210 lines
40 KiB
Text
210 lines
40 KiB
Text
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Support Vector Machines"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 61,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn.svm import SVC"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 62,
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"metadata": {},
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"outputs": [],
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"source": [
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"X = np.array([[ 0.46613554, 0.92048757],\n",
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" [-0.92129195, 0.06723639],\n",
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" [-0.15836636, 0.00430243],\n",
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" [-0.24055905, -0.87032292],\n",
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" [ 0.06245105, -0.53698416],\n",
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" [-0.2265037 , -0.43835751],\n",
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" [-0.00480479, -0.17372081],\n",
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" [-0.1525277 , -0.34399658],\n",
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" [-0.27360329, 0.35339202],\n",
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" [-0.77464508, -0.48715511],\n",
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" [-0.58724291, 0.74419972],\n",
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" [-0.97596949, -0.72172963],\n",
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" [ 0.42376225, -0.72655597],\n",
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" [ 0.96383922, -0.23371331],\n",
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" [ 0.16264643, -0.46949742],\n",
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" [-0.74294705, -0.42576417],\n",
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" [ 0.05089437, -0.20522071],\n",
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" [-0.19442744, 0.09617478],\n",
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" [-0.97102743, 0.79663992],\n",
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" [ 0.0596995 , -0.70129219],\n",
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" [-0.83934851, -0.95616033],\n",
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" [-0.38249705, 0.4973605 ],\n",
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" [ 0.3474666 , 0.70664397],\n",
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" [ 0.35871444, 0.88679345],\n",
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" [-0.05914582, 0.23124686],\n",
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" [-0.52156643, 0.32986941],\n",
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" [-0.53579646, 0.67530208],\n",
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" [ 0.13683914, -0.96158184],\n",
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" [ 0.65904541, -0.12015303],\n",
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" [-0.69078363, 0.5615536 ],\n",
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" [ 0.47738323, -0.70919275],\n",
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" [ 0.93069669, 0.44019132],\n",
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" [ 0.19750088, -0.68869404],\n",
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" [-0.75048675, -0.18170522],\n",
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" [-0.45288395, -0.25894991],\n",
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" [-0.74644547, 0.87781953],\n",
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" [ 0.14620452, 0.56864508],\n",
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" [ 0.25719272, -0.58405476],\n",
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" [ 0.87149524, 0.01384224],\n",
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" [-0.71473576, 0.31568314],\n",
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" [-0.252637 , -0.67418371],\n",
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" [ 0.24718308, 0.95191416],\n",
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" [-0.38149953, -0.64066291],\n",
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" [-0.23112698, 0.04678807],\n",
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" [ 0.72631766, 0.7390158 ],\n",
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" [-0.91748062, -0.15131021],\n",
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" [ 0.74957917, 0.66966866],\n",
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" [ 0.76771849, 0.06662777],\n",
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" [-0.04233756, -0.91320835],\n",
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" [ 0.63840333, 0.06277738],\n",
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" [-0.78887281, -0.90311183],\n",
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" [-0.73099834, -0.69587363],\n",
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" [-0.50947652, -0.99144951],\n",
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" [ 0.14294609, 0.5474932 ],\n",
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" [ 0.4367906 , 0.31953258],\n",
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" [-0.13970851, 0.81817884],\n",
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" [ 0.6440873 , 0.79118775],\n",
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" [ 0.41714043, -0.66672029],\n",
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" [ 0.59283022, -0.71836746],\n",
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" [ 0.55379696, 0.98846202],\n",
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" [-0.91819517, 0.34203895],\n",
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" [ 0.02020188, 0.83696694],\n",
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" [ 0.6182918 , 0.04254014],\n",
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" [-0.09354765, -0.30050483],\n",
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" [-0.08489545, 0.06431463],\n",
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" [-0.11886358, -0.68738895],\n",
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" [ 0.44428375, 0.18273761],\n",
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" [ 0.26486362, -0.98398013],\n",
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" [ 0.13222452, 0.91495035],\n",
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" [-0.11101656, 0.00541343],\n",
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" [-0.07696178, -0.92720555],\n",
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" [ 0.22602214, 0.56040092],\n",
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" [ 0.74227542, 0.32930104],\n",
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" [ 0.43524657, 0.35332933],\n",
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" [-0.89277607, -0.59996171],\n",
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" [-0.94836212, 0.78777302],\n",
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" [ 0.1783319 , -0.2142071 ],\n",
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" [-0.07832238, -0.25046584],\n",
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" [ 0.17611799, -0.96927832],\n",
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" [-0.95938454, -0.26504646],\n",
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" [ 0.58666766, -0.94620881],\n",
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" [-0.77336565, 0.46735057],\n",
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" [-0.94414054, 0.39044333],\n",
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" [ 0.61524645, 0.15907662],\n",
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" [-0.09855302, 0.9816656 ],\n",
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" [ 0.53937097, 0.34487634]])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 63,
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"metadata": {},
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"outputs": [],
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"source": [
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"y = [\"red\" if x + y > 0.3 else \"green\" for [x,y] in X]\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 64,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.collections.PathCollection at 0x10b52ba50>"
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]
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},
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"execution_count": 64,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"text/plain": [
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"<matplotlib.figure.Figure at 0x10b07fad0>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"plt.scatter(X[:,0], X[:,1], c=y)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Exercise\n",
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"\n",
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"- import the support vector machine classifier from scikit-learn (the SVC class) and train a classifier for the examples above using a linear kernel;\n",
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"- read the documentation to find out how to obtain the support vectors and the associated (dual) weights; use this information to analyze the learnt model: \n",
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" - how many support vectors have been learnt? \n",
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" - are them in the position you would have expected [[1](#note1)]? \n",
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" - is there any margin error?\n",
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" - is there any classification error (check it using the classifier predictions)?\n",
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"- learn a new SVC model using custom C values:\n",
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" - how the answers to the questions above change when you use a very high C value (e.g., 1000)?\n",
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" - how the answers to the questions above change when you use a very low C value (e.g., 0.3)?\n",
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"- learn a new SVC model using a rbf kernel:\n",
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" - is the new kernel able to capture the linear model?\n",
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" - are you surprised by the above answer? Regarless to whether you are surprised or not: why?\n",
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" \n",
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"<a name=\"note1\">[1]</a> If you make two plots one after the other (in the same cell), the plots will be merged into a single one. You may want to use this feature to plot the support vectors on top of the scatter plot for the dataset."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
|
||
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"anaconda-cloud": {},
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
|
||
|
|
}
|