{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Support Vector Machines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "New R commands:\n", "- `svm(formula, data = , kernel = , cost = , scale = )` fit an SVM\n", "- `tune(svm, formula, data = ,kernel = , ranges = list(param = )` tune an SVM with cross-validation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the `e1071` library in R to demonstrate the support vector classifier\n", "and the SVM.\n", "\n", "The `e1071` library contains implementations for a number of statistical\n", "learning methods. In particular, the svm() function can be used to fit a\n", "support vector classifier when the argument kernel=\"linear\" is used. This\n", "function uses a slightly different formulation from the slides (or equations (9.14) and (9.25) in the book) for the\n", "support vector classifier. A cost argument allows us to specify the cost of\n", "a violation to the margin. When the cost argument is small, then the margins will be wide and many support vectors will be on the margin or will\n", "violate the margin. When the cost argument is large, then the margins will\n", "be narrow and there will be few support vectors on the margin or violating\n", "the margin.\n", "We now use the svm() function to fit the support vector classifier for a\n", "given value of the cost parameter. Here we demonstrate the use of this\n", "function on a two-dimensional example so that we can plot the resulting\n", "decision boundary. We begin by generating the observations, which belong\n", "to two classes, and checking whether the classes are linearly separable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Support Vector Classifiers" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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WrP3z/y7ofv9an3wE2DZq3FWQAArK41v2K3//UT9v/xrw+8YdiBa2UOAABrypsn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\nAImolPUAgLLnuw9eHfX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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "set.seed(1)\n", "x=matrix(rnorm(20*2), ncol=2)\n", "y=c(rep(-1,10), rep(1,10))\n", "x[y==1,]=x[y==1,] + 1\n", "plot(x, col=(3-y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are not. Next, we fit the support vector classifier. Note that in order\n", "for the svm() function to perform classification (as opposed to SVM-based\n", "regression), we must encode the response as a factor variable. We now\n", "create a data frame with the response coded as a factor." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "dat=data.frame(x=x, y=as.factor(y))\n", "library(e1071)\n", "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=10, scale=FALSE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The argument scale=FALSE tells the svm() function not to scale each feature\n", "to have mean zero or standard deviation one; depending on the application,\n", "one might prefer to use scale=TRUE.\n", "\n", "We can now plot the support vector classifier obtained:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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PixbxOLfkr2Xy+NnrLD2vbpVTvW/fjll3Ojt6+d1FG7pt757O9ZlTs8KgBtBwCA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"text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(svmfit, dat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the two arguments to the plot.svm() function are the output\n", "of the call to svm() , as well as the data used in the call to svm() . The\n", "region of feature space that will be assigned to the −1 class is shown in\n", "light yellow, and the region that will be assigned to the +1 class is shown in\n", "purple. The decision boundary between the two classes is linear (because we\n", "used the argument kernel=\"linear\" ), though due to the way in which the\n", "plotting function is implemented in this library the decision boundary looks\n", "somewhat jagged in the plot. (Note that here the second feature is plotted on the\n", "x-axis and the first feature is plotted on the y-axis, in contrast to the behavior of\n", "the usual plot() function in R.) The support vectors are plotted as crosses\n", "and the remaining observations are plotted as circles; we see here that there\n", "are seven support vectors. We can determine their identities as follows:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 1\n", "\\item 2\n", "\\item 5\n", "\\item 7\n", "\\item 14\n", "\\item 16\n", "\\item 17\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 1\n", "2. 2\n", "3. 5\n", "4. 7\n", "5. 14\n", "6. 16\n", "7. 17\n", "\n", "\n" ], "text/plain": [ "[1] 1 2 5 7 14 16 17" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "svmfit$index" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can obtain some basic information about the support vector classifier\n", "fit using the summary() command:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 10, scale = FALSE)\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: linear \n", " cost: 10 \n", "\n", "Number of Support Vectors: 7\n", "\n", " ( 4 3 )\n", "\n", "\n", "Number of Classes: 2 \n", "\n", "Levels: \n", " -1 1\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "summary(svmfit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tells us, for instance, that a linear kernel was used with cost=10, and\n", "that there were seven support vectors, four in one class and three in the\n", "other.\n", "\n", "What if we instead used a smaller value of the cost parameter?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 1\n", "\\item 2\n", "\\item 3\n", "\\item 4\n", "\\item 5\n", "\\item 7\n", "\\item 9\n", "\\item 10\n", "\\item 12\n", "\\item 13\n", "\\item 14\n", "\\item 15\n", "\\item 16\n", "\\item 17\n", "\\item 18\n", "\\item 20\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 1\n", "2. 2\n", "3. 3\n", "4. 4\n", "5. 5\n", "6. 7\n", "7. 9\n", "8. 10\n", "9. 12\n", "10. 13\n", "11. 14\n", "12. 15\n", "13. 16\n", "14. 17\n", "15. 18\n", "16. 20\n", "\n", "\n" ], "text/plain": [ " [1] 1 2 3 4 5 7 9 10 12 13 14 15 16 17 18 20" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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v/v33+/OuTUvlnt5NzC0e/+k121w8OM0XYAADVQV9hlb/319wTxffaDN1o75q5Y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\n+92RP4RUd3j6WVdXTx24KaFg0CcbR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"text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=0.1,scale=FALSE)\n", "plot(svmfit, dat)\n", "svmfit$index" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that a smaller value of the cost parameter is being used, we obtain a\n", "larger number of support vectors, because the margin is now wider. Unfortunately, the svm() function does not explicitly output the coefficients of\n", "the linear decision boundary obtained when the support vector classifier is\n", "fit, nor does it output the width of the margin.\n", "The e1071 library includes a built-in function, tune() , to perform cross-validation. By default, tune() performs ten-fold cross-validation on a set\n", "of models of interest. In order to use this function, we pass in relevant\n", "information about the set of models that are under consideration. The\n", "following command indicates that we want to compare SVMs with a linear\n", "kernel, using a range of values of the cost parameter." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Parameter tuning of ‘svm’:\n", "\n", "- sampling method: 10-fold cross validation \n", "\n", "- best parameters:\n", " cost\n", " 0.1\n", "\n", "- best performance: 0.05 \n", "\n", "- Detailed performance results:\n", " cost error dispersion\n", "1 1e-03 0.55 0.4377975\n", "2 1e-02 0.55 0.4377975\n", "3 1e-01 0.05 0.1581139\n", "4 1e+00 0.15 0.2415229\n", "5 5e+00 0.15 0.2415229\n", "6 1e+01 0.15 0.2415229\n", "7 1e+02 0.15 0.2415229\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "set.seed(1)\n", "tune.out=tune(svm,y~.,data=dat,kernel=\"linear\",ranges=list(cost=c(0.001, 0.01, 0.1, 1,5,10,100)))\n", "summary(tune.out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that cost=0.1 results in the lowest cross-validation error rate. The\n", "tune() function stores the best model obtained, which can be accessed as\n", "follows:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "best.tune(method = svm, train.x = y ~ ., data = dat, ranges = list(cost = c(0.001, \n", " 0.01, 0.1, 1, 5, 10, 100)), kernel = \"linear\")\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: linear \n", " cost: 0.1 \n", "\n", "Number of Support Vectors: 16\n", "\n", " ( 8 8 )\n", "\n", "\n", "Number of Classes: 2 \n", "\n", "Levels: \n", " -1 1\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bestmod=tune.out$best.model\n", "summary(bestmod)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predict() function can be used to predict the class label on a set of\n", "test observations, at any given value of the cost parameter. We begin by\n", "generating a test data set." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "xtest=matrix(rnorm(20*2), ncol=2)\n", "ytest=sample(c(-1,1), 20, rep=TRUE)\n", "xtest[ytest==1,]=xtest[ytest==1,] + 1\n", "testdat=data.frame(x=xtest, y=as.factor(ytest))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we predict the class labels of these test observations. Here we use the\n", "best model obtained through cross-validation in order to make predictions." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " truth\n", "predict -1 1\n", " -1 9 1\n", " 1 2 8" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ypred=predict(bestmod,testdat)\n", "table(predict=ypred, truth=testdat$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, with this value of cost, 17 of the test observations are correctly\n", "classified. What if we had instead used cost=0.01?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " truth\n", "predict -1 1\n", " -1 11 6\n", " 1 0 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=.01,scale=FALSE)\n", "ypred=predict(svmfit,testdat)\n", "table(predict=ypred, truth=testdat$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case 3 additional observation is misclassified.\n", "\n", "Now consider a situation in which the two classes are linearly separable.\n", "Then we can find a separating hyperplane using the svm() function. We\n", "first further separate the two classes in our simulated data so that they are\n", "linearly separable:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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Y1HnnjPuEUVni3//LE/7Tjw2tX8lAUAADVjFWGXWvDhsON6dd3tkv/MWPGLy2Wz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\nsw5AJhN2wDqq7Ul3XdW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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "x[y==1,]=x[y==1,]+0.5\n", "plot(x, col=(y+5)/2, pch=19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the observations are just barely linearly separable. We fit the support\n", "vector classifier and plot the resulting hyperplane, using a very large value\n", "of cost so that no observations are misclassified." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 1e+05)\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: linear \n", " cost: 1e+05 \n", "\n", "Number of Support Vectors: 3\n", "\n", " ( 1 2 )\n", "\n", "\n", "Number of Classes: 2 \n", "\n", "Levels: \n", " -1 1\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dat=data.frame(x=x,y=as.factor(y))\n", "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=1e5)\n", "summary(svmfit)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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AAciWNdPHFm585IqVvfPvmPutbs3LmmFLd/fyF3yT8SHp6lBg3ql0pCAAAAh+VY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"text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(svmfit, dat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "No training errors were made and only three support vectors were used.\n", "However, we can see from the figure that the margin is very narrow (because\n", "the observations that are not support vectors, indicated as circles, are very\n", "close to the decision boundary). It seems likely that this model will perform\n", "poorly on test data. We now try a smaller value of cost:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 1)\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: linear \n", " cost: 1 \n", "\n", "Number of Support Vectors: 7\n", "\n", " ( 4 3 )\n", "\n", "\n", "Number of Classes: 2 \n", "\n", "Levels: \n", " -1 1\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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SHO6QdXPHfz2Gd/nTXuqWv3vXSF7Wmjo6Pl0v8/Kx/vWXTVEtK+WkbGBaDtAACo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\n7XPnop8hvzIpVKiQiBiNbLIBgFa4l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"text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "svmfit=svm(y~., data=dat, kernel=\"linear\", cost=1)\n", "summary(svmfit)\n", "plot(svmfit,dat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Support Vector Machine" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to fit an SVM using a non-linear kernel, we once again use the svm()\n", "function. However, now we use a different value of the parameter kernel .\n", "To fit an SVM with a polynomial kernel we use kernel=\"polynomial\" , and\n", "to fit an SVM with a radial kernel we use kernel=\"radial\" . In the former\n", "case we also use the degree argument to specify a degree for the polynomial\n", "kernel, and in the latter case we use gamma to specify a\n", "value of γ for the radial basis kernel.\n", "We first generate some data with a non-linear class boundary, as follows:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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KPR2twkJCTU3NzcxXl4moaGBnfvh+4G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\nrkJggg==", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "set.seed(1)\n", "x=matrix(rnorm(200*2), ncol=2)\n", "x[1:100,]=x[1:100,]+2\n", "x[101:150,]=x[101:150,]-2\n", "y=c(rep(1,150),rep(2,50))\n", "dat=data.frame(x=x,y=as.factor(y))\n", "plot(x, col=y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data is randomly split into training and testing groups. We then fit\n", "the training data using the svm() function with a radial kernel and γ = 1:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "svm(formula = y ~ ., data = dat[train, ], kernel = \"radial\", gamma = 1, \n", " cost = 1)\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: radial \n", " cost: 1 \n", "\n", "Number of Support Vectors: 31\n", "\n", " ( 16 15 )\n", "\n", "\n", "Number of Classes: 2 \n", "\n", "Levels: \n", " 1 2\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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rIdH5NoN2frJ6sPN28GfIzPFpVvbNDTqHcbOfwa/V3m1y8fw1PYUkqtWqvICPO6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\nHBhn7Og2ftY7jDsWNNzp5oIGpXUWNAh5cDsBnz3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gvuvjTwmjEijgpyIR2TN+hJH9ktV5d/J7dRVZmyevNfIAACAASURBVOaM/XHf+yPW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\nTiDaIQAAAABJRU5ErkJggg==", "text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "train=sample(200,100)\n", "svmfit=svm(y~., data=dat[train,], kernel=\"radial\", gamma=1, cost=1)\n", "plot(svmfit, dat[train,])\n", "summary(svmfit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot shows that the resulting SVM has a decidedly non-linear\n", "boundary.\n", "\n", "We can see from the figure that there are a fair number of training errors\n", "in this SVM fit. If we increase the value of cost, we can reduce the number\n", "of training errors. However, this comes at the price of a more irregular\n", "decision boundary that seems to be at risk of overfitting the data." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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ygpzvsL03cEZfO7NgCAQgh2AACVyEt1lB20bfqFj9myUw7NNRaXsTq80FQy++3W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SsiGJ2+d0/O6avnafoxEHIu9uefB4/+WV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\n3hqWrHQswBCYsVO1lItTWreYeFTr3eTjXs1K5Xx8bsuipXvmfFD/idPFJe/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"text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "svmfit=svm(y~., data=dat[train,], kernel=\"radial\",gamma=1,cost=1e5)\n", "plot(svmfit,dat[train,])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can perform cross-validation using tune() to select the best choice of\n", "γ and cost for an SVM with a radial kernel" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Parameter tuning of ‘svm’:\n", "\n", "- sampling method: 10-fold cross validation \n", "\n", "- best parameters:\n", " cost gamma\n", " 1 0.5\n", "\n", "- best performance: 0.07 \n", "\n", "- Detailed performance results:\n", " cost gamma error dispersion\n", "1 1e-01 0.5 0.26 0.15776213\n", "2 1e+00 0.5 0.07 0.08232726\n", "3 1e+01 0.5 0.07 0.08232726\n", "4 1e+02 0.5 0.14 0.15055453\n", "5 1e+03 0.5 0.11 0.07378648\n", "6 1e-01 1.0 0.22 0.16193277\n", "7 1e+00 1.0 0.07 0.08232726\n", "8 1e+01 1.0 0.09 0.07378648\n", "9 1e+02 1.0 0.12 0.12292726\n", "10 1e+03 1.0 0.11 0.11005049\n", "11 1e-01 2.0 0.27 0.15670212\n", "12 1e+00 2.0 0.07 0.08232726\n", "13 1e+01 2.0 0.11 0.07378648\n", "14 1e+02 2.0 0.12 0.13165612\n", "15 1e+03 2.0 0.16 0.13498971\n", "16 1e-01 3.0 0.27 0.15670212\n", "17 1e+00 3.0 0.07 0.08232726\n", "18 1e+01 3.0 0.08 0.07888106\n", "19 1e+02 3.0 0.13 0.14181365\n", "20 1e+03 3.0 0.15 0.13540064\n", "21 1e-01 4.0 0.27 0.15670212\n", "22 1e+00 4.0 0.07 0.08232726\n", "23 1e+01 4.0 0.09 0.07378648\n", "24 1e+02 4.0 0.13 0.14181365\n", "25 1e+03 4.0 0.15 0.13540064\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "set.seed(1)\n", "tune.out=tune(svm, y~., data=dat[train,], kernel=\"radial\", ranges=list(cost=c(0.1,1,10,100,1000),gamma=c(0.5,1,2,3,4)))\n", "summary(tune.out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore, the best choice of parameters involves cost=1 and gamma=0.5. We\n", "can view the test set predictions for this model by applying the predict()\n", "function to the data. Notice that to do this we subset the dataframe dat\n", "using -train as an index set." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " pred\n", "true 1 2\n", " 1 54 23\n", " 2 17 6" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(true=dat[-train,\"y\"], pred=predict(tune.out$best.model,newx=dat[-train,]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SVM with Multiple Classes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the response is a factor containing more than two levels, then the svm()\n", "function will perform multi-class classification using the one-versus-one ap-\n", "proach. We explore that setting here by generating a third class of observations." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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LEiVq/G+vV48kS6ZKQAix0REf1fZiZW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\n3O35zPszuZFc3kuejpaOvb29tbV1jZOpYuvWrdO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GZ/n6+pbOyRCLP3v2jMPh3Lp1q7r5VLBlyxZFRdrznPoAACAASURBVEUjIyN3d/e2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\nSIKCglq1aiV0lpI4Y0dExaRL0y+lXxplPOrNo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bM/+GXPfy1disRE3LwJY+PCSseOcHFBx46YMgX79r31RA8PjBqFuXNRp06x+qZNkErl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\nX0zZAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "set.seed(1)\n", "x=rbind(x, matrix(rnorm(50*2), ncol=2))\n", "y=c(y, rep(0,50))\n", "x[y==0,2]=x[y==0,2]+2\n", "dat=data.frame(x=x, y=as.factor(y))\n", "par(mfrow=c(1,1))\n", "plot(x,col=(y+1))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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MBcrefAGsg+Qi9gGMQm4xkA7jnEF2B/TGg4ES0TLflIwU5EmqwYoQexd+BMJDYM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z7Md9Z6xJU+98rvPTxmkmrAwPbjS1a5h+6Lver28HRtUAACAASURBVO92RVSsHgZg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\nIfttRW9RxVVKNpO2yn5J9iKZJfKayj1I8RFydtel10YV4xX5t6xXdvy/b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717//\n8Zs+TTJYJwDkF3rsANRbyeyrL3xgtX3IpFfnTf55YdmcSWOnfb37j4if3jZh6nJ1veDZuQ+S\n6gAgrQh2AOpp2+tXjZu22uw+cerv+hxw8T03HB7e9vrV46atrvx2yUeP33nnnffPXVP59aLH\nH1viNT3z5luOa+5XxQCQLwh2AOqlbM6kcdNWeh0vmHL94RHJPHDitGv6WVtnXX3hA99Ikn54\n5a/jx4//3ePLt7++9N13l0jbnhjduvGuTvkXExQDQAoxgxSA+lj9zMOfdjh62Cm/m3xs5ZAJ\nq+/vp03+5OqZm2Y8/N7Z1wyMRjseWlzcuFm3ou3f/sFqW1xcvJutdWvJh0sASCEGTwAAAAQE\nn5YBAAACgmAHAAAQEAQ7AACAgCDYAQAABATBDgAAICAIdgAAAAFBsAMAAAgIgh0AAEBAEOwA\nAAACgmAHAAAQEAQ7AACAgCDYAQAABATBDgAAICAIdgAAAAFBsAMAAAgIgh0AAEBAEOwAAAAC\ngmAHAAAQEAQ7AACAgCDYAQAABATBDgAAICAIdgAAAAFBsAMAAAgIgh0AAEBAEOwAAAACgmAH\nAAAQEAQ7AACAgCDYAQAABATBDgAAICAIdgAAAAHx/wH2y7uyxbpuFAAAAABJRU5ErkJggg==", "text/plain": [ "Plot with title “SVM classification plot”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 }, "text/plain": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "svmfit=svm(y~., data=dat, kernel=\"radial\", cost=10, gamma=1)\n", "plot(svmfit, dat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application to Gene Expression Data (optional)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now examine the Khan data set, which consists of a number of tissue\n", "samples corresponding to four distinct types of small round blue cell tumors. For each tissue sample, gene expression measurements are available.\n", "The data set consists of training data, xtrain and ytrain , and testing data,\n", "xtest and ytest .\n", "We examine the dimension of the data:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "\t
  1. 'xtrain'
  2. \n", "\t
  3. 'xtest'
  4. \n", "\t
  5. 'ytrain'
  6. \n", "\t
  7. 'ytest'
  8. \n", "
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'xtrain'\n", "\\item 'xtest'\n", "\\item 'ytrain'\n", "\\item 'ytest'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'xtrain'\n", "2. 'xtest'\n", "3. 'ytrain'\n", "4. 'ytest'\n", "\n", "\n" ], "text/plain": [ "[1] \"xtrain\" \"xtest\" \"ytrain\" \"ytest\" " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(ISLR)\n", "names(Khan)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "\t
  1. 63
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 63\n", "\\item 2308\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 63\n", "2. 2308\n", "\n", "\n" ], "text/plain": [ "[1] 63 2308" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dim(Khan$xtrain)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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  1. 20
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 20\n", "\\item 2308\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 20\n", "2. 2308\n", "\n", "\n" ], "text/plain": [ "[1] 20 2308" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dim(Khan$xtest)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "63" ], "text/latex": [ "63" ], "text/markdown": [ "63" ], "text/plain": [ "[1] 63" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "length(Khan$ytrain)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "20" ], "text/latex": [ "20" ], "text/markdown": [ "20" ], "text/plain": [ "[1] 20" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "length(Khan$ytest)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This data set consists of expression measurements for 2,308 genes.\n", "The training and test sets consist of 63 and 20 observations respectively." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", " 1 2 3 4 \n", " 8 23 12 20 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(Khan$ytrain)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "1 2 3 4 \n", "3 6 6 5 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(Khan$ytest)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use a support vector approach to predict cancer subtype using gene\n", "expression measurements. In this data set, there are a very large number\n", "of features relative to the number of observations. This suggests that we\n", "should use a linear kernel, because the additional flexibility that will result\n", "from using a polynomial or radial kernel is unnecessary." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "svm(formula = y ~ ., data = dat, kernel = \"linear\", cost = 10)\n", "\n", "\n", "Parameters:\n", " SVM-Type: C-classification \n", " SVM-Kernel: linear \n", " cost: 10 \n", "\n", "Number of Support Vectors: 58\n", "\n", " ( 20 20 11 7 )\n", "\n", "\n", "Number of Classes: 4 \n", "\n", "Levels: \n", " 1 2 3 4\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dat=data.frame(x=Khan$xtrain, y=as.factor(Khan$ytrain))\n", "out=svm(y~., data=dat, kernel=\"linear\",cost=10)\n", "summary(out)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " \n", " 1 2 3 4\n", " 1 8 0 0 0\n", " 2 0 23 0 0\n", " 3 0 0 12 0\n", " 4 0 0 0 20" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "table(out$fitted, dat$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that there are no training errors. In fact, this is not surprising,\n", "because the large number of variables relative to the number of observations\n", "implies that it is easy to find hyperplanes that fully separate the classes. We\n", "are most interested not in the support vector classifier’s performance on the\n", "training observations, but rather its performance on the test observations." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " \n", "pred.te 1 2 3 4\n", " 1 3 0 0 0\n", " 2 0 6 2 0\n", " 3 0 0 4 0\n", " 4 0 0 0 5" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dat.te=data.frame(x=Khan$xtest, y=as.factor(Khan$ytest))\n", "pred.te=predict(out, newdata=dat.te)\n", "table(pred.te, dat.te$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that using cost=10 yields two test set errors on this data." ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }