SVM matlab 代码详解说明

subplot(2,2,2);
Struct2 = svmtrain(data,groups,‘Kernel_Function‘,‘rbf‘, ‘RBF_Sigma‘,0.41,‘showplot‘,true);
classes2=svmclassify(Struct2,data,‘showplot‘,true);
title(‘高斯径向基核函数(核宽0.41)‘);
CorrectRate2=sum(groups==classes2)/6
subplot(2,2,3);
Struct3 = svmtrain(data,groups,‘Kernel_Function‘,‘polynomial‘, ‘showplot‘,true);
classes3=svmclassify(Struct3,data,‘showplot‘,true);
title(‘多项式核函数‘);
CorrectRate3=sum(groups==classes3)/6
subplot(2,2,4);
Struct4 = svmtrain(data,groups,‘Kernel_Function‘,‘mlp‘, ‘showplot‘,true);
classes4=svmclassify(Struct4,data,‘showplot‘,true);
title(‘多层感知机核函数‘);
CorrectRate4=sum(groups==classes4)/6

svmtrain代码分析：
if plotflag   %画出训练数据的点
[hAxis,hLines] = svmplotdata(training,groupIndex);
legend(hLines,cellstr(groupString));
end

scaleData = [];
if autoScale   %训练数据标准化
scaleData.shift = - mean(training);
stdVals = std(training);
scaleData.scaleFactor = 1./stdVals;
% leave zero-variance data unscaled:
scaleData.scaleFactor(~isfinite(scaleData.scaleFactor)) = 1;

% shift and scale columns of data matrix:
for c = 1:size(training, 2)
training(:,c) = scaleData.scaleFactor(c) * ...
(training(:,c) + scaleData.shift(c));
end
end

if strcmpi(optimMethod, ‘SMO‘)%选择最优化算法
else % QP and LS both need the kernel matrix:
%求解出超平面的参数 (w,b):     wX+b

if plotflag  %画出超平面在二维空间中的投影
    hSV = svmplotsvs(hAxis,hLines,groupString,svm_struct);
    svm_struct.FigureHandles = {hAxis,hLines,hSV};
end

hSV = plot(sv(:,1),sv(:,2),‘ko‘);%从训练数据中选出支持向量，加上圈标记出来

lims = axis(hAxis);%获取子图的坐标空间
[X,Y] = meshgrid(linspace(lims(1),lims(2)),linspace(lims(3),lims(4)));%根据x和y的范围，切分成网格，默认100份
Xorig = X; Yorig = Y;

% need to scale the mesh    将这些隔点标准化
if ~isempty(scaleData)
    X = scaleData.scaleFactor(1) * (X + scaleData.shift(1));
    Y = scaleData.scaleFactor(2) * (Y + scaleData.shift(2));
end

[dummy, Z] = svmdecision([X(:),Y(:)],svm_struct); %计算这些隔点[标签，离超平面的距离]
contour(Xorig,Yorig,reshape(Z,size(X)),[0 0],‘k‘);%画出等高线图，这个距离投影到二维空间的等高线

svmdecision.m文件
function [out,f] = svmdecision(Xnew,svm_struct)
%SVMDECISION evaluates the SVM decision function

%   Copyright 2004-2006 The MathWorks, Inc.
%   $Revision: 1.1.12.4 $  $Date: 2006/06/16 20:07:18 $

sv = svm_struct.SupportVectors;
alphaHat = svm_struct.Alpha;
bias = svm_struct.Bias;
kfun = svm_struct.KernelFunction;
kfunargs = svm_struct.KernelFunctionArgs;

f = (feval(kfun,sv,Xnew,kfunargs{:})‘*alphaHat(:)) + bias;%计算出距离
out = sign(f);%距离转化成标签
% points on the boundary are assigned to class 1
out(out==0) = 1;

function K = quadratic_kernel(u,v,varargin)%核函数计算
%QUADRATIC_KERNEL quadratic kernel for SVM functions

% Copyright 2004-2008 The MathWorks, Inc.

dotproduct = (u*v‘);
K = dotproduct.*(1 + dotproduct);

clc;
clear;
close all;
%rng(1); % For reproducibility
r = sqrt(rand(100,1)); % Radius 0~1
t = 2*pi*rand(100,1); % Angle 0~2pi
data1 = [r.*cos(t), r.*sin(t)]; % Points

r2 = sqrt(3*rand(100,1)+1); % Radius 1~4
t2 = 2*pi*rand(100,1); % Angle 0~2pi
data2 = [r2.*cos(t2), r2.*sin(t2)]; % points

figure;
plot(data1(:,1),data1(:,2),‘r.‘,‘MarkerSize‘,15)
hold on
plot(data2(:,1),data2(:,2),‘b.‘,‘MarkerSize‘,15)
ezpolar(@(x)1);ezpolar(@(x)2);
axis equal
hold off

%Put the data in one matrix, and make a vector of classifications.
data3 = [data1;data2];%标签 +1 -1
theclass = ones(200,1);
theclass(1:100) = -1;

% r^2(r的平方) KMatrix = exp(-gamma*r2);
function KMatrix = getKRBF(X, Y, gamma)%rbf核函数
r2 =  repmat( sum(X.^2,2), 1, size(Y,1) ) ...
    + repmat( sum(Y.^2,2), 1, size(X,1) )‘- 2*X*Y‘ 
%K(x,y)     m*n
%sum(X.^2,2)   m*d  ->   m*1  ->   repmat ->  m*n
%              n*d  ->   n*1  ->   n*m    ->  m*n
%m*n

% XVec表示X向量。||XVec||表示向量长度。 r表示两点距离。r^2表示r的平方。 
% k(XVec,YVec) = exp(-1/(2*sigma^2)*(r^2)) = exp(-gamma*r^2)	
% 公式-1 这里, gamma=1/(2*sigma^2)是参数, r=||XVec-YVec|| 实际上，可看作是计算2个点X与Y的相似性。