【SVM之菜鸟实现】—5步SVM

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#翻译#了下余凯老师的心法

以前的一篇博文：二分类SVM方法Matlab实现

前几日实现了下，虽然说是Linear-SVM，但是只要可以有映射函数也可以做kernel-svm

function [optW cost]= svm5step(X, y, lambda)%% Linear-SVM Minimize(Cost + lambda*Penalty)% X: N×dim% y: {-1,+1}% lambda: coefficient for Penalty part  % By LiFeiteng Email:lifeiteng0422@gmail.com [N dim] = size(X);w = rand(dim+1,1);X = [ones(N,1) X]; % x = [1 x]% minFunc From: http://www.di.ens.fr/~mschmidt/Software/minFunc.htmloptions.Method = 'lbfgs';options.maxIter = 100;  options.display = 'on';[optW, cost] = minFunc( @(p) svmCost(p, X, y, lambda), w, options);endfunction [cost grad] = svmCost(w, X, y, lambda)% cost = HingeLoss^2 + lambda*||w||^2% 1 2 3 4 5 stepyp = X*w;idx = find(yp.*y<1);err = yp(idx)-y(idx);cost = err'*err + lambda*w'*w;grad = 2*X(idx,:)'*err + 2*lambda*w;end

测试用例：

clearclose allx0 = [1 4]';x1 = [4 1]';X0 = [];X1 = [];for i = 1:40    X0 = [X0 normrnd(x0, 1)];    X1 = [X1 normrnd(x1, 1)];endX = [X0 X1]';y = [-ones(size(X0,2),1); ones(size(X1,2),1)];save data X0 X1 X yplot(X0(1,:),X0(2,:), 'ko', 'MarkerFaceColor', 'y', 'MarkerSize', 7);hold onplot(X1(1,:),X1(2,:), 'k+','LineWidth', 2, 'MarkerSize', 7);lambda = 0.01;w = svm5step(X, y, lambda)k = -w(2)/w(3); b = -w(1)/w(3);h = refline(k,b); %已知斜率w 截距b 画直线set(h, 'Color', 'r')b = -(w(1)+1)/w(3);h = refline(k,b); %已知斜率w 截距b 画直线b = -(w(1)-1)/w(3);h = refline(k,b); %已知斜率w 截距b 画直线title(['5 steps Linear-SVM: \lambda = ' num2str(lambda)] )