【SVM之菜鸟实现】—5步SVM

#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:[email protected] 

[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.html
options.Method = 'lbfgs';
options.maxIter = 100;	  
options.display = 'on';
[optW, cost] = minFunc( @(p) svmCost(p, X, y, lambda), w, options);

end

function [cost grad] = svmCost(w, X, y, lambda)
% cost = HingeLoss^2 + lambda*||w||^2
% 1 2 3 4 5 step
yp = 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：

clear
close all
x0 = [1 4]';
x1 = [4 1]';

X0 = [];
X1 = [];
for i = 1:40
    X0 = [X0 normrnd(x0, 1)];
    X1 = [X1 normrnd(x1, 1)];
end
X = [X0 X1]';
y = [-ones(size(X0,2),1); ones(size(X1,2),1)];
save data X0 X1 X y

plot(X0(1,:),X0(2,:), 'ko', 'MarkerFaceColor', 'y', 'MarkerSize', 7);
hold on
plot(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)] )