SKsgTqSXXx6zGzV\nKDRYxbz+uXqsV3cV8fx753w/ab+tVfXrBquswtK60w9sVo9Mn68KMw6qpg2D1bEck1KmDNU6tL7a\neiC99EW2fNW1UZg6lF46rcLMP1XT0GtVQWnJ6ui659WtAx9SNrum9mx4TzVp2U0VWkvn/S3tmqrv\n952q+Alai1Wn1q3Uqu0HlVJKpf72tQqpF6b+SMlVmqap2eMHqbtnvF06ct5vqlnHHqrAZFVbP1qi\nmra6RxVZlbLl/KFCgkPUr8ey1IrEB9XwyfNPL6s2NaJHB/XSJz8pTdNU7onfVXhIPTX95S+UUkpt\neX2CqhvcUH1/OEMppdTQ3jephZ9uU0opZS04pZqFh6knF69SmlKq+OROFd6gntp9Ildpml2Nue8W\nFfnql0pTStlNuerm9i3Ut3+kqI/nR6tX1pd+3prdph4eP0nZNU3ZS9JV69CG6khm6bz7fcOr6roH\nnyo3L+xFJ1R4vbrqZI5JaZpN9bqug/pw6/7SenIOqObNWqqDaXlKKU3FjbhV1avbSmUWmJRSSl3X\nsrn6M73gnJ/11URO6rps9Nzesyd9Bj6Mr/vfe4eGs86wVhzc/zu9b20PwKgh17J3zxZ6DXgAg15H\nWOO25V7pFRBQ9lin04EOVs/sw2NzVrL1vcdZsTSeaj3GUJiTSVpaGk+O68MXG76ptHeplI4lX/5A\nrzb1wKM67yXcw9SIiVjsGnXb9eC3vX/SNtjPYdN74a3I0uPyfmEoiwmbUqT8to7f0j1oFqBIS0uj\nwf1T+fnbH7Ge52x3pYH99Hko8Q/cw413jcDvdA++w4BYMvev5+fDmegNBnQ6WDL+LiIXr2HDaw+j\nA9oajNz5yFR8PQzg5k9tfx1zn30Gg16Hm5cf+pyT2M8xaWUvJP6Fr5ke/9TpXq2OSRMf4flJD1Bi\n1cBuBU27wF5xIyMfGUWAp8apU6do2aohm/efPOeYBg9vspIjmfvsUrb9/BuPRgxHD+g9PPE4a7zA\narVwD7mP68NKl6vbWrmTmZEHwPbfdqIa3YvRoCOsS0/yUjIJCm9PTR933INqlTsEXaN24Hl2sYMh\nMIRRw4egFRWQcuIUwQZ30rOLTj/rid7uyag+3Xnpiw0sHPcgBQUFZf+Kik0ooFbLW2hVP5CXvvgV\npeC7Tz5gyvjRuPtUY/iox1DmQk5mmahd25/9qRnnrMPNPRCj219V17wmrOzxwuhnuWfkSAqz0klL\nS6N362C+XrezQhsbno9AX7cFvduHAlC7ZQ9CapUu37aSPN7/8gcm9O9MWloaaSU1CNBOciCtiKg5\nL/P4zBl4G0HnVZspU6dS399K4iubeOyxYad33xqIiRjMkqQoTFYNdw9f9AY3Jg6+DYCwttdS/7qe\n3BhSHQCjtyeppwoA0BkM6IDxA3uhA7zqtmHIHW15OPJNCo79xOc/7WNMn67oAL1HAEPuvpkp4+fg\n5unFs9Om8OyyZHbuOcjQPveXjuPmjs9ZH6jNbitdNs+id/fkzL6r1B/f5KAWxO1tS+eLMbARt11T\njWdf+QjQEVi9BoNmzae6b+nS5+FjoNBU/iSxq5EE8mXjg7ePD9XqhtG1VasLjKfnrhu78casVygs\nyOOZJd9xa4/7/9GU/M66tOTI7t+oW81ISkoKKSkpBLXqT8yovv/yPVxczomfeW35V2V/X3N9FwoO\nH6PkdCL5eHs7dHq1A860Z0CnAAVZp/ajEUzaqdL3fOpUIR8sn4/xEnaHrU01E9SgyVkHG/UY3T1I\nKQsM8PesuOv7mqYNTr9Eh14PNc8xzt/ZC7PIMCvqBXqWDasZFo7VasNsv4Qz7pWOEH+Nx4cP5pcD\naeisOaWDzzFq9db3kLxgAl/87x2G9bmbCYte53yTaNgypGzF4OYGnD4Bu0ePuzHue4+UzDy+efcN\nmlzXDr8KG5eXwC0A7eiPDHnwSdILbRTqVPkVkW8tAr3PLMMWenXvSreupf8ei1lw+gQJA89M6s+K\n5xMpsppZvdNIo9r+GNy8KUw9xPAhQzmSlgd203nnSUV/LR97rSW4W/Rl35tbIhbwSJ9rK7xi5y9p\n1A4ML3+J0+nlzGbJx2IyY87PJiUlhZNHT7L01WQa1fKhqKSEug1qAaD3COLJiCfwtaSRZTNQw++v\n70hw89Zk5xadtTzUx9erdN7o3dyoUe0i36eyN66jXpMmnNr8JSeOHEZTCh/vv5bRViEBWPL2c9Mj\nEcQM68L/li2m7923seTNz7jY+ffFxRXPWv9jy1aCArwwnnX46dpGXmRlnSj7u3m94Arz7GongewE\nL3/4EcYLHMPNLLIwf0IbFi9eypi3viSi77V/O7HGfuYBxTk5/P0g3dnLdoubbuT4/lzatWtH+/bt\nadeuDekpxx35dsjLyS7buv39s5d49fUPyr7EaX/uw+Djj1GnQ2l2MjMy0M57XbZj1Alrj1GXRrNW\nbWnfvj3t27fHlldwSZcz3dbQn1MHdpw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2FfKpL7aeUJrS1MBm5dS8jccf+Lxz586p4OBgu15TiKxGRtRCZBIdRsCATqfD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\n5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image('fig11_7.png', figsize=(8, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.2 Interpretation of SVD\n", "viewing the $r$ columns of $U$, $\\Sigma$, and $V$ as representing *concepts* that are hidden in the original matrix $M$.\n", "\n", "In Fig 11.7:\n", "\n", "+ *concepts*: \"science fiction\" and \"romance\".\n", "\n", "+ $U$ connects peopel to concepts.\n", "\n", "+ $V$ connects movies to concepts.\n", "\n", "+ $\\Sigma$ give the strength of each of the concepts." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.3 Dimensionality Reduction Using SVD" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yPKsGDpW23p9KLfWajJ4NVaRWiVlzMzicm0rBqowMDJdr8yozp/bBbNJ4cfwE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image('fig11_9.png', figsize=(8, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we set the $s$ smallest singular values to 0, then we can also eliminate the corresponding $s$ rows of $U$ and $V$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ec937eLrElWSJx55u798DPOj8/5WnRWQPPV8Gfi+elIwaV0anEvITtm35GIoX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hAAAg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\njRolmzZtkoiICGnYs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image('fig11_10.png', figsize=(8, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.4 Why Zeroing Low Singular Values Works\n", "Let $M = P Q R$, $m_{i j} = \\sum_k \\sum_l p_{ik} q_{kl} r_{lj}$.\n", "\n", "Then\n", "\\begin{align}\n", " \\| M \\|^2 &= \\sum_i \\sum_j (m_{ij})^2 \\\\\n", " &= \\sum_i \\sum_j (\\sum_k \\sum_l p_{ik} q_{kl} r_{lj})^2 \\\\\n", " &= \\sum_i \\sum_j \\left ( \\sum_k \\sum_l \\sum_n \\sum_m p_{ik} q_{kl} r_{lj} p_{in} q_{nm} r_{mj} \\right) \\\\\n", " &\\text{as $Q$ is diagonal matrix, $q_{kl}$ and $q_{nm}$ will be 0 unless $k = l$ and $n = m$.} \\\\\n", " &= \\sum_i \\sum_j \\sum_k \\sum_n p_{ik} q_{kk} r_{kj} p_{in} q_{nn} r_{nj} \\\\\n", " &= \\sum_j \\sum_k \\sum_n \\color{blue}{\\sum_i p_{ik} p_{in}} q_{kk} r_{kj} q_{nn} r_{nj} \\\\\n", " &\\text{as } P = U, \\sum_i p_{ik} p_{in} = 1 \\text{ if } k = n \\text{ and 0 otherwise} \\\\\n", " &= \\sum_j \\sum_k q_{kk} r_{kj} q_{kk} r_{kj} \\\\\n", " &= \\sum_k (q_{kk})^2\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "How many singular values should we retain?\n", "\n", "A useful rule of thumb is to retain enough singular values to make up 90\\% of the *energy* in $\\Sigma$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.5 Querying Using Concepts\n", "Let $q$ is the vector of user Quincy\n", "\n", "+ what movies he would like?\n", " \"concept space\": $q V$, select the one whose score is highest.\n", " \n", "+ find users similar to Quincy?\n", " measure the similarity of users by their cosine distance in concept space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.6 Computing the SVD of a Matrix\n", "The SVD of a matrix $M$ is strongly connected to the eigenvalues of the symmetric matrices $M^T M$and $M M^T$.\n", "\n", "$M^T = (U \\Sigma V^T)^T = V \\Sigma^T U^T = V \\Sigma U^T$\n", "\n", "\\begin{align}\n", " M^T M &= V \\Sigma U^T U \\Sigma V^T \\\\\n", " &= V \\Sigma^2 V^T \\\\\n", " M^T M V &= V \\Sigma^2 V^T V \\\\\n", " & = V \\Sigma^2\n", "\\end{align}\n", "\n", "similar, $M M^T U = U \\Sigma^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 11.3.7 Exercises for Section 11.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 11.4 CUR Decomposition\n", "SVD: even if $M$ is sparse, $U$ and $V$ will be dense.\n", "\n", "CUR: if $M$ is sparse, $C$ and $R$ will be sparse.\n", "\n", "\n", "#### 11.4.2 Choosing Rows and Columns Properly\n", "\n", "Let $f = \\sum_{i,j} m_{ij}^2$.\n", "\n", "1. find $C$\n", " + pick $r$ rows, and each row is picked with $p_i = \\frac{\\sum_j m_{ij}^2}{f}$.\n", " + normailize: each row is divided by $\\sqrt{r p_i}$.\n", " \n", "2. find $R$ \n", " selected in the analogous way.\n", " \n", "3. Counstructing $U$.\n", " + find $M$, that is the intersection of the chosen columns of $C$ and $R$.\n", " + compute the SVD of $W$: $W = X \\Sigma Y^T$.\n", " + compute $\\Sigma^+$, the *Moore-Penrose pseudoinverse* of the diagonal matrix $\\Sigma$: replace $\\sigma$ by $1/\\sigma$ if $\\sigma \\neq 0$.\n", " + $U = Y (\\Sigma^+)^2 X^T$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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87I+NEff4dsEVdrZK3MJv27o99Ju1114HFu08TdaM+VGAE6cDqVA2r/2+iDH0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image('fig11_13.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Eliminating Duplicate Rows and Columns\n", "it is possible that a single row or column is selected more than once, how to deal with it?\n", "\n", "+ let it go.\n", "\n", "+ or, merge same rows and/or columns\n", " $W$ will not be a sqaure matrix, then we need transpose the result to get $\\Sigma^+$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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I01pGo/s4JU1PBT9+8SEz564kISkOd0UZ6YU6N424g17t43w8LEdhlGYy+emn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\nycjIICsriy+++II2bdowc+ZMFi5cSFlZGX379qV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_image('ex11_17.png')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Exercise" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }