{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#Maximum Margin Classifiers - The Support Vector Machine" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Given a labeled scatter plot, such as the one below, the best way to classify points of different classes is to find a hyper-plane (straight line in the 2-d case) that separates the two classes.
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[The issue with looking for just any separating line is that an infinite number of lines might qualify, even if the space between classes is quite small. The following shows the same data above along with many qualifying lines.
" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 1)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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taJGxjc0DtGlT9XGy9nd1OaTmPny9RsXCPFCdXkcxT8lXRO6PpmxPjsMAfCVm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\n90ttV7BAuxK/bcQHJKKoYgz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"text/plain": [ "With so many hyperplane options, we need a principled way to choose an optimal separating line. Intuitively, we want a line that is simultaneously as far away from the positive instances as it is from the negative instances. In a sense, we want it to be in the middle of the empty region separating the classes. We can formalize this by searching for a hyperplane that maximizes the margin between the positive and negative classes.
\n",
"\n",
"Some Definitions\n",
"
\n",
"\n",
"With perfectly separable data, we then define the following objective function.
\n",
"\n",
"
In the above we plot the optimal linear hyper-plane $W$ and also the hyper-planes that define the margin. Circled are the support vectors.
\n",
"\n",
"Once we have found $W$ and $t$, classification of a point $X$ is defined as:
\n",
"
Let $\\xi_i = [\\xi_i]_+ = [1- y_i(W\\cdot X_i+t)]_+$ be the distance between a wrongly classified point $X$ and the optimal margin plane $y_i(W\\cdot X_i+t)=1$, where $[1-z]_+ = max(0,1-z)$. This last function is also known as the hinge function. We can then redefine our optimization problem to allow for some misclassification of our training points. Specifically,:
\n",
"\n",
"
When we presented the soft margin version of the SVM, we also introduced a new term $C$ which controls the amount of error we can tolerate (or conversely, the size of the margin). $C$ is thus a free parameter that we must choose to get the right fit. One way to think about it is as $C$ increases we increase the size of the 2nd term in our optimization function. This means we become less tolerant of training errors (and we thus decrease the size of the margin).\n", "\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Llai9Bw8ewNjYG0Dpi1x9+/ZF3759MWvWh9vY06dPY9CgQVIdB7sYGk+78mLV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\nyczMpF27dpQpU4ZNmzbRq1cvhg8f/o9t/fXXX7Rq1Qo/P78CltCLwus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69es4OTk9SOT3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\nSUVORK5CYII=\n", "text/plain": [ "As we increase $C$, we can see that the norm of $W$ increases and the number of support vectors identified shrinks. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#SVM vs. Logistic Regression\n", "\n", "Both SVM and Logistic Regression finds linear separating hyper-planes of the form $class(X)=f(W\\cdot X+t)$.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "We can see that the two classifiers behave very similarly when just looking for a linear decision boundary. The choice of which classifier to use is usually determined by comfort and familiarity as well as the need to exploit the specific properties of each.
\n",
"\n",
"