{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "PCA, Nearest-Neighbors Classification and Clustering\n", "====================================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour details [Principal Component Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis) (dimentionality reduction), supervised classification using nearest neighbors\n", "and unsupervised [clustering](https://en.wikipedia.org/wiki/Unsupervised_learning) using [$k$-means](https://en.wikipedia.org/wiki/K-means_clustering).\n", "\n", "\n", "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from [LibSVM](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/).\n", "\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "[Scikit-Learn](http://scikit-learn.org/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "library(plot3D)\n", "library(pracma)\n", "options(warn=-1) # turns off warnings, to turn on: \"options(warn=0)\"\n", "\n", "# Importing the libraries\n", "for (f in list.files(path=\"nt_toolbox/toolbox_general/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_general/\", f, sep=\"\"))\n", "}\n", "for (f in list.files(path=\"nt_toolbox/toolbox_signal/\", pattern=\"*.R\")) {\n", " source(paste(\"nt_toolbox/toolbox_signal/\", f, sep=\"\"))\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dataset Loading\n", "---------------\n", "We use here the famous\n", "[IRIS dataset](https://en.wikipedia.org/wiki/Iris_flower_data_set) of Fisher.\n", "The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor).\n", " Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.\n", "\n", "\n", "Helpers." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Load the dataset." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "data(iris)\n", "A = iris\n", "# Transforming the species to numerical categories :\n", "A$Species = as.numeric(A$Species)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Randomly permute it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = A[sample(nrow(A)),]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Separate the features $ (x_i)_{i=1}^n $from the class information.\n", "The feature are stored as the row of a matrix $X \\in \\RR^{n \\times p}$\n", "Be sure to start the class at index 1." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "X = as.matrix(A[,1:(dim(A)[2] - 1)])\n", "y = as.matrix(A[,dim(A)[2]])\n", "y = y - min(y) + 1" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features,\n", "$k$ is the number of classes." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n = dim(X)[1]\n", "p = dim(X)[2]\n", "k = max(y)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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5yN79Pe9LbB5gpXTBqn8RM4ODi4W7du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7Bfq/hUeJ0gwzJcowws5zPp54V1xTSGlG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\ngS3aYo6VZN6iMpRxFppP0zSzgMJbaN7qxmhMrswXmsGRrGSHHNfoG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MnIjWwsjofd+WciE0tR6nM+v5mbE0kcyMBP+VRoAhOA13gNGMSg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\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XMAsrJYt07+fp04Qf36vPee3P311zEY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\nJySE9HQsLOTmkSMYDOzfT+nSKHMP4eHUqyfrx8aSkoK19b/uTrF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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=6, repr.plot.height=6)\n", "\n", "panel.hist = function(x, ...)\n", "{\n", " usr = par(\"usr\"); on.exit(par(usr))\n", " par(usr = c(usr[1:2], 0, 1.5) )\n", " h = hist(x, plot = FALSE)\n", " breaks = h$breaks; nB <- length(breaks)\n", " y = h$counts\n", " y = y/max(y)\n", " rect(breaks[-nB], 0, breaks[-1], y, col = \"darkblue\")\n", "}\n", "pairs(X, col=c(\"red\",\"blue\",\"green\")[y], diag.panel=panel.hist)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dimenionality Reduction and PCA\n", "-------------------------------\n", "In order to display in 2-D or 3-D the data, [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction)\n", "is needed.\n", "The simplest method is the [Principal Component Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis) (PCA),\n", "which perform an\n", "orthogonal linear projection on the principal axsis (eigenvector) of the\n", "covariance matrix.\n", "\n", "\n", "Compute [empirical mean](https://en.wikipedia.org/wiki/Sample_mean_and_covariance)\n", "$$ m = \\frac{1}{n} \\sum_{i=1}^n x_i \\in \\RR^p $$\n", "and [covariance](https://en.wikipedia.org/wiki/Sample_mean_and_covariance)\n", "$$ C = \\frac{1}{n} \\sum_{i=1}^n (x_i-m) (x_i-m)^\\top \\in \\RR^{p \\times p}. $$\n", "Denoting $\\tilde X = X - 1_p m^\\top $, one has $C=\\tilde X^\\top\n", "\\tilde X$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Xm = function(X){X - rep(colMeans(X), rep.int(nrow(X), ncol(X)))}\n", "Cov = function(X){data.matrix(1. / (n - 1) * t(Xm(X)) %*% Xm(X))}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the covariance matrix." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtAAAALQCAIAAAA2NdDLAAAABmJLR0QA/wD/AP+gvaeTAAAY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\ngDjBAQDECQ4AIE5wAABxggMAiBMcAECc4AAA4gQHA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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "image(c(1:4), c(1:4), Cov(X), xlab='', ylab='')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute PCA ortho-basis using the\n", "[SVD decomposition](https://en.wikipedia.org/wiki/Singular_value_decomposition)\n", "$$ \\tilde X = U \\text{diag}(d) V $$\n", "where $U \\in \\RR^{n \\times p}$ and $V \\in \\RR^{p \\times p}$ have\n", "orthonormal columns. $V$ are the principal directions of variance\n", " and\n", "are order by decreasing variances." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "svd_decomp = svd(Xm(X))\n", "U = svd_decomp$u\n", "D = svd_decomp$d\n", "V = svd_decomp$v" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the feature in the PCA basis, $z_i=V^\\top (x_i-m) $, stored in matrix\n", "format as $Z=\\tilde X V$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Z = Xm(X) %*% V" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot the singular values of the covariances, which corresponds to the standard deviation of the data\n", "along the principal directions." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=4, repr.plot.height=4)\n", "plot(D, type=\"o\", col=4, ylab=\"\", xlab=\"\", pch=16)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The first dimensions of the $z_i$ are the optimal way to linearly\n", "embed the data in a low dimensional space.\n", "This can be used for display in 2-D using the first two dimension." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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WExP06oX163H4MLZuxezZ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\n797l3iU0FCNHgle5yER+S/zNO9y71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L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\nFCIiovK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+AgIiIiwTFwEBERkeAYOIiI\niEhwDBxEREQkOAYOIiIiEhwDBxEREQmOgYOIiIgEx8BBREREgmPgICIiIsExcBAREZHgGDiI\niIhIcAwcREREJDgGDiIiIhIcAwcREREJjoGDiIiIBPf/6WRlpQ7LMV8AAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=6, repr.plot.height=6)\n", "\n", "for (i in 1:k)\n", "{\n", " I = (y==i)\n", " plot(Z[I,1], Z[I,2], col=i + 1, xlim=c(min(Z[,1]), max(Z[,1])), \n", " ylim=c(min(Z[,2]), max(Z[,2])), xlab=\"\", ylab=\"\", pch=16)\n", " par(new=TRUE)\n", "}\n", "\n", "cols = c(2:(k + 1))\n", "legend(\"topright\", legend=c(1:k), col=cols, pch=16)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Similar display in 3-D." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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KZNm6FDh86YMWPWrFl8B7RMWKUChsQucPX29u7WrVt0dLREIpHL5RkZGenp6XK5\nHNVGq8LO4TCpXmUAllgsDgwMjIiISE9Pz8vLi4qKmjJlilKpTExMZBe5+Pj4hIWFFRUV8Z3U\nomCmHhhGenr6mjVrkpKS6uvrBQLBkCFDZs+eLZPJeJ+mBHxhJwKj4AAT17VrV7lcLpfLa2tr\njx8/npSUFBcXl5OTk5OTs2XLFnR7GBCGVOCpVFZWfvrppz/88ENRURHDMB06dJg9e7ZcLvfy\n8uI7GvAsMjIyLCxs27Zt8+fP5zsLQPPk5eUlJSUlJSXt3buXHReWSqXe3t7jxo1buXJlhw4d\n+A5oltDDAS20f//+Dz/8kF3gKhQKg4KC5HI5FrhCI5ylAubLy8uL7faoqak5ceJEUlJSbGws\n2+2xdetWR0dHf3//hQsXYn5Ss2AOBzRPeXl5WFiYs7Pziy++mJKS4uXlFRERUVxcrFAoQkND\nUW1AI8zhAAtgY2MTHBwcERGRk5OTm5sbFRUVEhJSWVmZmJg4adKkxtkeJSUlfCc1Ayg4QF/s\nCa7Ozs6RkZFVVVWhoaEKheLixYvh4eFubm58pwOTw1af2GkULAbb7REfH3/nzh2FQrF06dIO\nHTrk5ORERkZ27NjR2dk5JCRk7969fMc0XSg4QIeCgoJHT3D19fXdsmVLcXFxTExMcHAwttMA\nTbC1OVgqW1vb4ODgrVu3FhQUnDt3btOmTSNGjKioqEhMTJwwYYK1tXWXLl0yMzP5jmly0AEO\n6jU0NGzbtu3f//43u2eXg4ODTCZ78803+/fvz3c0MA8oOKA18PHx8fHxeeeddyoqKg4dOpSY\nmLhnz57CwsJ//vOfv//+O9/pTAsKDmgqIyPj/fffZxe4EpGfn59cLp81a5atrS3f0cCcYNIo\ntCpt2rR5+eWXX3755dLS0l27dn3yySd8JzI5KDjggfv372/ZsuWLL75gF7i6ubm9/vrr8+fP\n9/b25jsamCV2DgcKDmhV6urqDhw44ODg0KNHD76zmBwUHEAHDx5cu3YtFriCYWFIBVqhw4cP\nV1ZWjh8/nu8gpgifKK1XeXn5Rx99tH37dvYE127dus2cOXPu3Lk4wQgMgi042IE5gFYiPj6e\niN566y2+g5giFBytUXR09ObNm8+ePatUKq2srEJDQ3GCKxgc5nBAa8MwTHx8vFQqHTduHN9Z\nTBEKjlaksLBw9erVjSe4+vj4zJ49e968ec7OznxHAwvEDsmhhwNaj4yMjOcciIUAACAASURB\nVGvXrg0cOJDvICYKBUerEB0dvWHDBnaBa5s2beRy+YIFCwYMGMB3LrBk6OGA1iYuLo6IZDIZ\n30FMFAoOS5aZmbl69epDhw6xP/TZBa4zZ860s7PjOxpYPrbgaGho4DsIgJHEx8eLRCKcVqgJ\nCg4L1GSBq6ur65w5c+bNm9etWze+o0Ergh4OaFWKi4szMjK6du1qbW3NdxYThYLDoigUio8/\n/vjkyZP19fWNC1xffvll9kc/gDFhDge0KrGxsQzDvPTSS3wHMV0oOCxBkwWunTt3njlz5sKF\nCz08PPiOBq1XC4dUlEpauZL27aPaWvLyoq1bqU8fTvIBGFR8fLxAIFixYgXfQUwXCg7zFhsb\nGxERwe7ZJZVKscAVTEdLCo7YWHr1VVIqH/y2oID69qXhwyk5mYOAAAZTVVV1+PBhZ2fnTp06\n8Z3FdKHgMEtNFrg+++yz//d//zd37tz27dvzHQ3ggWZv/FVcTK+8QgzT9PWjR+nVVwnnYIEJ\nO3DgQF1dHcZTtEPBYWYeXeBqb28vl8tlMllgYCDfuQCaYudwNKOHY9IkNdUGa/duA4UC4AS7\nweiSJUv4DmLSUHCYh+zs7FWrVmGBK5iRZg+pnDunsYlhKC6OJk0yRC4AA1OpVPv27bO1tcXf\n/bRDwWHSGhoaPvvss8YFri4uLtOnT583b14fTKMDk9fsgkP7lefOoeAA03Tq1KmbN28OGzaM\n7yCmDgWHiTp9+vSHH36YlJSEBa5gptg/q8rGGaB6vEFbzeHnZ4hQAIbHjqfMnTuX7yCmTsBo\nGjQFPty7d2/dunWNC1w7deo0a9asN99809PTk+9oAM3T0NAgkUg8PDyuXr2q1xuGDqWTJ9U3\nCYWkf+ECYFzPPvvslStX6urqhEIh31lMGno4TMi33367YMEClUollUqnTZs2b968kSNH4k8w\nmCmxWCwQCJrRw7FvHzk5kUqlpumNNwwYDMCAcnNzL1y44OPjg5/VOqHgMCGdO3dWqVT9+/dP\nSkpycnLiOw7A0xKLxc0oONq2peRkCgqiJruhT55M33xj8GwABhEbG0tEoaGhfAcxAxhSMS2O\njo7379+/desWlp+ABbC1tW3Tpk1JSUnz3vbFF/Tzz1RdTX360GefkZsbN+kADGDkyJFHjx4t\nKSnBNkg6oeAwLa+++uquXbt27tw5ZcoUvrMAPC0HBwepVHr79m2+gwBwoqyszNXV1dXVtbi4\nmO8sZgBjTqZlzZo1RPTbb7/xHQTAAMRisUrtnAwAi5CYmKhUKseNG8d3EPOAgsO0+Pr6Ojg4\nxMXFVVVV8Z0F4GlJJBIUHGDB2AWxy5cv5zuIeUDBYXJGjRpVU1Nz4MABvoMAPC2pVNqMSaMA\nZqW+vn7//v1t2rTp27cv31nMAwoOk7N69WrCqApYBPRwgAU7cuTI3bt3AwIC+A5iNlBwmJyB\nAwe2adMmLi6upqaG7ywAT0UsFmNaOlgqdjxl0aJFfAcxGyg4TNHIkSOrqqowqgLmTiqVoocD\nLFV8fLxUKsWR9PpDwWGK2FGVnTt38h0E4KlIJBL0cIBFys7Ovnr1au/evfkOYk5QcJgif39/\ne3v7uLi42tpavrMAtBwKDrBU7HjKzJkz+Q5iTlBwmKiRI0dWVlYePHiQ7yAALYc5HGCp4uPj\nhULhwoUL+Q5iTlBwmKj333+fMKoCZg49HGCRSkpKUlNT3d3dbW1t+c5iTlBwmCh/f387O7s9\ne/ZgVAXMl0Qi4TsCgOHFxcWpVKqJEyfyHcTMoOAwXSNGjKisrFQoFHwHgVbshx9ozBh64QVa\nvbrpIa56QA8HWKT4+HiBQBAWFsZ3EDODw9tM1/Hjx4cNGzZ79uzt27fznQVan6QkGj/+sSJD\nIKDVq2n9et3vVSrp7bfpwIFbhYXnamtH/PUX+fpyl9QEXblC/+//UVYWEVHfvvTGG9Stm5rL\nqqtp7146d47EYvLzo9GjSSw2clJotpqaGmdnZ2tr67KyMr6zmBkUHCbN3t5eLBaXlJRYWVnx\nnQVak8JC8vAgtT8ctm6lpUu1vXfXLnrtNWqyo/nw4ZScbMiEJmzbNlqy5LFSTSqlzz+nBQse\nuywxkV5/nW7efPhKjx60Y0drq83MT1xc3EsvvfTyyy/v3r2b7yxmBkMqJm348OF3795NSkri\nOwi0MmPHqq82iGjlSm1vLC6mKVOaVhtEdPQovfqqYbKZtqNHaeHCpqNP9+/TwoV05MjDV9LS\n6JVXHqs2iOjSJRo9mq5fN0JMaDl2Qexbb73FdxDzg4LDpK1atYpwrgoY3+XLGpvu3yctPckT\nJ2qsVFrHXwc3biS1e6syDG3a9PC3a9dSXZ2ay27fps2bucoGT0+lUsXHx1tbWwcFBfGdxfyg\n4DBpw4cPt7W13b179/3mz9cDaDntR7z+9ZfGpnPnNDYxDO3d2/JIZiIlRXeTSkWHDmm8DB2a\npiw1NbWkpKR///58BzFLKDhMXWBg4N27dw9p+fkEYHBCrT8ZevbU2NTQoO2NZ8+2MI/5qKrS\n3VRZqb57g3X7toEjgQGx4ylz5szhO4hZQsFh6nCuCvDAzU1jk0hE7u4aW7VvvOHn1/JIZsLT\nU3dTmzZkY6PxMi3fe+BdbGysSCRCwdEyKDhM3QsvvGBjY7Nr1y6MqpixW7f4TvCIq1dpwgTy\n9iYfH1q6VP3oyS+/aHy79h+1WrqahUIKDtY7pbl67TWNTaGhD/5FIKBx4zRe9uKLBo4EhlJQ\nUHD27Flvb28xli+3CAoOM8COqvzxxx98B4FmSk4mZ2cSCMjVlQQCsrIi3ncKmjyZunalvXsp\nL49ycuiLL0gqpR9/bHrZCy/Qxx+TQND09VGj6JtvtN0/IUHjcMy8eS0NbU7eeYf69FHz+nPP\n0bvvPvztP/9J9vZqLuvcmf8/I6BJbGwsEb3aOtZbcYIBk8ce4TZ37ly+g0BzREczRGp+BQby\nFmnxYvWRiJicHDXXl5YykyYxHTowrq7M4MFMWppeTzl2jJFKm95/yhTDfimmrKyMeeONh98D\nqZSZM4cpLW162YkTjLf3Y9+kQYOYS5cYhmFu3WKys5kbN4yfHbQJDg4WCoUlJSV8BzFX2PjL\nPNja2trY2Ny4cQOHU5gNiUTjDMo9e+ill4ybhoiIxGKNy0+6d6dLlwz5rC++oJ9/LsnPP3Tz\nZsdffx0xdaohb24OqqoeLNnx8VHfmUFESiUlJ9PZsw92GvX3p+PH6d13KSXlweLifv1o/Xqa\nMMF4sUGTu3fvuri4ODk53bhxg+8s5gpDKuZhyJAhZWVlGFUxGzt2aFuvER5uxCj/c/mytsWu\n+fkGftySJZSS8vWiRTOJ7lpbG/jm5sDOjgYNokGDNFYbRCQS0ahRtHQpLVpE/v60dy+NHEmn\nTj3cyiQriyZNou++M05k0Gb//v319fWjR4/mO4gZQ8FhHt59913CDmBmRPuGE8XFxsrxCPZg\nD020b7zRUmyHHE481kddHc2fr6ZMZRhavrzpnqRgfOyC2OXLl/MdxIyh4DAPY8aMsba23rVr\nV4P2fQ7ARIhE2lq173LBhcREWr1a2wWaAsfFkbs7SSQkFlObNjRrVrMeyxYcWGCljyNHNG5q\nXllJCQnGTQOPUyqViYmJdnZ2fq1gaTd3UHCYjYCAgNLS0iOPnscAJmv6dG2tXboYKwcREfn7\nU0iItt3KidQfZjprFr30El27Rg0NpFRSZSX9/DPZ21NlpZ5PRg+H/vLytLXm5horB6hz7Nix\nsrIyf39/voOYNxQcZgOjKuZkzBjSMnHhyy+Nl2TmTPrzTx3XCARqxoDi4ujnn9VcXFVFDg5k\nb0/DhlFJifYbs9sVoODQh/YDobVsFAZGwI6nvPnmm3wHMW8oOMzGuHHjrK2tf/vtN4yqmAeF\nQs0+FkQ0bRoFBhovxq+/6rhAJKLffiMvr6avL16s8S0MQ1VVdPw4dehAWitgtoejTss+3vA/\ngwa1vBW4FhcXJ5FIsAPHU0LBYU78/f1LS0uPHj3KdxDQQ2Ag5eVRt24PZmwIBNS2LX3zDf33\nv8bLkJam/uhSlkBAa9ZQQwNNnqymVVfvBRERw9DUqVRTo6kdczj099xzNHas+qZ+/QhHk/Lo\n/PnzV65cefbZZ4XGn31lWfDtMydvv/024VwVM+Lp+WAxKsOQSkXl5cbbbXPDBrKyooEDdVz2\n0Ucam/TcoUel0vJFoYejWX76Sc3W8N7e9PvvOmYhA6fY8ZRp06bxHcTsoeAwJy+99BJGVUC3\n+fPp/fdJZ7+C9g8xW1t9H3fsmKYWdg4HCg49ubhQSgp9+y298go9/zxNmEBbt1JmJnl7852s\ndYuPjxcKhYu1DDKCflBwmJlBgwbdvn37+PHjfAcBnhw8SAsW0FtvUWam+gvKyujbb/W61bPP\namttPGpMJ831BHo4mksqpblzadcuSk2l+HhaulTbvmFgBLdu3Tp16lTHjh0dHBz4zmL2UHCY\nmWXLlhFGVVqnHTvIyorGjqVt2+g//6H+/cnBQU3Z8c47et1NKCSFQtsF335LbdvqdasOHTS1\nsAVHfX29XvcBMD0JCQkqlWr8+PF8B7EEKDjMzOTJk62srH777TclN1tDgolKTKRp05qOklRU\nkJ9f031Lte8o2ohhtJ1Bz7p5k/r21X2rDz7Q1IIeDjB38fHxAoEgDGf4GgIKDvMzcODAmzdv\nYlSlddG0k5hKRU0Od5BK9bohw1BYmPZFrSSVUlYWMQz9/jsNGKD+ml691C9yIaL/zeHAKhUw\nU3V1dQqFwsHBoUePHnxnsQQoOMwPO6qCHcBal7t3NTZdvPjYbydObMZt587V67LJkyk9neTy\nppuyjxhBOTla3odlsWDWDh06VFlZOWzYML6DWAgUHOZnypQpVlZWO3fuxKhKa3HhgrbWJn8M\nVq8msVjfO9+714wYUVGkVNLOnfTOOxQVRQ0NpOv4YrbgwKIqMFPsgtglS5bwHcRCoOAwS35+\nfiUlJSdPnuQ7CBhF587aWp/cz3TPHvWbnKqlpe9ErSlTaNMmksv12RoCPRxgvhiGiY+Pt7Ky\nGjNmDN9ZLAQKDrO0dOlSwqiKabp7lzIzm/0prp29vbZP9ydX640fT3l51KcPicW6Kw89l6K0\nCDuHA6tUwBz99ddfRUVF/fr14zuI5UDBYZamTp1qZWUVExOj0rJxNRjZJ5+QlRU5OlL//uTo\nSNbW9OmnBru5ll0ON29W86KnJ2VnU309qVTaSgrtJ4Y9NfRwgPlix1Nmz57NdxDLgYLDXA0Y\nMODGjRunTp3iOwgQEdGcObR69WPLVuvqaNUqg+1lHh2tZtdrIpoxQ/cj/vMfjU2aV7QaBOZw\ngPmKi4sTiURz9ZxYDXpAwWGu3nrrLcKoiokoLKQfflDf9N13TffJaLG//qJffyUvL7K1JTs7\neu45SklRf4J8EzNn0ttvq3l9xgxavdow2TTAxl9gpoqKijIzMz09Pa2trfnOYjlQcJirGTNm\nSKXSnTt3MnoesgXcWb685a3NMnUq5eZSVRVVVtKZM+Tvr+8bP/uMiopo7Fjq0IHc3GjECLp0\nSa9i5emwczjQwwFmJzY2lmGYV155he8gFkXv5XNgegYMGJCSkpKSkhIQEMB3ltbt3DltrWfP\nGiuHVh070v79Rn4mhlTATGGDUS6gh8OMLVq0iHCuiinQvkBUIjFWDpODggPMUWVl5R9//OHs\n7NxB8zlB0AIoOMyYTCaTSqUxMTEYVeHZ8OHaWlvxNoUoOMAcHThwoK6uLigoiO8glgYFh3nz\n9fUtKir6888/+Q7Sun32mcbtLoRC2rTJuGlMCOZwgDliF8Sy2x2BAaHgMG8YVTEJNjb09dfq\nm775hmxsjJvGhLA9HNiDH8yIUqlMSEiwtbUdMmQI31ksDQoO8/Z///d/Uql0x44dGFXhmVxO\naWnk4UFCIQkEJBSShwelpdEbb3D40JIS2raNduxoemy9ycCQCpidU6dOlZaWDhw4kO8gFgir\nVMxe375909LSUlNTBw0axHeW1s3Pj65e5fD+J0/Sb7+RlRXNn083btC4cVRR8bDVy4uyssje\nnsMAzScSiYRCIXo4wIyw4ynzDLVlHzxCgL8Zm6a9e/deunTpbbX7NT3u+++/nzt37sqVKzdu\n3GiEYMCD2FiaOpXq6nRcZmVFVVX6nKlmTFKp1NnZ+fqJE7R3L3XqRJMn850IQJtevXrl5ubW\n1dUJhRgBMDAUHCaqS5cuhYWFqampzz//vPYrVSqVtbV1x44d8/PzBfqfEQrm4uBBGjtW34tH\nj6aDB7lM02yzray+qa+3evTnjK8vpaWZWmEEQERXrlzp3r27j4/POe2b60CLoIIzUT4+PkQk\nl8t1XikUCvv27VtQUJCens59LjC6115rxsVHj3KWo0W+//7H+/etmvytJjOTXFx4CgSgTWxs\nLBG91qz/6UBvKDhM1MSJE4koIyMjKSlJ58ULFiwgnKtikZTK5p10b2qzRxcuVP/6nTuENYdg\neuLj44VC4bJly/gOYpkwpGKiGjcs9/HxOXPmjPbRRHZUpVOnTnl5eRhVsSiZmeoPidVEKCTT\nmaF58iQNHaqxtV07KiszYhrg0K1blJRExcXk5kajRlHHjnwHapGysjJXV1c3N7eioiK+s1gm\n9HCYKB8fH7Z0OH/+/Pbt27VfLBQKn3vuuatXr2ZkZBglHRhLly7Nu75tW25ytIj22SSVlcbK\nARxiGFq7ltzdacYMeucdksnI05PCwsgcl0Lv3btXqVSOGzeO7yAWCwWHiXJwcOjUqZNQKJRI\nJO+9917Fowsg1WFne2AHMEvj5KRxD1O1Pvywefc/f54mTKBevej55+nzz5v3Xp2cnLS1cr8E\nQEWqjJqM9Jr0BjLDTz/NsrLo/fdp6lR6/XX65hueK7e1a+mjjx5bQVVfT5GRZI6DEuyCWH3W\nBkLLYEjFdI0bN+7QoUPspklr165dt26dlovZUZXOnTvn5eUZKR8Yh7OzvkMPY8bQgQPNuHNA\nAKWkPPaKlRWdOEF+fs24iRZ375Kjo8ZWb2+6csUwD3rCPdW9CbkTTlScUJGKiIQk9Lf3T/BK\ncBJrrYFMHsNQeDht3kyP/tju3Jl27yZdq9k4UVJCXbqonzgkFFJODvXoYfRMLVVfX+/i4qJS\nqe7du8d3FouFHg7T5ePjw1Ybrq6uGzdu/Pvvv7VcLBQKfXx88vPzMzMzjRXQgvz4Iz3zDInF\nJBJRmzZkUnv+6PwkEYvpmWcoOrp51cbo0U2rDSKqqyN/f4PNPG3bltzdNbZu22aYpzzhnuqe\nxxmPYxXH2GqDiFSkOlV5yvOsZ1mDec8a+eIL2rSJmvwl8do1Gj+e7tzhIc/hwxr/sKhUprZA\nW4c//vjj7t272M6cUyg4TBe7MrZdu3ZWVlY1NTVr1qzRfj1GVVpo7Fj6v/+jkhJSKkmlospK\n+u47atfOVFZ8zJ6trXXaNDpzhlasoPr6ZgS+f580rX5SKik0tHkJtTh/vlbt0IlcTqNGGewp\nj5NdlZUry598vUJVMS1/GkcPNQKVij75RH3TzZvc1W/alJS0vNXUsOMpixcv5juIJUPBYbrY\ngqN3796FhYUBAQE//fRTamqqluvlcrlYLI6JiTFWQIvw9dfq/yJWXk4mcphCbq7GJoGAdu+m\nZ5+llStpzhyysiIfH6qp0X1P7dM1DLiZh739cD+/X4VCsrcnkYgkEvLwIIWCoqIM9ognKO4p\nNDUdrTSxfUqaIzeXbtzQ2HrihBGj/E/79i1vNTUJCQlSqZTdjwA4goLDdLEFR9u2bYmoR48e\nQqFQ+zQOsVjs4+Nz5cqVrKws4yS0BO+/r7EpO9sYS0wrK+lf/6J336XDh9W0rlxJa9dqfC/D\nNN3vPCeH3Nx0P/TiRW2ttbW676A3iUQiEwqpooIaGuj+fbp6lYKDDXj/J9UyGvPXMXWN4yxm\nR/vEcV3TyjkxciSJNZzHJRBw/d/ZkLKysq5evfrcc8/xHcTCoeAwXY6Ojp06dbp161b37t0V\nCkVkZOT48eO1v4U9cAg7gDVDuZq+94dOn+bw0TU11L07tWlD77xDmzZRUBBJJE37Hv71L41v\n17TKo6JC9xyUnj21td6/T50709ChlJys4z56kEgkpjMzXUACIWc/9IqL6eefadMm+uUXTkYT\nOnfWtmKpuQuoDaJTJ437t8lk1Lu3cdM8hbi4OCKaNWsW30EsHQMmbNq0af7+/uzsjcOHD+u8\nvr6+XiwWd+/e3QjZLIRAwBBp/BUby+Gj7e3VP3TTpgcXfP65tmxafrVtq+PRdXX63qpPn+Z9\nUaWlzMSJTIcOjKsr4+/P/PlncHCwSCRqyfdHP3fq7+TU5NxV3m18xTnLmdJJ7S/HLEcuMtTX\nM2FhjETy8NsmlTKrVzNKpYEfNHy4xv9Qe/YY+Fl6amhgli5lRKKHSQQCZs4cpqaGnzwtM3Dg\nQKFQWFVVxXcQC4eCw6Q1NDTcv38/JyeHiObPn6/PW/r06UNE2dnZXGezENbW2j5uy8u5eq5c\nru25CgXDMMyMGS0sOMRi3QFGjtT3bsOG6ftFffzxkwVchrOzUChs+TdKsx9Kf2if1b6xmHDJ\ndvml9BeGYdYVrdNUcIRfC+ciyZIl6r9zq1YZ+EEZGerL1EmTGJXKwM9qlvx85ssvmdWrmS++\nYC5c4DNJCxQXFwsEAk9PT76DWD4UHOahf//+7dq1q62t1XllZGQkEX3wwQdGSGUJJk7U+EHr\n4MDhc9u10/Exv2QJs2hRCwsOqVSvDAMH6nvDujrddztyRNPbvxMINL2pqIjZsIGZMoV5+WXm\nH/9gLl3S9/v3QdEHakuKiOsRDMMEXQ56sinwQqC+d2+O3FxGKFT/pUskTFGRgR+Xns4MGvTw\nEba2zDvvmFl3gqmJiooiomXLlvEdxPKh4DAPGzduJKI9enSbsqMqPXr0MEIqS9DQwNjYqPms\nEAiYI0c4fK5UqvtjfufOFhYcXbvqGyMjgwkOZry8NH5msr+2btV9q44dNb29gdT/nNm5k7Gz\ne+xasVivR92ovyFMF6otOETpojv1dxiG+ebWN93OdrP5y8Y6w9r7jPd/bv5H3+9JM335pbbv\n3PbtnDw0N5fZv585epSprOTk/q3KhAkTBALB1atX+Q5i+TBp1DzMnDlTKBT+97//1XmlWCzu\n2bPnpUuXzp07Z4RgZk8kotJS6tXrsRcdHOjoUXrhBQ6fq8/G3v/8p7aVhR4eGpv035PB15cU\nCsrNJYlE22WXLum+leZ5kiIiVUFBkxezs2nGDKqqeuzFhgZavpz27dPxqE0lmzQtNlGScsvN\nLUQ0r/28y70vV/evrvGtufLclUUui3R/CS1y82bLW1vMy4vGjqVhw8jOjpP7tx41NTWHDh1q\n166dh5b/ocBAUHCYh44dOw4bNiw2NlafbXfnzJlD2AFMfzY2lJNDDQ20Zw998w2VltLduxQY\nyO1Du3bVfU1eHp0/T1ZWapo2byYti59bcISbtbW21r59dd9BpW25aX12dpNX/vUvqq9XcyXD\naNzeqlF2ddO7PSqj1qhHGFrSXhSt0MGDB2tqakaMGMF3kFYBBYfZmD59em1tbWxsrM4rlyxZ\nIhKJUHA0j0hEL71E8+bpOHLMUH76Sfc1KhW5uFBVFc2cSW3bkkRC1tbk60uXLtGKFdr2A23B\ncZdaunMEApo7V/cdRCItjRXPPtvklZMnNV58+rT26oWkQqmWViuBuhKNM8HBGlerikTc7acK\nhsFuMLrMHM+aM0MoOMzGa6+9JpVK9RlVkUqlPXv2PH/+/Pnz540QDFrCz4/ee0/HNWzpIxJR\ndDSVl9P9+1RTQxkZ1L07EWnbJKOsrNn7su/cqXELp1df1V5MPMCmUqeOqOaJfhotZ5zW1+vY\ne2y4/XAtrSPsR2h7s6H17KmxHnvrLX62xwA9qVSqhIQEGxub4cO1/YkCQ0HBYTbatWs3duxY\nhUJRosemQuyoCnYAM2kbNtATAw2PCQtT82JmJn39NSUnqx+QaJSW1rwwUin99RfZ2jZ9fexY\n0rOr7MABTX/Tf5eo5okN17V8Eru4qAnyqKUuS62F6seAbIW2che59qQG95//0Pz5j03LEYlo\nyRLavNnIQaB5/vzzz5KSkgEDBvAdpLVAwWFOpk+f3tDQoE8ZsXTpUpFIhHNVuHL6NPXsSVZW\nJBZTmzY0fXoLN0Hv00fjsSYeHvT224+98sEHJJFQ//60cCGNGNH0zNAmnnmmJWGqqmj7dho+\nnPr2pWnTqKiI9u/X9+3u7nTwIEkfH+wQCA4OHPg5Ue0TXRZTpmi8k5YmlrXQ+veuv4uoab+L\nWCBO8E4Qk4auGs5IpbRtG128SP/+N/3jH/Tll3T5Mn3+ucY+IzAR7HjKG2+8wXeQVoPvZTLQ\nDFVVVfb29kOHDtXn4l69ehHR+fPnuU7V6qxcqWb5o7U1U1rawhtGRz+2/5hAwIwZ89gFv/6q\ne9+OJmt6lyxh+vRhevdm5sxhKiqe/otuhu3bmdGjmRdeYNasYerqVqxYQUQpKSlNrqquZvz8\n1GT38GBKSvR6zpWaKyMujrDPsJf8JWmT0SboctDVOqxshGbo3bu3SCSqr6/nO0hrgYLDzMyc\nOVMgEOTl5em8MiIigoj++c9/GiFVK5KRofFjvkOHp7rzjRvML78wJ040fd3bu9n7cDTZ7lMg\nYFaufKpsT2HVqlVEdETdpiZ37jBz5z7cEVwoZF55hSksNH5GaI3y8/OJqGfPnnwHaUUwpGJm\nZsyYwTCMPlNHly1bhlEVw9NyvNP161RY2PI7u7nR9Ok0ZMhjLwYEaDueXpMmoy0MQ5s20ddf\ntzzbU5BIJKRuDgcROTrSt99SaSkdO0bJyVRSQrt2UefORo8IrRK74m+KzgE8MBwUHGZmzJgx\nrq6u0dHROq+0trbu1q3bmTNnLly4YIRgrUV+vrbW774z5LPu36eUagg5cwAAIABJREFUFN2X\nCYUkEpFQSPb2ZGOj8bIVKwwYTX9isZiI6urqNF3Qpg0FBtLw4diyAowqPj5eKBQuX76c7yCt\nCAoOMyMWi6dMmZKTk5OtfYEDERHNnj2biH7//Xfuc7Ua2ieHJiTQkCE0fDh9+qkBnvXjj3pd\n1rEjNTSQUkkVFdqWk1ZXGyBS87E9HE9OGgXg0d27d48ePeri4tIeda4RoeAwP9OnTycifUZV\nli9fjh3ADEz7Jp7p6XTqFB07RqtWkVhMevw30ubqVb0uGzTo4b9rX7py69bTxGkZFBxgghIT\nE+vr68eMGcN3kNYFBYf5GTp0qKen5y+//MJo/3QhsrW19fb2zsrKunjxonGyWT599txkKZU0\nYwalprb8WY9WElqcPPnw8BRNe16yXFxaHqal2CEVFBxgUrDBKC9QcJgfgUAwbdq0v//++8SJ\nEzovnjVrFhHt2rWL+1ytw4YNzZtrMHZsy581aZJeZ7zduEELFlCfPkREzs4aL9MyvUODjJqM\nGVdnBFwICLoUtKVki6bz0rRjezjuN3fnUwDONDQ07Nu3z97e3s/Pj+8srQsKDrOk/6jKihUr\nMKpiYDdukP5bE965Q4MHt/xZS5boe+XZszR9urZpH82cVjIhd8KAnAH/LftvSnXK4crDbxe9\n7ZjpmF6T3qyb0P8KDi2TRgGM7OjRo+Xl5f7+/nwHaXVQcJilvn37PvfcczExMfXa97cmsrW1\n7dq1a0ZGxpUrV4yTzfKJRJSeTg0NFB1NERGkUOi4/vRpWry4hc/asoXkch0DJY127qQXX6SI\nCDXXL1nyoHYpK6PMTFK3SPVRs6/O3nt3b5MXK1QVgRcDq1XNm3yKORxgatjxlDfffJPvIK0O\nCg5zNX369Nu3byt0ftr9b1Slda1VycykXr1IKiWRiKytaehQKit72KpU6vzE1U0kopkzKTyc\nRo7UffG337b8QVFRVFtL779PwcE0ZYq24kOppPv3KTycqqpozhzq0YO8vGjqVCotpc8/p9Wr\nycqKnJ2pf3+ytSVbW007c9xX3f/5zs9qm2pVtWFF6k540UznslgAI0tISJBIJNiBw/hQcJgr\ndstRfUZVVq5c2bpGVSIjqX9/uniR6utJpaK6Ojp5klxcKDWVRowgkYjEYrK1JaGQfHzo7t2n\nfZxI1PQAkSc1dwbDjh3k6UnW1mRtTZ6etHs3rV9PCgXt3KljHQp7vMvQobR5M128SLm59Ouv\n5OREL71En3zyWIyaGlq4kN5998l7xN6LVTEap2sk3Utq1pfC9nDo7IoDMI5z585duXLFx8eH\n7yCtEQoOc+Xh4REQELB79+6qqirtV9ra2np6eqanp+e2YM9Ks3PrlvodrlQqGjSIkpNJ9b+P\nUoahnBxq3570OH33oW+/pVdfpenTKemRz93339f9Rv1Pdxs2jKZNo4ICqqujujoqKKBp02jY\nsAetOqeRKpWUkUGurtS44VtmJsXFqb948+Ynz4m/VndNy+0rlZrPlVcHczjApMTFxdH/psGB\nkaHgMGPTp0+vqqpixyO1mzlzJrWStSqvv66jD6CJhoamu4lr8uWXJBbT/Pm0axf9+iuNHk12\ndnT6NBHRBx/QtGna3isQkKjp0abqhYXR8eNqXj9+/EEh1bOnXvdRKh9OVtWylyLD0D/+0eS1\nHtY9tNy4nbjdo7+tq6P0dDp6lIqL1V+PggNMCrvB6OIWT6uCp4CCw4xNnTpVLBZjVOUxGRnN\nfov23cpZP/9Mixc37aWorqaAgAeftP/9r7ZTQPQ/LP7LLzU2/ec/RER//KHXWlkiunuXLl8m\nItI+X5itmR7xYtsXJQKJpstfafcK+y/19bRmDbm60vPP0wsvUKdONGIEnT3b9Hp2DgeWxYIp\nuHnz5unTpzt16mRvb893ltYIBYcZc3FxCQ4OTkxMLC0t1X6lvb29h4dHampqXl6ecbLxpgVz\nBRhG41/PG8nlGt87evSDf09OVj+jUyCgAwf0DaOlJ4BtcnOjc+eoXTuNlz3q55+JiMRibdeo\nVDRsGLVvT05ONGAAHT8uJOG7z6iZ20FETiKn9R3Ws/8+YwatX0/37j1sTU6mwMCmNQfmcIDp\nSEhIUKlU48eP5ztIK4WCw7zNmDGjvr5enxUo7Jil5Y+qdOrUkndJNP6Fnojo/n1tB5E07uLq\n5UWpqdSmzWOtdnZ09OiDXbkMpVcvKiuj/Hx6/30dIzVsjaJ915A//6Tjx6m0lO7coYwMGjaM\nRo9e32H9CrcVQsFjPx+6SrtmP5stJCERJSTQb7+pudndu9Rk80Zs/AWmIz4+XiAQhIU1b6UV\nGIpA5/bYYMqqqqrc3Nyef/75I0eOaL/y3r177dq1GzhwYIo+B5Car717acKE5r1FIHg4k1St\n1FRtu4w/+fYLF+j774lhaM4cau5keKFQ4xwUtTk7dqTr1zXeLSWF/P3p1i1yc2ve1JYlS+jz\nz8sbyr+6/dWZ2jNthW1nOs8MtAtsbH/9ddq+XeNXUFLycDvWEydOBAYGTp48uXUtzAbTU1dX\n5+zsLJFI7ty5w3eWVgo9HObNzs5uwoQJR48eLSgo0H6lg4NDly5d/vzzT51Xmrfx46m52xU/\n95yOCzw9tbU+OYzSqxdt3EibNjW72iCtPTRqm1at0ni9lRWxeym6uND69c2L8dVXROQodnzv\nmfd+8fzlqy5fPVptEJGWP0QqFRUWPvwtO4cDQyrAu6SkpKqqquHDh/MdpPVCwWH2pk+fzjBM\nTEyMziunTZvGMIzl/0UzLY1CQx+bWSmR0IYN6j+wbWyenDXZlIuLtpELJ6cWpdRAodA4EUTt\nJm9Ll1KvXupv9eh/6NWr6cgR6tSJhMIHS2a6ddO2h1hDg/a9Q+zstDQ+1soOqTQ0NGh7A6hz\n/Trl5Wmb1QPNwi7ow/oUPjFg5th+wv79++u88s6dO0KhMCAgwAipTMKJE8x33zE5OQ9fef11\nxsqKIWKIGLGYGTWKaWjQ61azZz9415O/fv/dwLFTUhh7+8ceYW/PpKRoe8uMGYxI9PB6Z2cd\n17M0fUXsr9xcLW/9+GON73N1feybmp2dTURBQUF6fvWgUjFRUYy394Pvp7U1M3Uq8/fffMfi\nj0rFHDjALFvGhIYyixczsbGMUtmCm6g6depkbW3NQUDQFwoOSzB//nwiOnv2rM4rPTw8BAJB\nQUGBEVJZmsGD1Xy6LlligDsfOMA4Oz9WXkRFMefOMe+8w7zzzmMFk3bl5c24mGEYoVBbwaHV\nrVuPRX701+bNj12Zk5NDRMOHD29GMD4cuXfkp9KfUir1KNQekZ/PKBRMcjJTUWGwJEuWqPmu\nurkxV64Y7BFmpKKCGTu26Xdj6FDm1q3m3Sc1NZWIBg8ezE1M0AsKDktw+PBhIlqzZo3OK1eu\nXElEkZGRRkhlgQ4cYHx8GAcHpl07ZsgQ7X0A+vr8c/Wf23PnGuDm2nl5aaw27O11vvvECcbN\nren7Rs+7oLib9Ohlly9fJqIhQ4Zw9mU8rRXXVkj/klI6sb+sM6w3XN+g811ZWUxAwMMv3Nqa\nWbaMqa5uSYDKSubvv5m6OoZhmGPHNP43CQlpyc3N3Wuvqf9uNLfL7IMPPiCir776ipuYoBes\nUrEEKpXKw8PDysrq8uXLAq0ni5aXlzs7Ow8ePPjEiRNGiwcaKZUklWpcI3PpEnXvzuHTL1+m\nnj3Vr175/XeaPFnnDcrL6ccf6cQJulh+Lccl/v7YH6j3n0QkFohntJux3XM7ERUUFHh6eg4a\nNOi0zrkyfJieP/3XO78++foKtxWbO23W9K6zZ2no0Mf2IGGNGUOJifpuzEZECQn00UeUlkYM\nQ9bWNH48WVnRL7+ov1gkopIScnbW9+YW4NIlbTvrnjxJAQH63qp///5nzpyprq6W6jz5CDiD\nSaOWQCgUTp06NTc3988//9R+paOjY+fOnU+dOlX46EICi6dU0tdf0/z59OmnBjgn1oA+/FDb\nitxFizh56Pnz9OqrNGgQvfUWRUSQldVjrSIRffWVPtUGETk60tKlNPzf/8n6xP1+2CK22iCi\nBqbhx7Ifh18eTqa98df52vNqqw0iiiyJvN1wW9MbV6xQU20Q0cGDpP92vp9/ThMnUmrqg5Kv\ntpZ+/520TP5WKvXaFNeSqN3lX8/WRxUWFmZlZXXt2hXVBr9QcFgIdl8vfbY5f+211xiG2b17\nN/ehTMO0aSSR0MKF9O23tGoV2do+WCzKtfv3af588vYmd3caOZIyM9Vc88cf2u6Qk2P4VP36\nUe/etGsXpabSwYMUHk5t2tAPP9DkyTR+PH31FTU00Jtv6n8/FanCrqnfRulYxbG9d/ea8iqV\nzSUa+zBUpPri5hdqm+7epUOHNN5Tz6318vNp5Uo1r2v/PtnY6HVzi1FR0fLWR8XFxTEM88or\nrzx9JHgaKDgshJ+fn4+Pz3//+1+dP9nDw8OFQmGrOFeFiEJCaMeOpqMGf/5J3t7cPveHH8jG\nhr79lvLy6No1OnKE+venUaOaXqZ1/EtHawv060fZ2U1fvH2bli6l33+nhIRmlRqsneU77zMa\nF9B+VvIZuw+HUv/DcjW4cYNWr6ZBg8jbm154gTZtIl3HJOt2ufayltbzdefVvl5UpO3o37//\n1uvRMTHa1x2r0aYNdevWvLeYO3f3lrc+it1g9O23/z975xkXxdm18TOzhV269CoIFgRRsIIN\n7IqiEUVERWNUMDEx0UTR2KJpWBL10TyKRqOEGOSxg4KiUSxoQKSIgCi9SJcOW9h5P6wv4jIz\nW9hCmf+PDzD3PWeupc3Zue9znQ2dl0TRGaiEo+ewaNGi8vLyu+RvmgEMDAzMzMzi4uKKi4uV\nI0xllJVBVBT+UE4OvjW3XHj1ClauxFkruXsXli794EjHFKQ9gwfLU1VODk62IaSuDvbulS1q\nUiNZt7xCXqFcnnA8fQqOjvDzz5CQADk5cP8+bN4MI0aI74FDjjqqTjKqgeKbjYiY10s12sYr\nslQHn3XroLYWDh6Ejz+Gjz+GgwehrEzqIN2LqVNBRwd/SE0NJOyI0tDQcPfuXQMDA1NTUzlq\no5ABKuHoOSxbtgxBEElWVby9vQUCQc/vq0LiwgkgtfmmWE6cAA8P8PAANzfCOWEf7hjYsYNs\nh6GwPay82LmTbPTUKdmiatO0SUZZKKvzCUdzMyxcCJUdNlS8fAl+fjJHBQCYrj2dZHS+Lv4T\neAsLsLIiPGvcOIkuTb6XoOPSyUcfwdChYGsLGzfC2bNw9ixs3Aj9+5Pt+egBaGvDL7/gD+3Z\nA2ZmEgWJjo7mcrlTpkyRozAKGVFxlQyFXBk1apS2tnaTuOK8iooKFEW7vjVCZ8F1zmjvbCAv\nQkMxOl2Mj1bbh4gl17Fj+NPWrpWbPCHjx5OpMjCQLerL5pdtBaUdP/wL/IWLKX379pVZ+Pnz\nZMJfvJA5MMbDeBrJGrjKjVKNSE48cQJfjL4+Vl4u0aVPniR8RSiKJSRgW7Zg48djw4djixZh\nFy9i8fEYg4EzmU7H/v1X9u9At+DcOczS8oM/3OBgKU5fvnw5AMTHxytMIIWkUAlHj+LgwYMA\ncOHCBbEzLSwsUBQtLi5WgiqV0dEwqP2HlZV8rnLnjqSpRvsPBMHMzbGkpHcRDAwwBHk3pK2N\nnTolH23tWbiQTE+/fjIHtnthh3vPpifSq3hVGIahKGphYSFz/C1byISHhsocGMMwLL4pXu2Z\nmohyzWTNrOYs8hO3bxc1TjM1xR4/lvS6tbWYiQn+K1q0CGe+lxfhd2D+fClfczeEz8cSE7Hr\n17F//8V4PKlO5Ovr66urqytMGoUUUEsqPYrFixfTaLRzRIX87ViwYIFAIOjhtSr+/mSjU6fK\n5yo+PrKchWFQXAzDh8PVqzB5MlRUgEAAGAYYBrW18Mkn8tHWHvIFpk5s4H8w8IEB3UDkIA2h\nnbc5r0fXAwAajdaZJRXyitqbN2UODAAwij2qfFj5Cv0VFgyLPvQ+VgyrdQbrKhwrBrDEOKB8\n/z2kpsL27bBoESxfDseOwcuX4OIi6XW1teHiRZw+PKNGwfHjOPNJSkAfPJD0ot0XGg2GDwcP\nDxg9Guh0KU589OhRVVXVqFGjFCaNQgoo46+exrRp0x48eFBaWqqrq0syrby83NTUdOLEiWI3\nmXZvtLSgoQHnOI0GTU1iFtKJef4c7t6FigqwtASPAEsLKJJdIZ0u5o4qRywtoQhPKpPZyRZh\nAhB8W/xt+Nvw6tZqNsJ21XQ9YnHEnGkOAJWVlSYmJgwGIz8/38jISIbgJ05AQADhqK4uVFRI\ndxPqOrx5A0eOwL17UFUF1tYwfz588gn+byWbDS0t+EE6/dPryWzevHn//v2hoaFLRfZrU6gE\nVT9ioZAzp06dAoBTEjyTNzMzQ1G0tLRUCapURm4uxmTiLJLfvClbvPp6zNv7g2AM4G6DHwSA\nED7yFvtx9qx8XzQhHA5mZCR6dRZLug4s0hAeHs5isYT/auh0+qJFi+qlbzpSXo6/faHtQ7gw\n1bPR1iZ8+ba2qhbXhRk0aBCdTm+VodsbhQKgllR6GgsXLmSz2ZLUqnh5efX8WhVra2hqguXL\nQU8P1NRARwdmzYLaWphOVp5Agq+vqJUkDxg/wrYfYZvsIq9ckf1cqWAyoawMzp2DYcPAzAwG\nDoQff4TmZsIG9wTwgX+g7MC019Mmvpr4acGnhVwc11oMw/z8/BYvXtza2nrgwIHg4GAjI6Pw\n8HA9Pb1Vq1ZJZTxqaAiOjmQT3r6VSn73Iy4O39hUyEcfKVFKt+L169cvX74cNGgQKrnbPIVC\nUXXGQyF/vLy8UBQtKioin1ZaWoogyKRJk5SjqgdA0liLDU01oCN6lMnEXF2xYcMwNTWyd+jd\natffrbpb7Gfs9lsskUTk88LP2895+fKlsbExAFhZWcXFxQkPcjic4OBgAwMDAGCxWBs2bJD8\nogEBZN8/hT2g6Sp8/TXZy3/0SNX6uir79u0DgD179qhaCMU7qLyvB+Lr6ysQCMR6iRobG5uY\nmMTGxpaXlytHWHcnJoZwqBnYj6CDA0NQEMTFQXIy2NuTxZ05Uw7ilEIxt9jjtUcz9kE/Ggyw\no+VHfyr9SfjloUOHHBwcysrKvL29k5OTXf+/vxaTyfT398/NzQ0KCqLRaAcPHtTW1j506JAk\n150zh3Cof3+y/l49A/LGRyQPP3o5ERERKIp+8cUXqhZC8Q4q4eiBzJkzR0dHR/JVlR5eqyI/\nqqrIRivhw0qNpUuhzUr5P/8hPA1FxVTTdCXWFK7hY/j1Jj+W/tjS0uLu7r5x40Y1NbWQkJDw\n8PCOO5c1NTUDAwNzc3MDAwM5HM6GDRv09fXF/q7Ono2fldFocPgwIAiUlsK1a/C//0FSEn77\n226NpibZqDaZ9Vrvpbq6Oi4uzsTEhHz7PIUyoRKOHgiLxZo/f358fHxWVhb5zG3btiEI0lv6\nqnQa8hoLo8H6oK8PBgYwdixkZEBo6Pux8eNh4kT80wQCOHNGjiIVyr8NhC3mmwRNhk6GsbGx\nzs7OSUlJfqQmoIaGhkFBQVlZWf7+/jU1NUuWLLG0tLxD3BINQeB//4NPPgEa7f1Bc3O4cAHG\njYMVK8DCAubNg0WLYPhwGDIE4uJkenlKIScHtm+HOXNg9mwIDITMTPGnjB9POKShAU5OclTX\nc4iMjGxtbZ01a5aqhVC0Q9VrOhQK4ebNmwCwe/dusTNNTExQFC0rK1OCqu7Ov/8SrqNramJi\nyi8sLAhP7j6uROwkNomvKOKKrF+/nsPhiI0T3xQ/+/Xs/mn9B78Y7Jnk6fmxJwAgCDJ48OAk\n0pqToiLs/Hns99+xu3cxDgfj87Fx4/C21LCxhAT5vWz5cfq06H4eOh07fFjMWc3NmK0t/u/O\njh1K0d0NWbhwIQA8f/5c1UIo3kMlHD0TPp9vYmJiZ2cndubatWsBIFgqr+BezOLF+P/3Dx4k\nOIHPxw4cwObOfW8kivshAUUcMbuAlYBBigFJwnEm6owkQXxzfUVORBPRr+K/cnNzAwAURV1c\nXPLy8iQJdfYs4XdUVcb9tbVYdjbW2IgzFBcnak4q/EAQLDpaTNjMTGzAANETV63C+HxFvIhu\nD4fD0dTU1NbWVrUQig+gEo4ey/r16wEgMTGRfFpJSQmCINOmTVOOqu5OczO2Zs0Htw0NDWzf\nvnYzysuxc+ewe/cwDMO++UZMntH2kZ1NdMVzVedMUkzePUJ4hvR93vdmnYwmIp3H67UXUbah\nlaQlSYRdxbvwn448Qx43PI6JiXFycgIAGo02a9asqqoq8mgLFhB+RxEEE3e2nLlzB3N1ffe7\nQadjU6eKPmUhsSefMkV8/JYW7OxZ7JNPMG9vbNMm0Z48FO2Jjo4GAA8PD1ULofgAKuHosTx+\n/BgAvvnmG7EzjY2NaTRauYRdpygwLDcX++MPbN8+7Pz5dne1ixcxNlui9KLjB8Eb1e+Kv8O5\nNyciJypOKOilvWh+4ZLhwkpioYkoK4k1KnNUSmNK22gVr6pj5xHhx/HK45LE10zWJEpZnDKc\nMAxrbW0NDw+3tbUFADqdPn/+fBKvMPL2fGlpnf9+SEpoKM7TCyYTi4l5P8fMjFCqhobypPYG\n1q1bBwCRkZGqFkLxAZS1eU9m4MCBjY2NBQUFtPZ77ToQEBBw4sSJkydPrl69WmnaehpnzsDK\nlTKeS+BN/Yb7xiLNQgCCjkMMhFEzrEYdVZfxigRcrb3qleMlwD64IgroeZvzC3UXCr9Mak6a\n8nLKW8F7sy0a0PaY7fnW5Fux8Wv4NX1S+xCNslF2k1OT8HMej/fHH3/s3LmzrKyMwWD4+Pj8\n8ccf9A4G5jNnkvVSKSoCc3OxouRAdTXY2EBtLc6QpSW8fv3OrVxXF38OAKAocLlA+mfak+Hx\n4OJFuHkTKirA1BTmzAFPT+iMWZe1tfWbN284lOV7F4OqUunJ+Pj4lJSUPBDX3Onbb79FEOTC\nhQvKUdUz6Uxp69atuId/Lv8ZN9sAAB7GO1ZxTPYr4sEVcH1yfESyDQAQgGBp3tImwbtUIDY4\ntn5UPWwCqzQrT3XPn8x+qnGqkSTbAIBSfinJaPuCWwaD4e/vn52dHRQUxGazQ0NDtbS0Nm7c\nKHKKuzthtP79lZRtAEBEBGEmUVgIsbHvPre2JozQt2/vzTbevAEXF/D1hTNn4Pp1+P13+Ogj\nmDKF8FsqluTk5Pz8/KFDh8pVJoUcoBKOnoywX5HY5rFWVlaGhoa3b9+urKxUiq4eR2ys7A3Y\nfHzgu+9wR1KbU0nOS2hKkPGKBPxW8RsHw39HyBVwD5cfbm+zEewTnLc875rdta0mWzVRUpuI\ndtgwbUhGNVAN0SMaGm2mHQBw8OBBHR2dI0eOtE1YuxZMTfGj7d4toSg58Po12egPP7yzBlm0\niHCOt7ecJXUXMAy8veHZM9Hj9+7J3jL52rVrAEBemE2hEqiEoydjZ2fn7Ox84cIFsY8WPT09\nW1tbhX+oFFITHS3dfAQBU1OYPBmysiAsjGgWDSN7z8tAGNJdVBz3G++TjEYWRQp9aYU2G/4y\nPdFhokxLpiXRqJuWG+5xPT29oKCg169f+/v7NzY2rl+/Xl9fX2geo6sL0dFga/vBfAYDDhyA\nJUvIlFyqueSR7THm5ZjZ2bMv1XS2nRCD9Edx/z789RcAwFdfwfDhOBPs7OBbiZ4Q9UDu34dH\nj/CHLl2Cly9liRkREUGj0WT7FaVQKFTC0cPx9fV9+/ZttLg74o4dOygHMNnR0pJu/uDBUFIC\nd+7AgAEks1y1XElG3TTxb88yQ7R8I+Txv4/r6urWr1//+PHjAaSyyTlrdRZBkI7H2Qj7TN8z\nJCeam5sHBwe/ePHCz8+vpqZm0aJFlpaWsbGxQ4dCejqEhcGXX0JAAPzyC7x+DV9/TRinhl9j\nk2azIGdBVG1UfGP8jdobC3IW2KbZ1glkdwgfOVLMhGPHAADU1eGff8DfH9TU3h1nMMDPDx48\ngF5rhklu0fb4sdQBS0pKEhMT+/bt29ammKLrQCUcPZylS5eiKCrWOtrKysrAwOD27dvV1dXK\nEdaj+Phj6eb/+Sc4OQGNBggCCAIMBsye3XHWZuPNRI8xNFCNTwxkfeJMwHAW3rvv/4eVz4qM\njDx8+DBTuAFSViZpTbpqc1UL/SBFs2JYpQxO0aWLv+sOGjQoJCQkOTnZ29u7qKho0qRJ9vb2\nmZmpPj5w6BAcPw4bN0LfvmQRRr4cmcvNFTmYw80ZmSEuayBm+nQx3XKSk999oqMDwcFQXQ3x\n8fDkCVRXQ0gIGBiQnduzaWwkG21okDpgREQEhmHz5s2TWRKF4qASjh6OmZnZhAkTrl69Wieu\nxZOnpyefz6dWVWTBzAyMjSWaiSDw44/g4gIpKSD4/ycKfD7cuNHxtqONap+xOoN2+COlAe2q\n7dWOxzvJBpMNdES0DOSdagHydP1TDw8PsUEEIEhrSstuySaZ46njWedUF2UbtcV4yy6TXSl2\nKXmOeQNYUjw1cXR0DA8Pf/jw4fjx4zMyMpydnV1dXQvJW5wBAEB0bXQ2B1/bK86rmHri7nyk\n0Olw8SLgPbh5h+DDh0fq6jBqFIwZI6ZJSm+APDu0spI6YEREBIIgX331lcySKBSIqutyKRTO\n8ePHASAkJIR8Wl5eHoIglFWOjJSXY0wmjsGCmxs2YACmrY3p62MzZmBVVYQm1QDYwoUdAyc1\nJo3KHCU0xmAnscdnjn/d/FpBL+Jo+VFch4xfSn8Re24Zr2x05mg0ERWeQk+kz82ey2kVb3Pe\nSWJiYhwdHeH/vcLevn1LMnlxzmISp9Rlucs6o2T4cMIfrJNTZwL3ZIqLMRYL/5ump4c1NEgX\nrbGxkc1m6+vrK0YsRWehEo6eT3V1NZPJnDVrltiZBgYGdDpdrL0jBT58PjZ7NsZmYyiK0WiY\nuTmG6ztE4j2qpqZ00aJcr7lulmT27h78FIwSja7UXBF7Vgn/+xuZAAAgAElEQVSnRD1JveMt\n3CzVjIfxFK1Z6BXWr18/AGAwGMuWLWtubsadOS1rGknCMSNrBu5Zr15ht29jhw5hEye+64Qy\ncCD23XdYU9MH0/77X8IfrNhuKb2ZX3/FN4r96y+pQwkbXy/ES9wpugJUwtEr8PT0pNPppaWl\n5NNWrFgBAGfOSNQRg0IWcnPJrDERRNX6sJMnTwp3acxZMYf8aUF7XDJciO7i/gX+ChXcBofD\nCQ4ONjQ0BAA1NbUNGza0traKzFmRt4Ik4ViVt0pk/u3bmIMD4Y/L2RmrqXk/mcfD5s7Fmebh\ngXG5in713ZszZz5obti/P3ZFfJaLwyeffAIAsbGx8hZIIR+ohKNXILTiOHr0KPm0rKwsBEHm\nzJmjHFW9keLiLptwcDgcNzc3BEFYLNahQ4ekOpeWSCO6i+sl6ylIMC719fVBQUFaWloAoKmp\nuX///vaj8U3xJAnH06an7Sdfv47R6WIs6T/77IOr8/nY4cPY4MHvRu3ssF9/xXgKf8TTE2ht\nxZ4/x2JisMxMmSO0Ghsbs9lsueqikCeUtXmvoKmpydjYeNiwYQ8fPiSfaWBgUFdXV1ZW1qcP\noQU1RadAUSD6o1NTg5YW5ap5x7///jtjxoza2lpnZ+ewsLCBAwdKfm4Zv8wk1YRolI7Qec6y\nuqLJSlVV1f79+w8dOsThcPT09A4dOtRmAzUua1xcA04t5gStCfcHvHciaW0FGxsoKBBzIS0t\nqKyEjoU7wh8jVZipTOLi4saNGzd+/Hix3soUqoKqUukVqKurz5s3Ly4uLjdXtCBQBA8PDx6P\nFxkZqRxhvRGSe/mCBUrU8Z4tW7aMGzeuzWZDqmwDANgom2QUAeLiDYWhr68fFBT06tUrf3//\nmpqa5cuXW1pa3rp1CwAeDHwwSXOSyPwp2lPuDbjX/kh8vPhsAwDq66GoCOc4i0VlG8omIiIC\nAD6R2aCUQvFQCUdvwdfXF8OwMGJfSyHbt2+n+qooln//fW/81B5j43eGlEqkpqbGyclp7969\nurq6ERERhw8fVsPVRkBSc9KkrEm2abYkc0wYhA8/FI2lpWVwcHBaWpq3t3dxcfGMGTMsLS3j\nHsb9M/CfnCE5W4y3LNNbtsV4S86QnNv9b4uUGefnS3qVXtsDpatx7do1Go1GOZp3Zaglld4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MUlJS3Nzc0tPTvb3J9hDIl0s1lya+mtjvRX1tGsUAACAASURBVD+HdIe1hWtFNjZG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\nAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for (i in 1:k)\n", "{\n", " I = (y==i)\n", " if (i == 1)\n", " {\n", " scatter3D(Z[I,1], Z[I,2], Z[I,3], col=i + 1, xlim=c(min(Z[,1]), max(Z[,1])), \n", " ylim=c(min(Z[,2]), max(Z[,2])), zlim=c(min(Z[,3]), max(Z[,3])), xlab=\"\", ylab=\"\",\n", " zlab=\"\", pch=16)\n", " }\n", " else\n", " {\n", " scatter3D(Z[I,1], Z[I,2], Z[I,3], col=i + 1, xlim=c(min(Z[,1]), max(Z[,1])), \n", " ylim=c(min(Z[,2]), max(Z[,2])), zlim=c(min(Z[,3]), max(Z[,3])), xlab=\"\", ylab=\"\",\n", " zlab=\"\", pch=16, add=TRUE)\n", " }\n", "}\n", "\n", "cols = c(2:(k + 1))\n", "legend(\"topright\", legend=c(1:k), col=cols, pch=16)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Supervised Learning: Nearest Neighbor Classification\n", "----------------------------------------------------\n", "Probably the simplest method for supervised classification is [Nearest\n", "Neighbor](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm) ($R$-NN), where $R$ is a parameter indexing the number of neighbor.\n", "Increasing $R$ is important to cope with noise and obtain smoother\n", "decision boundary, and hence better generalization performance.\n", "\n", "\n", "The class predicted for a point $x$ is the one which is the most\n", "represented among the $R$ points $(x_i)_i$ which are the closed to\n", "$x$.\n", "\n", "\n", "\n", "Split into training and testing." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n0 = round(.5 * n)\n", "n1 = n - n0\n", "X0 = X[1:n0,]\n", "y0 = y[1:n0]\n", "X1 = X[(n0+1):dim(X)[1],]\n", "y1 = y[(n0+1):dim(y)[1]]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Macro to compute pairwise squared Euclidean distance matrix." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "distmat = function(X,Z)\n", "{\n", " dist1 = diag(X %*% t(X))\n", " dist2 = diag(Z %*% t(Z))\n", " n1 = dim(X)[1]\n", " n2 = dim(Z)[1]\n", " out = matrix(0, n1, n2)\n", " for (i in 1:n1)\n", " {\n", " for (j in 1:n2)\n", " {\n", " out[i,j] = dist1[i] + dist2[j]\n", " }\n", " }\n", " out = out - 2 * X %*% t(Z)\n", "\n", " return(out)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute Euclidean distance between some $x$\n", "and all other $x_{1,j}$ in the training set." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "i = 1 \n", "x = X1[i,] # could be any point\n", "x = t(as.matrix(x, c(length(x))))\n", "D = distmat(X0,x)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Sort the distance and generate the list of sorted classes $ y_\\sigma = (y_{\\si(i)})_i$. This\n", "generate an indexing $\\si$ (a permutation of $\\{1,\\ldots,n\\}$) such that\n", "$$ \\norm{x-x_{\\si(1)}} \\leq \\norm{x-x_{\\si(2)}} \\leq \\ldots \\leq \\norm{x-x_{\\si(n)}}. $$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ys = y0[order(D)]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Function to compute the histogram of classes." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Defining an hist function\n", "hist = function(y, classes)\n", "{\n", " if (length(dim(y)) == 2)\n", " {\n", " out = matrix(0, dim(y)[2], length(classes))\n", " for (i in 1:dim(y)[2])\n", " {\n", " out[i,] = hist(y[,i], classes)\n", " }\n", " return(out)\n", " }\n", " else\n", " {\n", " count = c()\n", " for (i in classes)\n", " {\n", " count = c(count, sum(y == i))\n", " }\n", " return(count)\n", " }\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "For a given $R$, one can compute the histogram of class apparition\n", "$$ h_\\ell \\eqdef \\frac{1}{R} \\enscond{ i }{ \\si(i) \\in \\{1,\\ldots,R\\} }\n", " = \\sharp \\si^{-1}( \\{1,\\ldots,R\\} ). $$\n", "The decision class for $x$ is then the maximum of the histogram\n", "$$ c(x) \\eqdef \\text{argmax}_{\\ell} h_\\ell $$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1] \"c(x) = 1 [true class = 1 ]\"\n" ] } ], "source": [ "R = 5\n", "h = hist(ys[1:R], 1:k) / R\n", "c = which.max(h)\n", "print(paste('c(x) =',c,\"[true class =\", y1[i], \"]\"))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the histigram $(h_\\ell)_\\ell$ of reparttion of class indexes as $R$ grows." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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FSMFA4RSUtLS05OLioqOnLkyJkzZ27f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\nADXCAUCNcABQIxwA1AgHADXCAUDtfwHYmYUoGRHZaAAAAABJRU5ErkJggg==", "text/plain": [ "Plot with title \"Value of R : 4\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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PQQI4UjMzNTRLZs2ZKbm7tgwYKoqKiI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\nDgBqhAOAGuEAoEY4AKj9P/lWHwsNHEq4AAAAAElFTkSuQmCC", "text/plain": [ "Plot with title \"Value of R : 8\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "Plot with title \"Value of R : 38\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "Plot with title \"Value of R : 75\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=3, repr.plot.height=3)\n", "Rlist = round(c(0.05, 0.1, 0.5, 1) * n0)\n", "\n", "for (R in Rlist)\n", "{\n", " h = hist(ys[1:R], 1:k) / R\n", " barplot(h, main=paste(\"Value of R :\", R), col=4)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Perform the NN classification for all the points in the test set, and for varying $R$.\n", "Show how the classification score $S$ (number of correctly classified points)\n", "evolves with $R$\n", "lot(1:Rmax, S, '.-', 'MarkerSize', ms);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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bAALo0CVuXl+mdISEhxcbGnZwG4IwgBAErj0igAQGkEIQBAaQQhAEBpBCEAQGkE\nIQBAaQQhAEBpBCEAQGkEIQBAaQQhAEBpBCEAQGkEIQBAaQQhAEBpBCEAQGkEIQBAaQQhAEBp\nBCEAQGkEIQBAaQQhAEBpBCEAQGkEIQBAaQQhAEBpBCEAQGkEIQBAaQQhAEBpBCEAQGkEIQBA\naQQhAEBpBCEAQGn/Aavr5WVZFeFEAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_1_pca_nn/exo1.R\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Display, as a function of the position in 2-D PCA space, the class output by\n", "the $R$-NN method when applied in 2-D." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Plot with title \"R= 1\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "Plot with title \"R= 5\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "Plot with title \"R= 10\"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "Plot with title \"R= 40\"" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_1_pca_nn/exo2.R\")" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Unsupervised Learning: $k$-means\n", "----------------------------------\n", "In an [un-supervised setting](https://en.wikipedia.org/wiki/Unsupervised_learning), the class information $y$ is not\n", "available. The basic problem is then to recover class information from\n", "the knowledge of $x$ only. This corresponds to the [clustering problem](https://en.wikipedia.org/wiki/Cluster_analysis)." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The most basic algorithm is the , which tries to recover the\n", "class index $\\bar y_i=\\ell$ from the distance $ \\norm{x_i-c_\\ell} $\n", "between the feature point $x_i$ and the class centroid $c_\\ell$\n", "(which are the unknown of the problem).\n", "\n", "\n", "It does so by minimizing the following non-convex energy\n", " $$ \\umin{ (c_\\ell)_\\ell } \\sum_i \\umin{\\ell} \\norm{x_i-c_\\ell}^2 $$\n", "\n", "\n", "We first initialize the class centroids $ (c_\\ell)_\\ell $ at random among the points.\n", "They are stored in as the row of a matrix $ C \\in \\RR^{k \\times p} $." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "I = sample(n)\n", "I = I[1:k]\n", "C = X[I,]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The $k$-means algorithm iterate between first determining the class of\n", "each point using the distance to the centroids\n", " $$ \\forall i \\in \\{1,\\ldots,n\\}, \\quad \\bar y_i \\leftarrow\n", " \\uargmin{\\ell} \\norm{x_i-c_\\ell}. $$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "D = distmat(X, C)\n", "yb = apply(D, 1, which.min)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the centroids and the classes using colors.\n", "This correspodns to a Voronoi diagram segmentation in the high\n", "dimensional space, but here the display is done in 2D." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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wVM1STnSWpSv5Pyjo+5T2xZrIpU2nZtowBhgtOEZGVyobqQdyJkNebjj/Hxx+jY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\nb6eDAz09+eSJmSITCgcxajTXjB+PQYNQsiRWrkR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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for (i in 1:k)\n", "{\n", " I = yb==i\n", " plot(Z[I,1], Z[I,2], col=(i+1), xlim=c(min(Z[,1]), max(Z[,1])), \n", " ylim=c(min(Z[,2]), max(Z[,2])), xaxt='n', yaxt='n', \n", " ylab=\"\", xlab=\"\", bty=\"n\")\n", " par(new=TRUE)\n", "}\n", "\n", "CV = (C - rep(colMeans(X), rep.int(nrow(C), ncol(X)))) %*% V\n", "\n", "for (i in 1:k)\n", "{\n", " plot(CV[i, 1], CV[i, 2], , xlim=c(min(Z[,1]), max(Z[,1])), \n", " ylim=c(min(Z[,2]), max(Z[,2])), xaxt='n', yaxt='n', \n", " ylab=\"\", xlab=\"\", lwd=5, bty=\"n\")\n", " par(new=TRUE)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The second step of the $k$-means algorithm is to update the centroids\n", "position to be the mean of the points inside each class\n", " $$ \\forall \\ell \\in \\{1,\\ldots,k\\}, \\quad c_\\ell \\leftarrow\n", " \\frac{ \\sum_{i:y_i=\\ell} x_i }{ \\sharp \\{i:y_i=\\ell\\} }. $$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "for (l in 1:k)\n", "{\n", " C[l,] = apply(X[yb==l,], 2, mean)\n", "}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Peform several step of the $k$-means algorithm.\n", "nit" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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/diiYIzC07a2Yi33uLJk4yMpL8/GzfWf5V7j7T/9/8YGUlF0e/Y8vrrBPjjjz7e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\nLH5eneepAAAAAElFTkSuQmCC", "text/plain": [ "Plot with title \"Iter # 16 \"" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"iVBORw0KGgoAAAANSUhEUgAAAlgAAAFoCAIAAAAElhK7AAAABmJLR0QA/wD/AP+gvaeTAAAL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\nuzjX0wAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "source(\"nt_solutions/ml_1_pca_nn/exo3.R\")" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the histogram of (true, i.e. according to $y$) class inside\n", "each estimated class (i.e. according to $\\bar y$)." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Implement better initialization strategies such as farthest point sampling or\n", "[$k$-means++](https://en.wikipedia.org/wiki/K-means%2B%2B)." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "source(\"nt_solutions/ml_1_pca_nn/exo4.R\")" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }