{ "metadata": { "name": "", "signature": "sha256:78655f4d460780aeb246f9fbc83bf7827615967a4067f7e0e0cfea9911957428" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Supervised Learning In-Depth: Support Vector Machines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- *Jake VanderPlas*\n", "- *ESAC statistics workshop, Oct 27-31 2014*\n", "- *Source available on [github](http://github.com/jakevdp/ESAC-stats-2014)*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many machine learning algorithms available; here we'll go into brief detail one of the most powerful and interesting methods: **Support Vector Machines (SVMs)**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preliminaries\n", "\n", "Again, we'll start with some boilerplate imports and setup" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "\n", "# use seaborn plotting defaults\n", "# If this causes an error, you can comment it out.\n", "import seaborn as sns\n", "sns.set()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Motivating Support Vector Machines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Support Vector Machines (SVMs) are a powerful supervised learning algorithm used for **classification** or for **regression**. SVMs are a **discriminative** classifier: that is, they draw a boundary between clusters of data.\n", "\n", "Let's show a quick example of support vector classification. First we need to create a dataset:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets.samples_generator import make_blobs\n", "X, y = make_blobs(n_samples=50, centers=2,\n", " random_state=0, cluster_std=0.60)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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C0sPIbJZFnUej6TRGr2+L/1AZB7hlv1/EA2/2pb6jfvHYynUrOfKWg+aJhoXJqpaje46Q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\n3ozvsZ49v89HHy3nsce+LF4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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A discriminative classifier attempts to draw a line between the two sets of data. Immediately we see a problem: such a line is ill-posed! For example, we could come up with several possibilities which perfectly discriminate between the classes in this example:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "xfit = np.linspace(-1, 3.5)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "\n", "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n", " plt.plot(xfit, m * xfit + b, '-k')\n", "\n", "plt.xlim(-1, 3.5);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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iIeEkSUkJnD17msOHDzX7OSQZi3bj7OzMhEWT1Q5DCIvg7OzM3L8vIj8vH92V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\nvHkL3nprPjNmzKRxY/tfClAI8WS6dOlLly4y21w8TIqxDRQ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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are three *very* different separaters which perfectly discriminate between these samples. Depending on which you choose, a new data point will be classified almost entirely differently!\n", "\n", "How can we improve on this?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Support Vector Machines: Maximizing the *Margin*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Support vector machines are one way to address this.\n", "What support vector machined do is to not only draw a line, but consider a *region* about the line of some given width. Here's an example of what it might look like:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "xfit = np.linspace(-1, 3.5)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "\n", "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n", " yfit = m * xfit + b\n", " plt.plot(xfit, yfit, '-k')\n", " plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n", "\n", "plt.xlim(-1, 3.5);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sCNK8Xp7n8ODBA1RV7cPRo0dht9ug1erw4osvobx8OwoLp8PlYodtHMGQ5gcb\nhjUeHAokxsSoR9vV92mus1LrP2Ls4Ha70N1thdvt9E5NAsJVzlFGFEVwHAuW5ZRqVqIooL6+DlVV\nlTh79iwEgUdqahp27PgdbNy4CSkpqWEdw0AwDKDV6mE0xsVMyIHEmBj1uKZ4IEIE0+Oiw4EDOyUy\nBTMIIlqIogiHwwabzQaW9YR9apI0l1euZsVDEDiIopRYxXEczp37Cvv27UV9fR0AYMqUKaio2IGV\nK1dFuA+2CJVKDb1eD50usvHgUCAxJiKKy+UCwzDQ6yMXl5nz7+bj0InD2HJ9c8DyyqIqLPh+b/c1\nQYwGBEFQSlXyPB+WeLDUPIEFx7FKNStR5AH4V+BiYLfbcOzYURw4sB8tLY8BAAsXPoeKiu2YNWt2\nRIVQqhethV5vgFYbu54wEmMiIjR/Z8atf7yO1KvJEFUiOp+1oOBHJcgrmDTs+84clwn7r/Kx+x8/\nRNxlA0QV4JjjRNmfz0ZiYtKw758g+sNm60ZLy2Pk5OQiLi5u4DcMAMex6O62wum0KxbqUEVYLiPp\nK6jhs3pl/K3shw8fYv/+Khw/fhROpxMGgwGbN2/Btm3lmDjxmac+tsGi1UpTk9Tq2J8XTmJMDDuP\n7jxE1+8/wc47fqUFjwH7miuR/HEyUlKHP140qWgyJv3r5F4t0AgiWng8Hpz6z8eR/VkGJj2chGsT\nv0Pbui48/99eHJJ4OBwOtLW1wOVyQ6ViIFmrob8/uNUrFT7xt3p7blMURdTW1qCych/OnfsKoigi\nIyMTu3a9jg0bNiIpKZI3vCIYRuWNBxtH1O+cxJgYdqp/eRm77rzca/m2pq348F8j0/5PZiT9OInR\nzYk/O4pdH7wCHSTXaeG9Qth/acd+1WGs++sNIW1Dal1og91ug8Gg8s4RDu0c53kOLMsqVi/PS/kT\noRbUYFkWZ858gcrKfWhqMgMATKYCVFRsx/LlKyKcnSxCpdJ448H6Efk7JzEmhh3jXX2v5ClAav+n\nvxO7MRyCGC462tuRd2qiIsQy8YhH2vEkOP7c0a/LWhAEWK0WOJ12CILgdUUb+ny9ZPXKzRMk8e1p\n9YYqYFarFR9/fBgHDx5AW1sbVCoVli5dhvLy7SgtLY1wPBjeeLA+puPBoUBiTAw77jRP3+tS3REc\nCUHEBncbb6OktTDoukn3J6Gl5TEmT87vtY5lWaVeNNB360KOk6xeQZA6F/G8gKftXHT37l3s31+J\nTz/9BG6xlmepAAAgAElEQVS3G3FxcSgvr8DWreUYPz6yncOAyJaqjAQkxsSwk/vyM6g5Vosya2DD\n768yzsH02tjofEMQ/kyYngdzehNy2nN6rbs7/i6KsmYHLHM6nbDZrHC7Xd6pST4hla3e7m4W3d0O\npXkC8PSdi0RRxOXLv0Vl5T5cvCi1LszOHodt27Zh/fqXIlrf3VeqUge9fmTFg0OBxJgYdooXluL8\nX5zFzZ/dxJpbq8GBw8npnyH+PyaiwDQj2sMjiIiTkZmBCyvOYnHVImj8LsNuuNGyph1z4+O98eBu\n2GxSdyLZCva3ejmOV1oGCoIOPB/YPnCoeDwenD79Gaqq9uHGjRsAgJKSEpSXb8fixUsiGg+WWxfq\ndAbodLpRJ8IyJMZERFj05jI4dzjx6fHTUGnVeO6F5RGe8E8QscXq/70e76l2Y9LpPExvn4aGrEbc\nf+Eh1vz1enR1dcDhkOLBHMf6xXqDWb3hE6fOzk4cOXIIhw4dQmdnB1QqNVauXIWKiu0oLCwK235C\nQ/QrVamN8L4Hx5MnT1BTcxU1NTVobm7C11+fG/Q2SIyJiGE0GrF024poD4MgYgKj0YgN/7wN7W3t\nMN+8hdzJk5AjTMS9e7e9sV5BsXqHu2XgzZs3UVW1D6dOnQLLehAfn4CXX34FW7ZsQ3Z2dtj3NxCx\nHA/2eDxobGxAdfVV1NbWoKbmKh4/fqysH+qcZhJjgiCIKCAIApxOBzjehbg0A548eQRg+IXXf//f\nfvsNKiv34bvvvgUA5OZOwLZt5XjhhXVhKUASKnI8OC4uDnq9KmZc0aIooqXlMaqrq1FbW42ammo0\nNNSDZX3NLFJT07B8+QqUlc1AaekMlJSUDGlfwyrG9+/fh8XiAMOolFJsarUaDMNAo9FCo9FArdZE\nrG8mQRBENBBFER6PB263Eyzrgcfjgd1uB8u6lalJkRIgl8uFkydPoKqqEnfv3gEAzJw5CxUV27Fg\nwcKIVquS48F6vQE6nR7x8QZ0d7sitv+euFwuNDTUo6ZGEt/q6mq0tj5R1ms0GkyfbkJZ2QzlLzd3\nQlhuoIZVjKUC4sEL8YuiAEEQvVl+KqjVDFQqtVLEXK1WQaVSex+rodVqFeGOlbsmgiCIYPA8D5fL\nCY/HDY5j4fF4lHm90nLfdL9IXc/a29tw8OBBHDlyGFarBRqNBmvXPo+Kiu2YNm16RMYgI4qikhUd\nrdaFoiji4cOH3livZPWazY0BmpWRkYGVK1crwltYWASj0Tgs44mam1oSWd9zUYR3Phzf67WiKEIU\nBYgioFIxfpa2WrG45edqtQpqtWx1q0m4CYIYViSr1w2Xy+ktJykV15BaFErXH57n4XZLIhzpa1Jz\ncxMqK/fh889Pg+M4JCUlY9eu17F58xZkZGREdCxA9OLBTqcT9fV1SqJVTc1VtLe3K+s1Gg0KCgpR\nWjoDM2bMQFnZTOTk5ETs+xoRMWPJhRP4xQmCAEEQer1WEm4RgAipjqoKKhXjFWZylxME8XRIVq8D\nHo8HLMuCZSWr119cVCq1ItJut8srzpFzRfM8jwsXvkZl5T5UV18FAOTl5aG8fDvWrFkLg6Hval3h\nxjc/WA+9PjKtC0VRxP379xTRrampRlOTOcDYy8rKxurVaxWrt6CgMKKfS09GhBgPhmAnvNTsOri7\nXBAEiKK/u9xnZTMMA7VaBYZxw2p1QaNRQ6Mhd/lwc7PhBm5+24y8mfmYVhZZ9xlB+OMvqJL4Sh2M\n/K3ensaCKIre17sD5gdHAofDgU8//QRVVZV4+PABAODZZ+eiomI75s6dF2GDQ4RarYHBYIBWO7wt\nUx0OO+rqrvmJbw06OzuU9VqtFsXFpZgxY4Zi+WZnjxvWMQ2WUSfGg6XnySmKYi93udUqwmZz9eku\n72l1S+5yNdRqDbnLB4HNZsPp//AJ5pyZjR32bag3NuDw4kos+3+rkZI2/J2dCILneTidDrCs22v1\nshBFMeA60Zd7VRD4qMWDnzxpweHDB3H48GHYbDZotTqsX/8iysu3Iz+/d1nN4UaqFz088WBRFHH3\n7h1lalF19VVcv94c4CnNycnB88+vQ2lpGWbMmAmTqSDm6xqMeTEeDEN3lwMMo1aS1BhGrbjO/cVb\nq9UqcfCxyJkfncTbx96ECtLxlziLUXyqCO/86bvY8M62KI+OGG1IFqwbbW1utLVZvFZvoCUbilXL\ncZySJT2UkpNPQ0NDPSor9+HMmTMQBB6pqal46623sXHjZqRGoDVpT3Q6vTceHL5rmM1m81q9V5Up\nRhaLRVmv1+u9ruaZiuWblZUVtv1HChLjYSLYj1gQRAgCB6C3y9znLmeUZuC+JLXATHONRuN1l6tH\njbvcarUg9+x4RYhlGDAwfTUNLY8eIzsnttxKxMiC41i4XC4lw1m2epOT4+DxSA1LQhUR2X0tbYvz\n/gYj8zvkOA7nzn2Fqqp9uHbtGgAgPz8fr776KpYsWQ69fnhdwj1RqVTe1oVPHw8WBAG3bt0MmNd7\n/XqzUnUMkOZCL1y4CDNmzERpaRlMJtOI79gEDLMYb9q0CQaDEWlp6UhLS0N6err3cbr3cRrS0zNi\n3n0QCUJxl/uvk6ZJSI2+B3KXS+KtCTihY422tjbktgXv/DLJOgkNt2+QGBMhI8dtpditL8PZ/+Z1\nKLFcabtObzw4svODbTYbjh8/iv3796OlRar4tGDBApSX78CcOXNgNOrgcrEDbCU8SPODtd548NCv\n31arFdeu1Srzemtra2C1WpX1BoMRs2c/i7KyMpSVzURpaSkyMjLDcQgxx7CK8Z07d9DV1TXg6xIS\nEhWxTk9PR2qqJNKyYPvEOx3x8fGjwhJ8GobqLu/uboPdzvbrLpetblnQI0Vu7gR8N/k8im/07uJU\nm1sLU2lZxMZCjDwkq9epJFlxHOvN7fCdw09TzCKa8eBHjx5i//4qHD9+DA6HA3q9Hhs3bsK2bRXI\ny8uLyBj80WqlqUmD/TwFQcDNmzeUOb01NdW4detmgJGQl5eHJUuWKRnOU6dOg1Yb23Wpw8Wgxdhk\nMqkB/CuA6ZACor9nNpvrgr326tWrePKkEx0d7Whvl/46OjrQ0dHm91j6397ejvv37wUVFH/0en0v\ngQ60tNORlpaBtLQ0pKSkjNn4q4z/nbtkObN9ustl4ZZ+HIzXPR5sTrcs4uFzl+v1eji2uNH2D23I\nEHxzHy2woGVDO+YkJA5528ToQhRFpaCGZPW6wXF8D6tXhXBoJct64HZLyVyRtAFEUURtbS2qqvbh\n3LmvIAgCMjIysHPnLrz00kYkJydHbjAQwTAqaLV6GI2hty60WLpQW1urxHrr6mphs9mU9XFxcZg7\nd56S3VxSUoa8vPFRrcAVTYZiGb8EQDCbzYtNJtMyAP8dwOa+XqzT6TBuXA7Gjevdt7MnPM/DYulS\nhLq9vU0R7MBl7WhqMgfUBw2GWq1GSkpKgED7BLyn9Z02KuIOT0Nf08L6c5dLpfzkix/jJ8yBrnN/\nd7k8bawnq3/4Aj7TnYLqiICUhymwZFvgWcfjhT97adiOmYh9WJb1FtTweP+k3324rN6e+KYzub03\nrUzEhJjjOJw58wUqK/fBbG4EAEyfbkJFxXYsX74iwlaiCJVK440H6/sVYZ7ncf16s5LdXFtbg9u3\nbwW8ZtKkyVixYhVmzJiJsrIZmDJlakRLb8Y6gxZjs9l82GQyHfU+nQSgM1yDUavViqU7EKIowmaz\neS3rnpa3/Fj6/+DBAzQ1NQ24zcTEpB6uckmox48fh/j45ABXutEYR+5yr/j603+cW1SS1Pwrp/ln\nms99ex5U31PB42GRkJDoFe+x7d0YSwiCoMR65YIagsAHzOsdrvNBFEU4nU6wrFvJyYhUUpbVasXH\nHx/BwYMH0NbWCoZhsGTJUlRUbEdpaVlErzWiCGi1Ur3ovgyUzs5OpXZzbW01rl2rhcPhUNbHx8dj\n/vyFSnZzaWkZUlJSInUIIxJmqEk9JpPpNwC2ACg3m82ngr3mzp07YrALczRwuVyKYLe1taGtrU15\n3PN/Z2fngMlOBoMBGRmSZS3/93+ckZGhPCZ3+eCQRVsuoO9fNU3+7/9Yq9VCq9Uqwj3Wb5JGEnLD\nBLfbDY/Ho8RkI/l74TgOdrs9IB4cKe7evYuPPvoIx48fh8vlQlxcHDZs2IDt27cjNzc34uPR6/WI\nj48PuMnmOA5msxlXr17F5cuXceXKFdy5cyfgfVOnTsWsWbMwc+ZMzJo1C1Onjl2rl2EYTJ48edAX\noSGLMQCYTKZsAJcAFJrNZmfP9Xfu3BG7uuxD3n604DhOcZe3t7fD6ezGgwePlNh2e3s7Ojvlx219\nVveSkSz+ND9rO9D69o99S+7y4XFFJSZGtyNKOAh2DIN1l8dC05HMzES0tnZHZd/hYrDHENzqjWxG\nsj8s64HL5YJGA7jd/f+Gw4koirh8+beorNyHixcvAACys7OxbVs51q9/CQkJCUParsGgHXQ2tVSq\nUuUtVSnFg9vb2wIqWdXVXYPL5bu8JyYmobS0FGVlM1FWVoaSkjIkJSUNacw9GQ3XKIZhUFZWOOgT\neigJXK8BmGA2m/8HACcAwfs3atBoNN54spRI1N8JIooiuru7e7jK23vEuaXn9+/fQ1OTecD9Jycn\nBySm+WeV91xmNEau52isMnh3uVRFrT93ebSzy0cDLOvxun09yrxe+YZJJtKfqRQPdnnjwTwAJmJx\nWI/Hg9OnP0NV1T7cuHEDAFBcXIKKiu1YvHhJRLsXya0LVSoVbt26jdraGiXD+cGD+8rrGIbBlClT\nlaIaZWVlmDRpMv0WhoGhfPtVAH5jMpnOAtAC+COz2ewO77BGDgzDICkpCUlJSZg0afKAr3c6nX5x\nbf+sct8y+fGtWzcH3J7RaER6eoafWPtPEQvMMk9IyA7HIY9o+p8WxsE/J5CajoSOIAhKhnNfVm80\nPxMpHuxQintIRMYa7+rqxOHDh3Do0CF0dnZApVJjxYqVKC/fjuLi3lP5hpO2tlaYzWY0Njbg2rVr\nqK+vg9vt+0ySk5OxePFSZV5vSUnpkC11YnAMJYHLCWBHKK+V3Id8QC3nsY7RaERubm5I8SCWZdHV\n1RUkq7ynq7wd9fV1A7rLtVotUlJSg87f7pllnpKSMmbm9/XFYJuO+PfoloW7rx7dBgPg8bij7i4f\nCtJnwHq9Pl1ey7d3V6JYuCGRSlW6vKUqI8utW7dQWbkXp06dAst6EB+fgB07XsbWreXIzh7+G2OP\nx4Pr15tRV1eH+vo61NfXK8VCAOn7mTp1mjKnt6xsBvLyJo2oc3E08VQx4xAQW1os4HkOHMd5J+JL\nU2Vka0QUBe9zuaqUbIVEJ44UjJEQxxBFEVarpUdcO9BVbrF0orW1De3tbXA6e4X4e5GSkhIg0IEC\nHrhsuBpu92QkfBehkJCgh9XqGBE9ugVB8DZPkKYWeTwsRFFAcnJczH4XLOuGy+UCz0tTk/pjKLHW\nvhBFEd988w2qqvbi22+/BQCMH5+L8vJyvPDCesTFDV9YyWrtxOXLV1FXdw319fVoamoKuAlJTU1F\nWZmva1FRUQni4+OHbTxDYTT8viMWMx4s0gVFF9IcXlmgOY4Fx3He5z7h7vlcbn3oP+1hrMIwDJKT\nU5CcnILJk4N3afE/0Z1OR0A8O/B/h1/cuw03b94YcP9xcXF9FGBJQ1paRsCyxMQk+r4Yplf3n1jo\n0S2Kot+8Xsnl3NPq7Rn3jRWCtS6MlCva7Xbj5MkTqKrap2Qaz5gxAxUVO7Bw4XNhzyx2u91obm5C\nfX0d6uqkv7a2VmW9Wq3GtGnTMGPGLK8Al2HixGfG/O8ulompRhHyRSWURAY5g5bnObAsC57n/axs\nwesy9FndgNz6kIQbAIzGOOTmxiE3d8KAr2VZFp2dnf3M6fa50evqaoMmTvmj0WgCRDuYu1xel5KS\nGtHElljkadzlUo9u2V3u69Etu8tVKhU4jvUmvHFgWQ6CwAeIRyy4m/sjmqUq29vbcOjQIRw+fAhW\nqwVqtRpr1qxFefl2mEymsOxDFEW0tLQoFm99/TU0NzcHfP+pqWlYunQpiotLMGvWsygtLaXkzhHG\niL3KyRm0arUaOl3/XUpky8LfXS6VhOT7tLj9OyiNdbRaLbKyskJqSyYIAiwWi+Im93eby2IuL7t1\n6yYaGur73R7DMEhJSVWs6uzsLCQmJisu8p4lUSPdsSYWkeLTvueiKGWXcxzn/Q2w4DgegsArF3TJ\n2mUAqLxWuxwqUin/5Ri4Wq2KCctYbl3o8US2VCUANDc3o6pqH06f/gwcxyEpKQm7dr2GzZu3IiMj\nY+AN9IPb7YbZ3KhYvfX1dWhvb1fWS1bvdBQXF6OoqBhFRUV45pk8ZGamweGITKMIIvyMWDEeDL62\nhENzlycl6cHzaggCD54XIYqBrnN/4R7r4q1SqZCamurtpTq139fKGa49LW1/61tOUmttfYIbN64P\nuP/4+Ph+EtMClyUkJIzq70sQBG+PXk6Z6iWfqzK9rV75xrX39nrml7jdOrjdfD/irfKb7x2+z1kq\nVenyc5+HbdP9IggCLl68gMrKfbhy5TIAYOLEZ1BRsR1r1z4Pg8Ew6G2KoohHjx55hVeyfK9fbw7w\nLqWnp2Pp0mUoKipGcXExpk83QafTKYaIXm/wm95HYhxpZONNo9FAq9VCpxv8eQCMETEeLD3d5enp\niRCE4CIuZ4xLFjdH7vJBwDAM4uLiERcXj4kTnxnw9VLRfjvu3XukFFzpWbu8o0NaVlv7YEB3uU6n\n6zV/O7jbXHKXx3JFIdnzI4dseJ5Tphb58zTnXLD3ynO2g/V3CRRvX59uhvE//2WL25e81pdbvmc8\nOFK/H6fTiU8//QT791fi/n1pDu6cOc+iomI75s2bPyg3vtPphNnc6JfhXIfOTl9FYa1WC5OpAEVF\nRSguLkFRUTGysrL8jlWEWq3xti4kL1A04HkeKpUaOp0WWq1k4BmNcU8dziExfkqkO1IpWWYgD6kv\nzs1743TcoNzlY128tVod0tKSkJCQOuBr/d3lskAHWtu+ZTduXEd9fdDGYwoqlSrAXR6sepq/mA+3\nuzwUqzfa50vv/YveQhvodaMUeK4DsrscEBUPle83IIu39Hi4jvPJkyc4eHA/Pv74CGw2G7RaLdat\nW4/y8gpMmdK/10c+pgcP7ge4m2/cuKl8BgCQlZWFFStWoqioCEVFJZg2bVqf/d21Wi30euOYz6GI\nJIFWr05pH6nVasN+3tG3GkEC49xDyS7nFcH2d5fzvABR5JWqUiTcg3eXOxwOpQiL7BrvmV3e3t6O\nlpYWXL/ePOD+ExISgljbvqzyCRNyYDQmhtSjW07W8k+0CrfVG216nrOSt4kNOjXJZ3HL2eXo8d8n\n0j4XenCLOxiNjQ2orNyHM2e+AM/zSElJwRtvvIVNmzYjLS2tz/c5HA40NjYEWL0Wi0VZr9XqvKJb\nrMR7MzMzBxyPTqeHwWCM+US60YAgCFCpVN569+GzekOBxDiGGXx2eaC7PNDKFhQ3q+xalPuUjuSL\neDhgGAbx8fGIj4/HM88M3Kzd4/EEJKL1tL79RTz0Ht2Bce3k5GSkpKQgJSUZyckpXqs8FUlJyaM6\nxCGduyx4XlBEtSe+Y+8p0oAc8/Yt83eV+8Tbt20GosjB5WJx4cLX2L+/CnV11wAAkydPRkXFDqxa\ntbqXp0MQBNy7d08R3bq6a7h9+3bAdz1uXA6efXauIr5TpkwNuZCOSqXyti40jNrvOtrI10F/q9do\nNEKjCb/VGwokxqOEUNzlmZmJiIvr7uUu5zhOiW1LAi726S6nu/On79Hd3t4Ou92KR49a/Eqihtaj\nW6VSe2uXpyI1Nc1bmEWKaaempgY8Tk1NHTFV1DjO483wDm/jiMDt+B7Lwm2323Do0EkcPHgQLS0t\nAIC5c+di06YtmDVrFlQqBqLIo729DY2NjWhsbERDQz3M5kZ0d/uaZOj1epSWlnqzm6W/9PSBW8H6\nI7lDtd548NjurR5u5GuYZPXqvIlWseVxIDEegwzVXS7FKH0WtxynlJ77XOfevZC7HL17dAsCD5b1\nQKdTw2Zzguc5JbwgiiLsdjs6OzvQ2dnl/d/p/etAV1cXOjqkZY8fP1aaDfRHQkICUlPTFHGWHqcE\nWZYKo9EY0e9LKjDiCYgfR2r/jx8/xuHDh3DixAk4nQ7o9XqsX/8iNm/ejNzcCbh37x5OnTqJhoYG\nNDY24O7duwFWtmT1PouCgkKYTAXIz8+HVquBfwzb7XYFuMz7c5fLschYThIcScgeCqm1qlaxemP5\nJofEmBiQobjLWZZTkot6usv9M81Hs7tcruEshQ54CALrLcbBQBS1XhHyTc1hGAYJCQlISEgIKbvc\n7Xajq0sS7Y6ODuWxv4DLon7//r0Be3Tr9XrFHe5vdQezwJ+mZZ7/+RFp8a+rq8OhQwdw4cIFCIKA\ntLQ0bN26Bc88k4e7d+/i5z//OczmRtjtvtavstVbWFiIggLpLyUlpd/9+P/v+VhGqqKmg8GgByDC\n7XYi1OxywofciU2lUitWr15vgF5viBmrNxRIjImw4u8uHwj/KmpyIQrJXS6Lt+hnhUudOuUyqbH4\nI5Pc/pK7VUqy8iXVyYTzoqrX65GdnR1S0wHJXW4JEOiurk50dHT2eNyJ69evh+QuT01NCXCJ92d1\nazQav4I7ke1hzHEczp37CgcOHEBzcxMAIDMzE9nZ49DV1Yk9e/YEvD43NxcLFixUxHfSpElPbbH6\nT01iGJVSshQI3u4zWHa5by63HC5ivAVepGIsgqDrlVE/GvG3eiXLV0qyGikhmb4gMSaixmCqqAHS\njzA11YjHjzuj3nQk0OrlvO7mnhfCyBWkGAjJXZ7WbzawjCiKsNlsftZ1b0u7s7MTFksXHj58EFIx\nFsldnoqUlFSkpCQrIi4lqaV4l6cgNTV1SMUzgtHd3Y2DBw/g6NGj6O62ApA+B57n0draitbWVhiN\nRsyaNctr8RbAZCpAcnJyWPbvjygCarUkwqEIe+9zVvTWKQi2baluucfjgNstTwHrr5KaChqNekR4\nowKtXj10Oq1S6CQWb8ifBhJjYsSgUqmg0+lCqrkrC7V/dm5fTUd6tj4MdoHieb7XvF5g+KzeaMIw\nDBITE5GYmIhnnunbXS53O3K5XEHi2h1K0prF0oXOzk50dXXh3r17A+7fYDAoAp2aKjU/SU1N9f73\nF+4UJCQkKp87z/O4ffs2Llz4GmfOnMHDhw96uYfHjx+vuJoLCwvxzDPPwGDQgWX7LxDzNKjVkvt0\nuM4P/7nX8j76KsbS213uH8vuvxhLJMRP/j3KcV6dTge93jjird5QIDEmRiUMw0Cj0Xhdgf1bWj2b\njsg1j6WKTyw4zpdk5B8PHC3i+7QYDAbk5OQgJyfHr6AN3+dNjcXS5Y1vd6GrSxJp6XmnV7il59ev\nBzZDCIY8BUiq0OXuJTbp6emYNWs2Zs2ahVmzZiE1dWDPwNMinxvylJlYIngVNV/iZTjc5XJDkoF+\nH/LvTqNRQ6ORrN6cnHTY7cHPndHOsPczbm3tHvhVMU5mZiLoOGKD4TgGlvXA6XSCZT3gOFaJl/Zl\nCfSuliaXORW9d/a+zkmSq9yHfJEJZw/daOF/DP5T5MLVtlByl3ejq6sLbW3taG5uQnNzM+7du4sn\nT1rhdDoGvc2kpKReFnZ6ehoSE5P83OiS63yw7nJ56ox/PDiSRPuc8gm3z1qXG4zI571KxShzevV6\nI+LjE5Ta2sDouEYBQGZmYuz1MyaIWEIQBG+7PalXL8t6eiUUDeSO87nsQktSk2PZUqU0SbR1Og04\nTvQKuC/GLb0+eNvEWEMURXg8Hm+VLJnwjLmjo0OZVtTY2IDm5ma43W5lfXx8PMaPz0VHRwdcLicY\nhsHChQuxYsVKpKdnBLjGpb/OAGv83r27A47BaDT6CXdKgFAHus1TkJSUAr1e26tH9Vii5zkrCbMI\nhpHyQiRPlVaZxud0OuB02uEv2i5XArq73WHt0T1SIDEmRi1ykpVs9UqWL6fEhmWG88ctXaDU3gQU\n3/LERANUKlev8faety2JtH/xFZ94w8+FGDnh9pVodQ/YjCMUWJbFzZs3vOLbiIaGBjx50qKsV6lU\nyMvLQ2FhITIysnDz5g1cunQRDx8+QFxcHLZu3YaNGzeFlFUuw3EcLBYLurq60N1tQVtbe5/CbTab\nB6yiptFolBh3sGxy/2lhycnJo66+tHweygmZarXkou/rt9VXMxD5Brn39vvq0a3yush9Pbolt7dW\nEe5Yv6mVGV1nBDGmEQQBTqdDEV6Ph4UoDs7qjSaBcbj+E1Z8wvx07vLBIMeDpUYHzJCtwLa2tl5W\nr/9UqqSkJMybNx8FBQUoLCzCtGnT0NjYgIMHD+D48eMAgHHjxmHz5i1Ys2Yt4uIGTujriUajURp9\naLXqfhO4BEHwyy7vhNVqgdVqhcVi7ZFt3om7d++iubn/2uUMwyApKQmpqWlIS0v1irT/40Ahj8Ue\n3bJLXq3WQKNRQ62WLNfhS1IL3qM72M2g7I2SuuMFtvOUH8uJafKNg2R1q6Mq3CTGxIhEvot2uZxg\nWbeSeOUvvD0t4NFEoHCH7i6XS07K7nL5v2Rt+577xJvxzgP3b04R+gXL4/Hgxo3rShnJhoYGtLW1\nKetVKhUmT873Cq+U4ZyTMx4Mw8DtduOLLz7Hz3/+U9y5cwcAUFJSgs2bt2LBggURq1alUqmQmJiI\nlJRkTJ06rV+rVnK/Or0u8k6lYpo8j7urq9NbpKUTbW2tuH371oD7j4uL62FtB4q1/DduXBY0Gv2w\nTOMbjNUbbWRvlD9ynkdP5Jta+XyXXOqM18pWewuz+CxwOSl0ONzlJMbEiEC2egEXWlu74PFIFpr/\nBTlWLw6xgHyB0ukGFjC5N7LDYffGaUXlYuS7cPmyyuWLtSiKaG+XrF7Z5Xz9+nVwnM/qTUlJwYIF\nC1wWhrwAACAASURBVFBYWISCggJMmzYdRqMxYP8dHR04evRjHDt2DFarBWq1GitWrMSWLVsxbdq0\nMH4qAyO3z9NotCGdXwzDIC4uDnFxccjNzR3w9SzLKmIdOJ+7s8dfBx49ehTQfjEYWq1OSU4LbnX7\nHicnJwe9oelp9cou35Hi7h0MwdzlUrEhDkDvTH45XOR/M+yb/iWJuEajQWZm4qDHQmJMxBxyYpDb\nLcd6fVavIBjBsiwYBlTHdxiQp3V5PNJn3P/8Th719WbU11/ztg2sR3u7z+pVq9XIz5+CwsICpYbz\nuHHj+pybffPmDRw8eBBnzpwBx7FISEjA9u07sGHDRmRkZAzH4fbLcM8PBqTPNysrC1lZWQO+VhAE\nWK3WXla3LN5Wq9y/uxO3b99CU5O53+0xDIPk5GSvQKd5u4ZlICMjExkZGb06icWiuzzS9Lwhk+sZ\nhKO+OokxEXV4nlcynDmOhcfjUaruyJDVO7x4PG643S4/V3/gelEU8fjxI9TX16Ou7hrq6+t7zQNO\nT0/H0qXLlJ6906ebek0Pki1pOZbN8zy++eYSDhyowtWrVwEAubkTsHnzZqV1oWx1D7dl5puaJFnC\nsYZKpVKyuYHJvdb7T22S3eVSzXLJuva5zH1Jah0dHWhtbcWtWzcH3L/co9tfoOWe3T2fD9Sjm+gN\niTERUSSr1+2N9bLeWs5cQOWrYDEfIvxIhTJc8HjcSpEO+TtwOp0wmxsDxLezs0N5r0ajgclkQmFh\nkbdfbwmysrIGvADL+3A63Thx4lPs31+pVOWaPXsOKiq2Y/78BVCpfC5xyW3oP/VLVBqM+E8H8xfs\nwQiBJMIMNBpdSDXVRwIMw8BoNGLChAnIy8vzxnq10OmCW/putzugR3dHR0evHt3y49B7dKcp4iwL\ntSzk/stSUlLoZhskxsQwI1m9Dng8HmXaQm+rl4Q3kgiC7ImQppCIoogHDx6gvr4O9fV1qKu7hhs3\nbgbEJzMzs7B8+QrF6p02bTqSkxMGXWTiyZMn3nrRR9Dd3Q2tVot169ajvLwCU6ZMDXitnCymVg8c\nkpCLF/l3A/MJty/O7S/koshAo1EjLi4OLNu/uIwE5AYqvgxhbcgZwnq9Hjk545GTM37A1wbr0S2J\ndzva29v9xDvUHt0qpKamIj09HZmZmUhOTvWKdVov6zs1NS2ktq8jERJjImzIJQk9HpdXfD3eNnlk\n9cYCcjzYYumC2WxGXZ0c662DxWJRXqfValFYWIji4mIUFUl/ocQ0+6OxsRFVVfvwxRefg+d5pKSk\n4I033sKmTZtDal4xEPL5JYn2wOeXVAFKD0EQYTRqYLO5Bsgu772vaBKY4Sxl96alJcJu7z1HN9z0\n7NE90DhtNptiafsE3CfY8rKHDx+iqalpwG0mJib1EGvZ2s7osSwDcXFxMfF9hQKJMTFkeJ73zuuV\nq1mxStxNhqze6CIIAm7cuI4rV36La9dqUVdXh1u3bga4GbOzx2H27DkoLi5BUVERpk6dFhbrg+d5\nnD9/DpWV+1BbWwMAmDRpMioqtmP16jURTQgSRVHpDuZffhEA4uIM4Pm+3aSyde3rze0T6Z7iLc3z\nDn8xFnn8vqlFWqUGtEwsunr9m47k5eUN+HqdjsGdOw/8XOU+S7u9vV1pQNLe3o47d24HaXwRiMFg\nQGpqmiLekmAHustTU6X/ycnJUf0MSYyJkJDji263Wymq0TPOOBJKOI52bDYbrl2rRXX1VVRXX8G1\na7WwWq3Kep1Oh+LiEhQXS3HewsKisGcq2+12HD9+DAcOVOHRo0cAgPnzF6CiYjvmzHk2wueICLVa\nC4PBMOSmDcNRjEV2p/fcj7wNyerVKGUkhzurO1YYrLu8q6uzX2tbfm42Nw7oLler1d5qael+se7A\nuLcv1p0a9iYgJMZEUDiOVeKKcvOE3lZv7N2JjyUEQcDt27dQU1Ot/N24cT3AWsjJycG8efMVd/PU\nqVOHrRTjo0ePcOBAFY4fPwa73Q6dTocNGzahvLwceXmThmWf/aHV6mAwGCM6BW6wxVgEgQfH8VCr\nVUp1KLmgRs8e3b4Y/vD06B5pqNVqpKdnID194JtJURTR3d3tl4jW1sv6lixvKUFtoGlhgFQpzt81\nLlvaGRmZKCv7y0EfD3VtCoFR1Ekk6HH4rF5fy0CO42KyrmtiogHd3a6BXxjjDOU4rFaL1+qtRm1t\nNWpra9Hd7bN6DQYDTKaCgFhvOOKxfWEwaOF0elBXdw2Vlfvw1VdfQhAEpKenY/PmrdiwYaN3Gk7k\nYBgGWq0eRqMx5HM3UueUbDXLgqvVaqHXG6DXG0K6sR2oR3dioh6dnbaQe3THIrHy+5anhfW0tHta\n33IP7546KooidW0iBsbf6pXbBkp1XH0XBCqoEV14nsfNmzcUi7e2tho3bwbOBZ048RksXrwEBQUF\nKCgowJQpw2f19oTjOJw6dQYffPABGhoaAADTpk1DRcV2rFixKsLN4EWoVGro9XrodIaYER4pLs9A\nq5VivBqNDkZj3JA/m4F6dGdmJkKvl262e/bo5nneK9C+7mGyK53nfbFuuZbzWMdoNCI3NzekKmoc\nx3nncUsC3d09NMONxHiUI4qiUlDD47Girc0CQeB7ZDirehV5ICKLxdKFmpoa1NRcRU1NDa5dq4Hd\nblfWx8XFYd68+SgtnYGysjJMn25CXJzRr150ZOju7sbRo0dw4MABtLY+AcMwWLRoMcrLt2PmzJkR\nHYsoiop1Ge743VDGIk/Z02p10Ol0SrJYNMI5/rWkdbqBE+Vk4eY4zntzLiesCb3c5XInMXKXS0jl\nLzORmZkJgCpwEV5YloXT6QDHeZQMZ0DuwWvwPiarN5rwPI+GhgZcvPgtqquvoqamGnfu3A54zaRJ\nk7Fq1QyUlc1AaWkZpk6dBoaB0g4SCCxyMdzcv38f+/dX4pNPPoHL5YTBYER5eTk2b96KCRMmRmQM\n/uh0Ujw4WueydBMEaDRaRXz1emOEPQLhQ7o+6EK6qZEFWmqjyfVIVhMCno9Ud3k0IDEewQiCoMR6\n5YIaPa1eSrKKPh0dHaitrVYs32vXauF0OpX1CQkJWLDgOZSVyeJbiuRkX6yVZT1wOu3emtyRtTyv\nXr2Kqqp9+Prr8xBFEVlZWXjzzTfx4osbkJmZNuiiH08zFpVKBZ1OD4Mh9HhwuPYtioI3s1kPnU4b\nlXHECnJzhFBCIj3d5U+e3EdT03vQ668D0MDtLkB+/lbExycr5VF5nh+T7nIS4xGEbPXKcV5/q1eG\nrN7ownEcmpubUF19FbW1kvjK5R5l8vOn4Nln56CgoBhlZTORn58ftAC9VC/a7e0gEzl3IMuy+Pzz\n06is3Ifr16XevIWFhaio2IGlS5dFLC4NyPNrNd54cPjbAwYjmNVrMBhjsl51rOPvLnc6Hbh+/S3s\n2lXn94qjeP/9U1i8+DgSEhKRlhaHlpYuxV0uZ5H3tLjl7kn+87lH+o3RoH9VJpNJC+DXAPIA6AH8\nrdls/jjcAxvrBLd6hYCTjqze6NPe3qZkN9fUVKOurg4ul8/qTUxMwqJFi72x3hkoKSlFUlJSn1mj\nUoF/h7dsqK+ncCTo6urCxx8fwaFDB9De3g6VSoVly5ajomI7iotLIj4/WKPRwWAwDKsIyrFRKTlK\nB51OikHLn3nPRhfE0Ll48V/wyit1vZa/8ko19u79Kdau/ZHSKWto7nIe/klpohjoOo914R7KLe5O\nAK1ms/k1k8mUCuAqABLjp0RyRToDrF45ziJD4htdWJZFU5MZNTXViuX74MF9ZT3DMP9/e+8dHtWV\nJfr+KqqyyMkEWYRDkkTGZAMGA8bYZCMJudtutzvPm56Znrk97/bM6zuh7zfhTs+dmX5ze9rdBokk\nwGRjDMbGYIwxGEkEH5IJBhMEQqlynXP/OKqShESQkE5VSfv3ff6Mzq6wdu2qs/baKzFgwEAyMjJj\nR85paU8/1rpFO1dF/cF6cvnyJTZuLOS993YTDAZxOBwsW7achQsX07NnT93lsVis2O2t4w+Obmi1\n6GbtuLl3767cu6dtjC5dOoUs/x0dO36GwQBlZSNJT/8zBgwY2+KytDdstrM0lqRhNoPV+mWTX685\nx+VRxR2NLo8GqUWjy7Xr0cpq6Jre2RxlXAhsrPm3kcY6MAseiqIosQhnYfUmLrdu3aKkpChm+Z4+\nfYpAIBAbT01NZcqUaWRmZpKZOYJhw4bjcrma9B6hUBC/308kEkIvCxi0m9OxY5+zYcN6PvvsCKAV\nCFm0aAnz5r2A0+nUVRYt6lcLgmrJEpLR145aW1peb/3jbi3oys+9e3e5dOlVcnPr1kfezfbtX+Jy\n7aBHj74tIld7JRh88G8jFHK36nvXPS5/VBXW6PcmelQeiYR1OS5vdtEPSZLcwFbg/8iyvO5B82rW\ni7chNN9fkOrq6pomCkGCwWBCFtRozwQCAc6cOcMXX3zB8ePHOXHiBNevX4+NG41GBg8ezIgRIxgx\nYgSjRo0iLS2tWWsY7TXr8/lixVX0IhAI8N5777F+/XouXLgAQFZWFq+88gpTp07VNb9cURQsFgt2\nux2b7cnzg7XAH2ONUk8hJSUFl8v12HPasuUXvPji/2hgvakqbN78xyxe/M9PJF9759ixvbjdLzFo\nkLfe9dOnnYRC75KVNSVOkj0ZUYs62pnOYDCQmpqqT9EPSZL6AJuBf3+IIgZo05WrGkNRlJjPLxQK\nEgyGavIP42/pJkp1myehpeZw48Y39fJ6z5w5Va92bceOnXj22ekxX++wYcNwOOpbi1VVgftf9qFo\nJyJaO8m6jeAh8tDntQR3795l69YtbN36Dvfu3cNkMvHcc7NYsmQZgwcPBiAUUprUSrD+HJqCWmOl\nOjGbzYTDTf8sayOczbEgK7vdXS/IKxiEu3e9j3il2t93MCg3eoxqMICinE34e1miVwrs23c8+/b9\nGVev/obp028BsG9fd8rKfsz06SO4fbsy4efwaJq/mW1OAFd3YA/wA1mW9zf7ndsAqqrGjhmjnYvC\n4fB9zRPq+30F+hMIBDh9+lQsurm4uJhbt27Gxk0mE5I0uMbXO4KsrCyeeqp3i51cRFsXBoMh3Yur\nXLhwnsLCDezbt5dQKITb7SY7O4eXX170xG0Rm0Nz84OjKXvRMpLa6zha1JIPhR5cOjQYfHS7QMGj\nmTnzTygtXcm6dWsBGD06hxEjWrZRSbLSHMv450Aq8AtJkn5Rc22uLMvJbXI9BlGrt9bXG0JVI/Vu\nLIlgAbdnVFXl+vXrMV9vcfEJZPlLwuHa0IbOnTszffpMMjOzyMoawZAhQ7Hb7S0ui5aa5CcSiaYm\ntfhbNIqiKBw58imFhRs4fvwYAH369GHJkqXMnj2nVeb6IB7WuvBhz1FVpab0Y7Sghq3VU5sGDvw2\nBw9uZPLk0nrXT5zw0Lt3dqu9b3ujS5duzJr1R/EWI+FosjKWZfmPgDb/SUbzPP1+H+FwFaWl5YTD\nofvKSILBIPJ644nP5+PMmdP18npLS2tvpmazmcGDh8TKSGZmjqBXr16tdlOPNt0IBgOxlBm9ArN8\nPh979uxm48aNXL16BYBRo0axZMkynnlmgq4bRVVVMZvNMSX6MKJWr9VqjUU42+0O3Te2Tz89hM8+\n+3s2bvxHZs/Wjqzff78/8CMmTZqoqyyC9oco+lGDllrijTnhtTxPrdas0WhDURRRUCPOqKrK5cuX\nOXz4KMXFmvI9e1auZ/V27dqN556bRWbmCDIyMhkyZKguuaKKEok134iiV4De7du3eeedTWzfvo3K\nykosFgtz5sxlyZJlDBgwQBcZoqgqNbm69kZTTqKRp1qPXkuN79iO1ZoY/XrHjVtOMLiQfft2oChh\nxo59UdeTBEH7pV0q49rqRv5Y56JIJHyf1WsQVm+c8XqrOXXqVKxrUXFxMXfv3omNWywWhg4dVlNC\nMousrCx69NA3L7bWHxzUXZnIskxh4Xr27/+ASCRCamoqr776LRYseJnOnfX3cTbmD9YinE1YrZZY\nelE8rN6mYLVamTx5UbzFELQz2oUyjkQiNRHOdX29qigjmUCoqsqVK5djLQOLi4s4d+5sTRs6jR49\nejBv3jyGDs0gMzOLwYOHYLXq360nmq4WDPobBOy1NpFIhE8+OURh4QaKi4sASEtLY8mSZcyaNZuU\nRyVRtiDaaZEx5g+G2hrSUcVrs2nNExLB6hUIEpk2p4w1n12gpoxk1OqN3BfhnJjl0NoTVVVVnDp1\nkuLiE7GiGuXl5bFxq9Uaq2IVtXy7d+8e1/Qs7bulWcH3f6daG6/Xy65dO9m8eWMs/3ncuPEsXbqM\nMWPG6l6q0mg043a7iUTqRjin1FjGiWv1CgSJStIr40gkXFNG8mFWr7g5xBNFUbh8+VIsurmkpJjz\n589Rt+BMr15PMWHCpJjylSQp7j1qoyhKpF7rQtDPH3zjxg02b97Ezp3bqa6uxmq1Mn/+iyxZspS0\ntKd1kQGivl6w2ey43W7sdid9+nTj3j2/2NgKBC1AUinjaKRq3eYJ0QpGwupNHCorKykpKY41Tygp\nKaaioiI2brPZGDVqdCyvNzMzky5dusZR4sYJh0P4/X7C4SB6lqoEOHXqJIWFGzhw4CMURaFTp04s\nX76CBQsW0KFDx1Z97+gmqbaEoBm320Pnzt3qBWVpQVdNK9YhEAgaJ6GVsXYz1I4FteYJwVjx7ih6\nlu8TNERRFC5evBizeIuKTvDVVxfrWb19+vRhypRpZGRkkpU1ggEDBiZsE/a6rQu1oD79UpPC4TAH\nDnxEYeEGzpw5DUD//gNYunQZM2bMbDX/uLZWBkwmIyaTCaPRjNlswmaz43S6cDrdYoMrELQyCaOM\nVVWNNU8IBkOEwwHC4ch9Vq9R9wpGgvqUl9+jpKQkFmR18mQxVVVVsXG73c6YMWNjFm9GRhadOj24\nslGiUPf7d3/TjtamsrKSnTt38M47m7h58yYGg4GJEyexdOkyRowY2aJy1Fq9xhrla65JM9JSixRF\nwWaz4XR6Ejal59q1S1y7JjNgwGg6dRLVmwRtg7gp41AoFAuGibYNFFZvYhGJRLhw4Xy9COdLl76q\n95h+/dJi1awyM7Po33+Ars3nn5R4+oOvXbvGpk2F7Nq1C7/fh81m4+WXF7FkyRJ69+7TIu8RVb4m\nkzmmfC0WCyaTucFjNH9wasKeWpSX3+XAgR8zbNiHPPNMJSdOdOfQoReYO/cfk+o7JxA0hi7fYEVR\nYlWJoso3WnVHWL2JQ1lZWZ36zUWcPFmC11tbaN/pdDJ+/IRYJauMjEw6dOgQR4mbTygUrIk9COv6\nvVNVlaKiE2zevJGPP/4YVVXp0qUrr776KvPnL8Dtbn4rubpWr9lswmg0YTZbHphaFC1q43S6cLtT\nEz7Q8aOPfsBrr+2KrdfMmTfx+d6isNDB3Ll/F1/hBIInpFWV8e3bt7l5826sG47I600cwuEw58+f\nq2f1Xrlyud5j0tPTY0o3K2sETz+dntSnFXX9wYqib73oUCjE/v0fUFi4nnPnzgEwePAQli5dxrRp\nzzbLstN6qILRaI71arVYrI9cI611obXGH+xKCn/wpUsyI0YcaLBedju4XO8SDP51XHLOBYKWolWV\nsdfrjfUYFcSXu3fv8Omnp/nss88pKiri1KmT+P2+2LjL5WbixEmxSlbDh2fg8aTGUeKWQ+sf7K0J\nAIwGlumjgMrLy9m+fSvvvLOZO3fuYDQamTp1Gjk52QwaNOSxFaEmt4rBYKqxes2xkpKP+xqaP9iO\n2+2JFelIFr7++iSzZ1c1Otat2y0qKiro0kX4jwXJi3C0tEFCoRBnz8r1rN5r176OjRsMBvr3HxCz\neDMzs0hLe7rNbZq0euP1/cF6cfnyZTZtKuS993YTCARwOBwsXbqMRYsW07Nnr0f2Aq5r9UaVr+br\nbdrJRPR17HYnbrcHs/nh/uCLF4s4e/Y/sdsvEAp1wG5fwKRJOU16z9agf/+xFBV1ZOLEsgZj33zT\nm/79k9NdIhBEEcq4DXD79u2Yn7e4uIjTp08RCNTmf3o8HiZNmsLYsaORpGEMH57xRL7JRCfaY1rr\nsqXfEayqqhw79jmFhRs4cuRTAHr27MmiRUuYN+8FnE7nA58HdX29ZiwWM2Zz88tIKorWgtDhcOJy\neR5royXLhwkGX2flytqN2/Xre3nvvfM8//xfNUuOlqJnz75s2zaLsWM3UDe+7M4dA6HQQhHAJUh6\nxDc4yQiFgnz55Zd1rN4TfPPNN7Fxo9HIgAED65WS7NcvDYPBENdSkq2N5g/21/iDtXrWeiniQCDA\nvn172bhxAxcvXgRg+PAMli1bzqRJkxtYs6qqyacFWJlqIpytLXIyoSgKVqsVp9ODw+EgEolw6NAa\nQqHPiUSc9O+fQ3r60Eafe+XKr8nO/rretV69QvTqtZrS0u/TpUu3J5bvSXj++X9nzRoXXbq8T8+e\nt7h8OQ2fbyHPPffncZPpzp2bfPbZr7HbzxCJ2LFYZjNlyqtJ4YcXJBZCGSc4N2/erGf1njlzul6b\nvo4dOzJ16rSYr3fYsIwHWmBtEUVRYvnBenP37l22bt3Ctm1bKCsrw2QyMXPmcyxduozBg4cAtS0D\njcbaghoWi4WOHV1UVbWczKqq+YNdrtRYs4jq6mp2785m+fL9dKwp2nXkyCo++ugvmDbth/c9X8Vu\nL270tZ999hZr125i9uzvt5i8zSElJYV58/4Fr9dLWdldxo3rFtegrZs3r3Ly5HJWrjwZCywrLd3F\n1q1fsGDBr+MmlyA5Eco4gQgGg5w5c7pG+RZTXFzEzZs3YuMmk4lBg6SYrzcjI5M+ffq2y114tHVh\nNFJfTy5evEBh4Qb27n2fUCiEy+VixYocFi5cRNeuXeuUkXyw1dsSaxatnOVwOHC7Uxsc1R448Pe8\n8cZ+6hrm48eXU139z1y//iKnTm3CZDqEwaAQCIzEYGj8duDzQUqK54nlbSkcDgcOhyPeYvDFF//E\nypUn613r0kVh/Pj1nD37LQYNGhknyQTJiFDGcUJVVW7c+KZekNWXX56pp1w6derMs8/OICsri8zM\nEQwdOhS7Pf43oXji9/uprCwnEtFSk/RCURQ+++wIhYUbOHbscwB69+7N4sVLmTv3BVwuZ72CGq25\nQar1B7twuz0PfC+b7TCNxXtNn36bv/zLhfziF+ew1QRVRyJ7+cd/7Ep1Ndx/sPLuu4N45pklLTyL\n5MduL2r0+vDhXtas2S6UsaBJCGWsE36/nzNnTtVYvJrle/v2rdi42WxGkgbX8/X26vVUu7R67yfa\nICQYDGCxGIlEIuiliP1+P++9t5uNGwu5evUKAKNGjeKVV7KZMmUaKSk23aLQNX9wCi6XG4fj0a4I\no7HxKHKDATIzaxUxgMkEP/3pbX75yz786Z9eJTUVFAXee68XHs9/17VPcrKgKI3fPrV4vMSsYiZI\nXIQybgVUVeX69Wsxi7eo6ARnz8qEw+HYY7p27crMmc/FajgPGTIMmy25cj9bG0WJxBqFRDEY9Ck6\ncvv2bd55ZzM7dmyjoqICs9nM/PkLyM3Ni/mD9SDautBut+NyeZqkFH2+EUBD6+34cTMjR4YbXLdY\nYNiwYezd++eEw6cIh1MZPfoNOndOvI5aiYDfP4FI5EiD04ePP+7E8OHZ8RFKkLQIZdwC+HxeTp06\nRUlJEUVFRZSUFHHnzp3YuNlsZsiQoTUWr6Z8e/ToKazeBxD1BweDQd0+o6j/9cKF8xQWrmffvr2E\nw2E6dOjAG2+8ybJlK+jaVT+lpOUHG3A4nHg8qfVqST8uWVl/QmHhZyxZcqZOgJGR7dsH8Fd/9WWj\nzzEYrEydmvckorcbpk37C37726J6AXLHjrm5efOPGTKkX3yFEyQdQhk3EVVVuXr1Sj1f77lzZ2uO\nTjW6d+/BrFnPx2o4Dx48RBzzPQJVVWP1osPhcKt2TYrm9UZTi1QVPv30MGvWFHD8uOYPTk9PJycn\njxdeeFHXEwvNH2zB6XThcj1Z68KePdMwmTaTn/+/sdnOoChOzOZZPPNMHy5efIX09PrH2Pfugck0\n40mn0G5wOBy89NIm9u9fRyh0lHDYTnr6Cp59Nqve4+7cuc3Ro/9OSsolgsHODBjwKv37Z8ZHaEHC\nIpTxI6iurqak5DiffnqUkpIiSkqKKSurrQJktVoZPjwjFt2cmZlF9+494ihxclHXHxyJRFpFCUet\nzGh0s9ms1XD2en1s3foOa9fmc/XqVQAmTJhIbm4eEydO1rlgSK0/2G5vudS0bt2eYs6cXzW4vmPH\nd4hEfsfAgVp61bVrJrZvX8TChd9qsfduD5jNZqZMyQVyGx3/6qsirl79Njk554mGFhw+vIkjR/6O\n8ePFUbagFqGM66CqKpcvX6Ko6ESse9H58+djRSQAevbsxZw5z5CRoQVZDR48GItFFKhvKo37g1sq\n3afW6q1bRjL6+t98c521a9ewefNGqqoqsVqtLFy4mJycPAYMGPDEMjRVVpvNgdvtxmrV7/Rk/vxf\nUVIyj6NHt2E0KqSmzmTRonnCddLCnDv3K3Jyzte7NmHCXTZt+meCwSWiuYUgRrtWxlVVVZw8WUJx\n8QmKioo4ebKY8vLy2LjNZmPEiJGMGTOawYOHkZGRpavfsC0SDodqSlUGedKI6NoyknWtXi2vtzGl\nUlxcRH7+Kvbte59IJELnzp3Jy/sRS5Ysp1OnTk8kS1PlNhgMOJ0uPJ4OcasJnpExlYyMqXF57/aA\n3++nY8fPGx2bNess+/btYPLkRTpLJUhU2o0yVhSFS5e+ikU3l5QUc+HC+TpdfKB37z5MmjSFzMxM\nMjKyGDRIwmKxtOkyknpQt3VhJBKuUZRNV8QPqmb1sLrE4XCYffv2UlCwiuJiLbJ40KBB5OTkMXfu\nC7paJqpa6w9OS+tFaWnjXYgEbYNop63G0PZfjY8J2idtVhlXVJRz8mRJLLq5pKSEysqK2LjNIWBz\nLgAAIABJREFUZmf06DGx6ObMzCw6deocR4nbHqqq1nRNChCJKE3yBz/I6u3UyfNYZSQrKyt5551N\nrF2bH6vdPWXKNFauzGPs2PG6HscqikJKig2Xy4Pdbgf0q5stiB92u52ystHAuw3G3n9/IGPHztdf\nKEHC0iaUcSQS4eLFC7Ho5pKSoljB/ih9+/Zj2rRnYwU1BgwYKDq9tBLN8QdHlW+0jOSDrN5Hvc7V\nq1dYs6aArVs34/V6sdnsLFv2Cjk5K+nXL615E2oG0fnY7VqpSovl8YpAXLok88035xg0aLzI720D\n9O//M7ZulVmw4GIsvezYsQ4YjT8RGRaCeiSlNrp3715M6RYXF3HyZAnV1dWxcYfDwfjxz5CZmUVG\nRhYZGZl0jCYCClqNaGpSKBTmYTqzbstAk8lYY/VasFia1zJQVVW++OI4q1e/zYcffoCqqnTr1p03\n3niTRYuWkJqqX69bVVUwGk04HC48ntTH9geXlt7g8OGfMGLEx0ydWs3x49345JP5zJv3T03uYSxo\nHteufcWpU7txu3sxbtz8Fvnc+/cfjcu1k/z832CzaalN/frlMnHi2BaQWNCWSHhlHA6HOX/+HCUl\nxTFf7+XLl+o95umn02NpRVlZI0hP7y9uYDpR1x+sKFq96Pv1abTBvdFojinfaA3nJyEUCrJnzx4K\nClZx+vQpAIYOHUZubh6zZj3/2NZoS6D5g604nS6cTleTNxWffPJDXnvt/dhnN2PGLbzet9i0KZU5\nc/6/VpBYEEVRFLZt+zHDhm0lO/sed+7A7t0jSE//BwYOHB97XG07yoOoqhGHYyYTJix+5Fp37/4U\nc+b8TWtPQ5DkJJwyvnv3bp2uRSc4deokPp8vNu5yuZgwYWKsZeDw4Rm6Wj4CDVVV8fk0f3BtEJwh\nFrRiMERTi0xPZPU2Rnn5PTZuLGTdujXcvn0Lo9HIzJnPkZubx4gRo3T2B6vYbDZcLjc2m71Zr/Hl\nl8eZOPFgg02MwwE22y4U5a/iFnHdHti+/W9YvvxtXC7t7y5dIDf3BGvW/JS0tA+xWCyEw2G2bv0W\ny5dvi1XbunlzDe+8s5eFC38jYgAET0xclXEoFOL8+XMUFZ2IHTtHiy+A5h9MT+8f8/NmZGSRnp4u\nbkxxJBKJ1ARlaf7g+lav5u+1WKytcjJx6dJXbNiwhs2bN+P3+3E6neT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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice here that if we want to maximize this width, the middle fit is clearly the best.\n", "This is the intuition of **support vector machines**, which optimize a linear discriminant model in conjunction with a **margin** representing the perpendicular distance between the datasets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fitting a Support Vector Machine\n", "\n", "Now we'll fit a Support Vector Machine Classifier to these points. While the mathematical details of the likelihood model are interesting, we'll let you read about those elsewhere. Instead, we'll just treat the scikit-learn algorithm as a black box which accomplishes the above task." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.svm import SVC # \"Support Vector Classifier\"\n", "clf = SVC(kernel='linear')\n", "clf.fit(X, y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.0,\n", " kernel='linear', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False)" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_svc_decision_function(clf, ax=None):\n", " \"\"\"Plot the decision function for a 2D SVC\"\"\"\n", " if ax is None:\n", " ax = plt.gca()\n", " x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n", " y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n", " Y, X = np.meshgrid(y, x)\n", " P = np.zeros_like(X)\n", " for i, xi in enumerate(x):\n", " for j, yj in enumerate(y):\n", " P[i, j] = clf.decision_function([xi, yj])\n", " return ax.contour(X, Y, P, colors='k',\n", " levels=[-1, 0, 1], alpha=0.5,\n", " linestyles=['--', '-', '--'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YZKUpSrFoNBpMmjRF1k7UkjDhEoWI6tIUi8WimLS2bNmIsrIy38Lw1Qn0W9/6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\nVbKVJODePQ1u376K8vI1ePH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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the dashed lines touch a couple of the points: these points are the pivotal pieces of this fit, and are known as the *support vectors* (giving the algorithm its name).\n", "In scikit-learn, these are stored in the ``support_vectors_`` attribute of the classifier:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf)\n", "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Nt9uluVKQ0+nkL3/5o6rdYDBoJlyz2UzXrt2wWCz+khSTyYTFop30TCYTL7zw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\n7FFnKaFo26SHK0SEOXp0GzdvbsDr1ZO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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use IPython's ``interact`` functionality to explore how the distribution of points affects the support vectors and the discriminative fit.\n", "(This is only available in IPython 2.0+, and will not work in a static view)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.html.widgets import interact\n", "\n", "def plot_svm(N):\n", " X, y = make_blobs(n_samples=200, centers=2,\n", " random_state=0, cluster_std=0.60)\n", " X = X[:N]\n", " y = y[:N]\n", " clf = SVC(kernel='linear')\n", " clf.fit(X, y)\n", " plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", " plt.xlim(-1, 4)\n", " plt.ylim(-1, 6)\n", " plot_svc_decision_function(clf, plt.gca())\n", " plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none')\n", " \n", "interact(plot_svm, N=[10, 200], kernel='linear');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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G2hn9w/Ek6bRB2X5n1+2Z7pzee5r8qny/5euGfcSsJU8EfXszfzGPFbEfkLgtjtSyVG5m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\nODhUUVbWlwED3qJjRyu1FZvQ5MnvceJEAikp3+DoqMNkGsCkSYvRas2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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the unique thing about SVM is that only the support vectors matter: that is, if you moved any of the other points without letting them cross the decision boundaries, they would have no effect on the classification results!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Going further: Kernel Methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where SVM gets incredibly exciting is when it is used in conjunction with *kernels*.\n", "To motivate the need for kernels, let's look at some data which is not linearly separable:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets.samples_generator import make_circles\n", "X, y = make_circles(100, factor=.1, noise=.1)\n", "\n", "clf = SVC(kernel='linear').fit(X, y)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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DGYd18fHJXLqUzMiRpc/m5s2z7N9vZNiw1+r82hqNhvz8Bdy+/XsiI8s2srh2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\nW1uL4ycm807Oi6YNCw7jrvXfZM3DLzLvBwuTWDo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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, no linear discrimination will ever separate these data.\n", "One way we can adjust this is to apply a **kernel**, which is some functional transformation of the input data.\n", "\n", "For example, one simple model we could use is a **radial basis function**" ] }, { "cell_type": "code", "collapsed": false, "input": [ "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot this along with our data, we can see the effect of it:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits import mplot3d\n", "\n", "def plot_3D(elev=30, azim=30):\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='spring')\n", " ax.view_init(elev=elev, azim=azim)\n", " ax.set_xlabel('x')\n", " ax.set_ylabel('y')\n", " ax.set_zlabel('r')\n", "\n", "interact(plot_3D, elev=[-90, 90], azip=(-180, 180));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EYDCIefNuQENDI2bNmgXB3PWgzNiVuwBIE9B8my9kLneh+AeqADS5hwH61uMWNS+Y0WgE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\nlYXA4EboE6AbojUXU6pJ2dBMHQDqfKi0rQxVD6Tw5GpuKiic8zuH0N6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Tk5HUJDQ98G4JOTk7Oh+ueJACQATuTk5Mx15joJBHtBDCaBQCAQCCZAQrIEAoFAIJgAMZgEAoFA\nIJgAMZgEAoFAIJgAMZgEAoFAIJgAMZgEAoFAIJjA/wOWCgjH3HbEOQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that with this additional dimension, the data becomes trivially linearly separable!\n", "This is a relatively simple kernel; SVM has a more sophisticated version of this kernel built-in to the process. This is accomplished by using ``kernel='rbf'``, short for *radial basis function*:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "clf = SVC(kernel='rbf')\n", "clf.fit(X, y)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf)\n", "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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PjCElZSUvvLCMhob6flX9zs4ugx7f0dHxwNoGmebBU4EqNGIUqWBaIjELAnDmzCna29uZ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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here there are effectively $N$ basis functions: one centered at each point! Through a clever mathematical trick, this computation proceeds very efficiently using the \"Kernel Trick\", without actually constructing the matrix of kernel evaluations.\n", "\n", "We'll come back to SVMs in the breakout session following this lecture." ] } ], "metadata": {} } ] }