svmlspex02.m

数据挖掘的新方法－支持向量机书中算法例子

%SVMLSPex02.m
%Two Dimension SVM Problem, Two Class and Separable Situation
%
%%Difference with SVMLSPex01.m:
%           Take the Largrange Function (16)as object function insteads ||W||,
%				so it need more time than SVMLSex01.m 
%
%Method from Christopher J. C. Burges:
%"A Tutorial on Support Vector Machines for Pattern Recognition", page 9
%	
%  Objective:   min "f(A)=-sum(ai)+sum[sum(ai*yi*xi*aj*yj*xj)]/2" ,function (16)
%  Subject to:  sum{ai*yi}=0 ,function (15);
%					 and ai>=0 for any i, the particular set of constraints C2 (page 9, line14). 
%The optimizing variables is "Lagrange Multipliers": A=[a1,a2,...,am],m is the number of total samples.
%

function mm=SVMLSex02(mm) %mm -- select sample number

echo off;
close all;
fclose all;

%Generate Two Set of Data each set with n data
	m1=mm;					% The number of class A
   m2=mm;					% The number of class B
   n = 2;					% The dimension of sample vector
   al=pi/4;				%
	d=0.05;				%
   
	x=rand(m1,2);
	x(1:m1,1)=2*x(1:m1,1);
	x(1:m1,2)=x(1:m1,2);
	X1(1:m1,1)=x(1:m1,1)*cos(al)-x(1:m1,2)*sin(al);
	X1(1:m1,2)=x(1:m1,2)*cos(al)+x(1:m1,1)*sin(al);

	x=rand(m2,2);
	x(1:m2,2)=2*x(1:m2,2);
	x(1:m2,1)=x(1:m2,1)+d;
	X2(1:m2,1)=x(1:m2,1)*cos(al)+x(1:m2,2)*sin(al);
	X2(1:m2,2)=x(1:m2,2)*cos(al)-x(1:m2,1)*sin(al);
   
   clear x;
   
   X=[X1;X2];							%X1 is Positive Samples Set and X2 is Negative Samples Set
   m=m1+m2;								%Total number of samples
     
   figure(1);
  	whitebg(1,[0,0.1,0]);
   
   plot(X(1:m1,1),X(1:m1,2),'m*');
   hold on
   plot(X(m1+1:m,1),X(m1+1:m,2),'c*');
   
   Xa = min(0,min(X(1:m,1)));
   Xb = max(X(1:m,1));
	axis([Xa,Xb,min(X(1:m,2)),max(X(1:m,2))])
   
      asw = 0;
   while (asw~=1)&(asw~=2)
      asw=input('Continue or no? (1/2)');
   end
   if asw==1
   	%
 		%Note!Program below can processes any dimension sample set with (m*n)matrix, m-sample number/n-sample dimension.
		%
		%Transmiting Samples to Object and Constraint Function, in SVMLSex02FUN.m,
		%Reference to MATLAB function "constr"
		fid=fopen('a.dat','w');
      fwrite(fid,[m1,m2,n],'float');
      for k=1:n
         fwrite(fid,X(1:m,k),'float');
      end
      fclose(fid);

		%
		%Keep to MATLAB prescribe,Here
		%x0 is start point to optimizing;
      %Set options(13)=1 indicate the first constrained function contained in SVMLSPex02FUN.m is a equality,
      %and others are "<=0",Reference to MATLAB function "CONSTR";
      %
		%Return parameter: 
		%  A=[A(i)] is the optimizing variables, that is {ai} in function (14)/(15)/(16);
		%  L=[L(2),L(3),...,L(m+1)] is Lagrange Multipliyers correspondence to each constrained function;
   
		x0 = 0.5*ones(m,1);	%Initial of op					
		options(13) = 1;					
		[A,options,L] = constr('SVMLSPex02FUN', x0, options);

		%From function (14)
	   Y=[ones(m1,1);-ones(m2,1)];	%The classfication value for both Positive and Negative Samples Set
		W = sum((diag(A)*diag(Y))*X);

		% Note!!!!, the Comprehension to "Lagrange Multiplier" A=[ai] and the return parameters L:
		% L=[L(2),...,L(m+1)] is the Lagrange Multipliers for function f, the function (16);
		% L(i)=0 indicate the corresponding constraint "x(i)>=0" is active and the point x(i) is a "Support Vector" 
		% Note!!! a(i) in function (16), is also "Lagrange Multiplier" but it is for object function ||W||
		% and here, the actual object function to be optimized is function f, the function (16);
		% and the function (16) can be considered as an alternation of original object function ||W||
		% and a(i)or,in function (16),is only new variables of an alternation of origin variables.

		[z,I]=min(L);			%The Support Vectors are corresponding to L(i) = 0;
		X0=X(I-1,1:n)';		%Pick out a arbitrary Support Vector to determine the "b" in classifying function

		%The classifing function should be X*W+b=0. It is y = k*x +b, here k and b are
      k = -W(1)/W(2);
      b = -1/W(2)+W*X0/W(2);
		plot([Xa,Xb],[k*Xa+b,k*Xb+b],'y')
   
   	for n=2:m+1
 	     if L(n)<=1e-6,
 	        plot(X(n-1,1),X(n-1,2),'wo');
 	     end
	   end
   

delete('a.dat');

end