{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 1, "metadata": { "image/png": { "width": 200 } }, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('../../Python_probability_statistics_machine_learning_2E.png',width=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Support Vector Machines (SVM) originated from the statistical learning theory\n", "developed by Vapnik-Chervonenkis. As such, it represents a deep application of\n", "statistical theory that incorporates the VC dimension concepts we\n", "discussed in the first section. Let's start by looking at some pictures.\n", "Consider the two-dimensional classification problem shown in [Figure](#fig:svm_001). [Figure](#fig:svm_001) shows two classes (gray and white\n", "circles) that can be separated by any of the lines shown. Specifically, any\n", "such separating line can be written as the locus of points ($\\mathbf{x}$) in\n", "the two-dimensional plane that satisfy the following,\n", "\n", "\n", "\n", "
\n", "\n", "

In the two-dimensional plane, the two classes (gray and white circles) are easily separated by any one of the lines shown.

\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\beta_0 + \\boldsymbol{\\beta}^T \\mathbf{x} = 0\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " To classify an arbitrary $\\mathbf{x}$ using this line, we just\n", "compute the sign of $\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}$ and assign one\n", "class to the positive sign and the other class to the negative sign. To\n", "uniquely specify such a separating line (or, hyperplane in a higher-dimensional\n", "space) we need additional criteria. \n", "\n", "\n", "[Figure](#fig:svm_002) shows the data with two bordering parallel lines that\n", "form a margin around the central separating line. The *maximal margin\n", "algorithm* finds the widest margin and the unique separating line. As a\n", "consequence, the algorithm uncovers the elements in the data that touch the\n", "margins. These are the *support* elements. The other elements\n", "away from the border are not relevant to the solution. This reduces\n", "model variance because the solution is insensitive to the removal of\n", "elements other than these supporting elements (usually a small minority).\n", "\n", "\n", "\n", "
\n", "\n", "

The maximal margin algorithm finds the separating line that maximizes the margin shown. The elements that touch the margins are the support elements. The dotted elements are not relevant to the solution.

\n", "\n", "\n", "\n", "\n", "\n", "To see how this works for linearly separable classes, consider a\n", "training set consisting of $\\lbrace (\\mathbf{x},y) \\rbrace$ where\n", "$y\\in \\lbrace -1,1 \\rbrace$. For any point $\\mathbf{x}_i$, we\n", "compute the functional margin as $\\hat{ \\gamma_i }=y_i (\\beta_0 +\n", "\\boldsymbol{\\beta}^T \\mathbf{x}_i)$. Thus, $\\hat{\\gamma}_i >0$ when\n", "$\\mathbf{x}_i$ is correctly classified. The geometrical margin is\n", "$\\gamma = \\hat{\\gamma}/\\lVert\\boldsymbol{\\beta}\\rVert$. When\n", "$\\mathbf{x}_i$ is correctly classified, the geometrical margin is\n", "equal to the perpendicular distance from $\\mathbf{x}_i$ to the line.\n", "Let's look see how the maximal margin algorithm works.\n", "\n", "Let $M$ be the width of the margin. The maximal margin algorithm is can be\n", "formulated as a quadratic programming problem. We want to simultaneously\n", "maximize the margin $M$ while ensuring that all of the data points are\n", "correctly classified." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{aligned}\n", "& \\underset{\\beta_0,\\boldsymbol{\\beta},\\lVert\\boldsymbol{\\beta}\\rVert=1}{\\text{maximize}}\n", "& & M \\\\\\\n", "& \\text{subject to:}\n", "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq M, \\; i = 1, \\ldots, N.\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The first line says we want to generate a maximum value for $M$ by\n", "adjusting $\\beta_0$ and $\\boldsymbol{\\beta}$ while keeping\n", "$\\lVert\\boldsymbol{\\beta}\\rVert=1$. The functional margins for each $i^{th}$\n", "data element are the constraints to the problem and must be satisfied for every\n", "proposed solution. In words, the constraints enforce that the elements have to\n", "be correctly classified and outside of the margin around the separating line.\n", "With some reformulation, it turns out that\n", "$M=1/\\lVert\\boldsymbol{\\beta}\\rVert$ and this can be put into the following\n", "standard format," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{aligned}\n", "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n", "& & \\lVert\\boldsymbol{\\beta}\\rVert \\\\\\\n", "& \\text{subject to:}\n", "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1, \\; i = 1, \\ldots, N.\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " This is a convex optimization problem and can be solved using powerful\n", "methods in that area. \n", "\n", "The situation becomes more complex when the two classes are not separable and\n", "we have to allow some unavoidable mixing between the two classes in the\n", "solution. This means that the contraints have to modified as in the following," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq M(1-\\xi_i)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " where the $\\xi_i$ are the slack variables and represent the\n", "proportional amount tha the prediction is on the wrong side of the margin. Thus,\n", "elements are misclassified when $\\xi_i>1$. With these additional variables,\n", "we have a more general formulation of the convex optimization problem," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{aligned}\n", "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n", "& & \\lVert\\boldsymbol{\\beta}\\rVert \\\\\\\n", "& \\text{subject to:} \n", "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1-\\xi_i, \\\\\\\n", "& & & \\xi_i \\geq 0, \\sum \\xi_i \\leq \\texttt{constant}, \\; i = 1, \\ldots, N.\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " which can be rewritten in the following equivalent form," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{aligned}\n", "& \\underset{\\beta_0,\\boldsymbol{\\beta}}{\\text{minimize}}\n", "& & \\frac{1}{2}\\lVert\\boldsymbol{\\beta}\\rVert + C \\sum \\xi_i \\\\\\\n", "& \\text{subject to:}\n", "& & y_i(\\beta_0+\\boldsymbol{\\beta}^T \\mathbf{x}_i) \\geq 1-\\xi_i, \\xi_i \\geq 0 \\; i = 1, \\ldots, N.\n", "\\end{aligned}\n", "\\end{equation}\n", "\\label{eq:svm} \\tag{1}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Because the $\\xi_i$ terms are all positive, the objective\n", "is to maximize the margin (i.e., minimize $\\lVert\\boldsymbol{\\beta}\\rVert$)\n", "while minimizing the proportional drift of the predictions to the wrong side\n", "of the margin (i.e., $C \\sum \\xi_i$). Thus, large values of $C$ shunt\n", "algorithmic focus towards the correctly classified points near the\n", "decision boundary and small values focus on further data. The value $C$ is\n", "a hyperparameter for the SVM.\n", "\n", "The good news is that all of these complicated pieces are handled neatly inside\n", "of Scikit-learn. The following sets up the linear *kernel* for the SVM (more on\n", "kernels soon)," ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import make_blobs\n", "from sklearn.svm import SVC\n", "sv = SVC(kernel='linear')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We can create some synthetic data using `make_blobs` and then\n", "fit it to the SVM," ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n", " decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n", " kernel='linear', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X,y=make_blobs(n_samples=200, centers=2, n_features=2,\n", " random_state=0,cluster_std=.5)\n", "sv.fit(X,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " After fitting, the SVM now has the estimated support vectors and the\n", "coefficients of the $\\boldsymbol{\\beta}$ in the `sv.support_vectors_` and\n", "`sv.coef_` attributes, respectively. [Figure](#fig:svm_003) shows the two\n", "sample classes (white and gray circles) and the line separating them that was\n", "found by the maximal margin algorithm. The two parallel dotted lines show the\n", "margin. The large circles enclose the support vectors, which are the data\n", "elements that are relevant to the solution. Notice that only these elements\n", "can touch the edges of the margins." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from matplotlib.pylab import subplots\n", "import numpy as np\n", "xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n", "\n", "fig,ax=subplots()\n", "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n", "_=ax.plot(sv.support_vectors_[:,0],sv.support_vectors_[:,1],'ko',markersize=20,alpha=.2)\n", "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- sv.intercept_/sv.coef_[0,1],'k',lw=3.)\n", "margin = np.linalg.norm(sv.coef_)\n", "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi-(sv.intercept_+margin/2.)/sv.coef_[0,1],'--k',lw=3.)\n", "_=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi-(sv.intercept_-margin/2.)/sv.coef_[0,1],'--k',lw=3.)\n", "fig.savefig('fig-machine_learning/svm_003.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", "\n", "

The two class shown (white and gray circles) are linearly separable. The maximal margin solution is shown by the dark black line in the middle. The dotted lines show the extent of the margin. The large circles indicate the support vectors for the maximal margin solution.

\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "\n", "def draw_margins(sv,X,y,ax=None):\n", " sv.fit(X,y)\n", " xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n", " if ax is None: fig,ax=subplots()\n", " _=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n", " _=ax.plot(sv.support_vectors_[:,0],sv.support_vectors_[:,1],'ko',markersize=20,alpha=.2)\n", " _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- sv.intercept_/sv.coef_[0,1],'k',lw=3.)\n", " margin = np.linalg.norm(sv.coef_)\n", " _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- (sv.intercept_+margin/2.)/sv.coef_[0,1],'--k',lw=3.)\n", " _=ax.plot(xi,-sv.coef_[0,0]/sv.coef_[0,1]*xi- (sv.intercept_-margin/2.)/sv.coef_[0,1],'--k',lw=3.)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "X, y = make_blobs(n_samples=50, centers=2, n_features=2,\n", " cluster_std=1,random_state=0)\n", "\n", "fig,axs = subplots(2,2,sharex=True,sharey=True)\n", "#fig.set_size_inches((12,6))\n", "sv = SVC(kernel='linear',C=.0100)\n", "draw_margins(sv,X,y,ax=axs[0,0])\n", "_=axs[0,0].set_title('C=0.01')\n", "sv = SVC(kernel='linear',C=1)\n", "draw_margins(sv,X,y,ax=axs[0,1])\n", "_=axs[0,1].set_title('C=1')\n", "sv = SVC(kernel='linear',C=100)\n", "draw_margins(sv,X,y,ax=axs[1,0])\n", "_=axs[1,0].set_title('C=100')\n", "sv = SVC(kernel='linear',C=10000)\n", "draw_margins(sv,X,y,ax=axs[1,1])\n", "_=axs[1,1].set_title('C=10000')\n", "fig.savefig('fig-machine_learning/svm_004.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Figure](#fig:svm_004) shows what happens when the value of $C$ changes.\n", "Increasing this value emphasizes the $\\xi$ part of the objective function in\n", "Equation [1](#eq:svm). As shown in the top left panel, a small value for $C$ means that\n", "the algorithm is willing to accept many support vectors at the expense of\n", "maximizing the margin. That is, the proportional amount that predictions are on\n", "the wrong side of the margin is more acceptable with smaller $C$. As the value\n", "of $C$ increases, there are fewer support vectors because the optimization\n", "process prefers to eliminate support vectors that are far away from the margins\n", "and accept fewer of these that encroach into the margin. Note that as the value\n", "of $C$ progresses through this figure, the separating line tilts slightly. \n", "\n", "\n", "\n", "
\n", "\n", "

The maximal margin algorithm finds the separating line that maximizes the margin shown. The elements that touch the margins are the support elements. The dotted elements are not relevant to the solution.

\n", "\n", "\n", "\n", "\n", "\n", "## Kernel Tricks\n", "\n", "Support Vector Machines provide a powerful method to deal with linear\n", "separations, but they can also apply to non-linear boundaries by\n", "exploiting the so-called *kernel trick*. The convex optimization\n", "formulation of the SVM includes a *dual* formulation that leads to a\n", "solution that requires only the inner-products of the features. The\n", "kernel trick is to substitute inner-products by nonlinear kernel\n", "functions. This can be thought of as mapping the original features\n", "onto a possibly infinite dimensional space of new features. That is,\n", "if the data are not linearly separable in two-dimensional space (for\n", "example) maybe they are separable in three-dimensional space (or\n", "higher)? \n", "\n", "To make this concrete, suppose the original input space is\n", "$\\mathbb{R}^n$ and we want to use a non-linear mapping\n", "$\\psi:\\mathbf{x} \\mapsto \\mathcal{F}$ where $\\mathcal{F}$ is an\n", "inner-product space of higher dimension. The kernel trick is to\n", "calculate the inner-product in $\\mathcal{F}$ using a kernel\n", "function, $K(\\mathbf{x}_i,\\mathbf{x}_j) = \\langle\n", "\\psi(\\mathbf{x}_i),\\psi(\\mathbf{x}_j)\\rangle$. The long way to\n", "compute this is to first compute $\\psi(\\mathbf{x})$ and then do the\n", "inner-product. The kernel-trick way to do it is to use the kernel\n", "function and avoid computing $\\psi$. In other words, the kernel\n", "function returns what the inner-product in $\\mathcal{F}$ would have\n", "returned if $\\psi$ had been applied. For example, to achieve an\n", "$n^{th}$ polynomial mapping of the input space, we can use\n", "$\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)=(\\mathbf{x}_i^T\\mathbf{x}_j+\\theta)^n$.\n", "For example, suppose the input space is $\\mathbb{R}^2$ and\n", "$\\mathcal{F}=\\mathbb{R}^4$ and we have the following mapping," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\psi(\\mathbf{x}) : (x_0,x_1) \\mapsto (x_0^2,x_1^2,x_0 x_1, x_1 x_0)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The inner product in $\\mathcal{F}$ is then," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\langle \\psi(\\mathbf{x}),\\psi(\\mathbf{y}) \\rangle = \\langle \\mathbf{x},\\mathbf{y} \\rangle^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " In other words, the kernel is the square of the inner\n", "product in input space. The advantage of using the kernel instead of\n", "simply enlarging the feature space is computational because you only\n", "need to compute the kernel on all distinct pairs of the input space.\n", "The following example should help make this concrete. First we create\n", "some Sympy variables," ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import sympy as S\n", "x0,x1=S.symbols('x:2',real=True)\n", "y0,y1=S.symbols('y:2',real=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Next, we create the $\\psi$ function that maps into $\\mathbb{R}^4$ \n", "and the corresponding kernel function," ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "psi = lambda x,y: (x**2,y**2,x*y,x*y)\n", "kern = lambda x,y: S.Matrix(x).dot(y)**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Notice that the inner product in $\\mathbb{R}^4$ is\n", "equal to the kernel function, which only uses wthe $\\mathbb{R}^2$\n", "variables." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x0**2*y0**2 + 2*x0*x1*y0*y1 + x1**2*y1**2\n", "x0**2*y0**2 + 2*x0*x1*y0*y1 + x1**2*y1**2\n" ] } ], "source": [ "print(S.Matrix(psi(x0,x1)).dot(psi(y0,y1)))\n", "print(S.expand(kern((x0,x1),(y0,y1)))) # same as above" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Polynomial Regression Using Kernels.** Recall our favorite\n", "linear regression problem from the regularization chapter," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\min_{\\boldsymbol{\\beta}}\\Vert y -\\mathbf{X}\\boldsymbol{\\beta}\\Vert^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " where $\\mathbf{X}$ is a $n\\times m$ matrix with $m>n$. As\n", "we discussed, there are multiple solutions to this problem. The \n", "least-squares solution is the following:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}_{LS}=\\mathbf{X}^T(\\mathbf{X}\\mathbf{X}^T)^{\\text{-1}}\\mathbf{y}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Given a new feature vector $\\mathbf{x}$, the corresponding estimator\n", "for $\\mathbf{y}$ is the following," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\hat{\\mathbf{y}} = \\mathbf{x}^T\\boldsymbol{\\beta}_{LS}=\\mathbf{x}^T\\mathbf{X}^T(\\mathbf{X}\\mathbf{X}^T)^{\\text{-1}}\\mathbf{y}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Using the kernel trick, the solution can be written more generally as\n", "the following," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\hat{\\mathbf{y}}=\\mathbf{k}(\\mathbf{x})^T\\mathbf{K}^{\\text{-1}}\\mathbf{y}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " where the $n\\times n$ kernel matrix $\\mathbf{K}$ replaces\n", "$\\mathbf{X}\\mathbf{X}^T$ and where $\\mathbf{k}(\\mathbf{x})$ is a $n$-vector of\n", "components $\\mathbf{k}(\\mathbf{x})=[\\kappa(\\mathbf{x}_i,\\mathbf{x})]$ and where\n", "$\\mathbf{K}_{i,j}=\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$ for the kernel function\n", "$\\kappa$. With this more general setup, we can substitute\n", "$\\kappa(\\mathbf{x}_i,\\mathbf{x}_j)=(\\mathbf{x}_i^T\\mathbf{x}_j+\\theta)^n$ for\n", "$n^{th}$-order polynomial regression [[bauckhagenumpy]](#bauckhagenumpy). Note that ridge\n", "regression can also be incorporated by inverting $(\\mathbf{K}+\\alpha\n", "\\mathbf{I})$, which can help stabilize poorly conditioned $\\mathbf{K}$ matrices\n", "with a tunable $\\alpha$ hyper-parameter [[bauckhagenumpy]](#bauckhagenumpy). \n", "\n", "For some kernels, the enlarged $\\mathcal{F}$ space is infinite-dimensional.\n", "Mercer's conditions provide technical restrictions on the kernel functions.\n", "Powerful and well-studied kernels have been implemented in Scikit-learn. The\n", "advantage of kernel functions may evaporate for when $n\\rightarrow m$ in which\n", "case using the $\\psi$ functions instead can be more practicable.\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import cm\n", "xi = np.linspace(X[:,0].min(),X[:,0].max(),100)\n", "yi = np.linspace(X[:,1].min(),X[:,1].max(),100)\n", "\n", "fig,ax=subplots()\n", "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='o',alpha=.3)\n", "Xi,Yi = np.meshgrid(xi,yi)\n", "Zi=sv.predict(np.c_[Xi.ravel(),Yi.ravel()]).reshape(Xi.shape)\n", "\n", "_=ax.contourf(Xi,Yi,Zi,cmap=cm.Paired,alpha=0.2);\n", "fig.savefig('fig-machine_learning/svm_005.png')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }