% 支持向量機Matlab工具箱1.0 - Nu-SVC, Nu二類分類算法
% 使用平臺 - Matlab6.5 
% 版權所有：陸振波，海軍工程大學
% 電子郵件：luzhenbo@yahoo.com.cn
% 個人主頁：http://luzhenbo.88uu.com.cn
% 參數文獻：Chih-Chung Chang, Chih-Jen Lin. "LIBSVM: a Library for Support Vector Machines"
%
% Support Vector Machine Matlab Toolbox 1.0 - Nu Support Vector Classification
% Platform : Matlab6.5 / Matlab7.0
% Copyright : LU Zhen-bo, Navy Engineering University, WuHan, HuBei, P.R.China, 430033  
% E-mail : luzhenbo@yahoo.com.cn        
% Homepage : http://luzhenbo.88uu.com.cn     
% Reference : Chih-Chung Chang, Chih-Jen Lin. "LIBSVM: a Library for Support Vector Machines"
%
% Solve the quadratic programming problem - "quadprog.m"

clc
clear
close all

% ------------------------------------------------------------%
% 定義核函數及相關參數

nu = 0.2;            % nu -> (0,1] 在支持向量數與錯分樣本數之間進行折衷

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 - 核參數(結構體變量)
% 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).

% ------------------------------------------------------------%
% 構造兩類訓練樣本

n = 50;
randn('state',6);
x1 = randn(2,n);
y1 = ones(1,n);
x2 = 5+randn(2,n);
y2 = -ones(1,n);

figure;
plot(x1(1,:),x1(2,:),'bx',x2(1,:),x2(2,:),'k.');
axis([-3 8 -3 8]);
title('C-SVC')
hold on;

X = [x1,x2];        % 訓練樣本,d×n的矩陣,n為樣本個數,d為樣本維數
Y = [y1,y2];        % 訓練目標,1×n的矩陣,n為樣本個數,值為+1或-1

% ------------------------------------------------------------%
% 訓練支持向量機

tic
svm = svmTrain('svc_nu',X,Y,ker,nu);
t_train = toc

% svm  支持向量機(結構體變量)
% the following fields:
%   type - 支持向量機類型  {'svc_c','svc_nu','svm_one_class','svr_epsilon','svr_nu'}
%   ker - 核參數
%   x - 訓練樣本,d×n的矩陣,n為樣本個數,d為樣本維數
%   y - 訓練目標,1×n的矩陣,n為樣本個數,值為+1或-1
%   a - 拉格朗日乘子,1×n的矩陣

% ------------------------------------------------------------%
% 尋找支持向量

a = svm.a;
epsilon = 1e-8;                     % 如果小于此值則認為是0
i_sv = find(abs(a)>epsilon);        % 支持向量下標
plot(X(1,i_sv),X(2,i_sv),'ro');

% ------------------------------------------------------------%
% 測試輸出

[x1,x2] = meshgrid(-2:0.1:7,-2:0.1:7);
[rows,cols] = size(x1);
nt = rows*cols;                  % 測試樣本數
Xt = [reshape(x1,1,nt);reshape(x2,1,nt)];

tic
Yd = svmSim(svm,Xt);           % 測試輸出
t_sim = toc

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