nu_svc.m

各人用Mtalab编写的SVM程序

%****************************************************************************************************
% 支持向量机 Nu-SVC, Nu二类分类算法

clc
clear
close all

% ------------------------------------------------------------%
% 定义核函数及相关参数

nu = 0.2; % nu -> (0,1] 在支持向量数与错分样本数之间进行折衷

ker = struct('type','linear');
%ker = struct('type','ploy','degree',3,'offset',1);
%ker = struct('type','gauss','width',1);
%ker = struct('type','tanh','gamma',1,'offset',0);

% ker - 核参数(结构体变量)
% the following fields:
% type - linear : k(x,y) = x'*y
% poly : k(x,y) = (x'*y+c)^d
% gauss : k(x,y) = exp(-0.5*(norm(x-y)/s)^2)
% tanh : k(x,y) = tanh(g*x'*y+c)
% degree - Degree d of polynomial kernel (positive scalar).
% offset - Offset c of polynomial and tanh kernel (scalar, negative for tanh).
% width - Width s of Gauss kernel (positive scalar).
% gamma - Slope g of the tanh kernel (positive scalar).

% ------------------------------------------------------------%
% 构造两类训练样本

n = 50;
randn('state',3);
x1 = randn(n,2);
y1 = ones(n,1);
x2 = 5+randn(n,2);
y2 = -ones(n,1);

figure(2);
plot(x1(:,1),x1(:,2),'bx',x2(:,1),x2(:,2),'k.');
hold on;

X = [x1;x2]; % 训练样本,n×d的矩阵,n为样本个数,d为样本维数
Y = [y1;y2]; % 训练目标,n×1的矩阵,n为样本个数,值为+1或-1

% ------------------------------------------------------------%
% 训练支持向量机

tic
svm = Nu_SVC_Train(X,Y,nu,ker);
t_train = toc

% svm 支持向量机(结构体变量)
% the following fields:
% ker - 核参数
% x - 训练样本
% y - 训练目标;
% a - 拉格朗日乘子

% ------------------------------------------------------------%
% 寻找支持向量

a = svm.a;
epsilon = 1e-8; % 如果小于此值则认为是0
i_sv = find(a>epsilon); % 支持向量下标
plot(X(i_sv,1),X(i_sv,2),'ro');

% ------------------------------------------------------------%
% 测试输出

[x1,x2] = meshgrid(-2:0.05:7,-2:0.05:7);
[rows,cols] = size(x1);
nt = rows*cols; % 测试样本数
Xt = [reshape(x1,nt,1),reshape(x2,nt,1)];

tic
Yd = Nu_SVC_Sim(svm,Xt); % 测试输出
t_sim = toc

Yd = reshape(Yd,rows,cols);
contour(x1,x2,Yd,[0 0],'m'); % 分类面
hold off;