opt1.m

svm classification and regression code

    % Construct the Kernel matrix
    X=rand(150,2);
    Y=ones(150,1);
    figure(1);
    hold on
    plot(X(:,1),X(:,2),'*');
    plot(-1,-1,2,2);
    C=Inf;
    n=size(X,1);
    ker='poly';
    global p1;
    p1=0.5;
    epsilon = svtol(C);
    fprintf('Constructing ...\n');
    H = zeros(n,n);  
    for i=1:n
       for j=1:n
          H(i,j) = svkernel(ker,X(i,:),X(j,:));
       end
    end
    c = -zeros(n,1);  

    H = H+1e-10*eye(size(H));
    
    vlb = zeros(n,1);      % Set the bounds: alphas >= 0
    vub = C*ones(n,1);     %                 alphas <= C
    x0 = zeros(n,1);       % The starting point is [0 0 0   0]
    neqcstr = nobias(ker); % Set the number of equality constraints (1 or 0)  
    if neqcstr
       A = Y';, b = 0;     % Set the constraint Ax = b
    else
       A = [];, b = [];
    end
    A=Y';
    b=1;

    % Solve the Optimisation Problem
    
    fprintf('Optimising ...\n');
    st = cputime;
    
    [alpha lambda how] = qp(H, c, A, b, vlb, vub, x0, neqcstr);
    nsv=length(find(alpha>=epsilon));
    fprintf('Support Vectors : %d (%3.1f%%)\n',nsv,100*nsv/n);
    
    Xt=[];
    for i=-0.5:0.05:1.5
        for j=-0.5:0.05:1.5
            Xt=[Xt;i,j];
        end
    end
    
    i=1;
    while i<=n&alpha(i,1)<=epsilon
        i=i+1;
    end
    i0=i;
    
    f0=0;
    for j=1:n
        f0=f0-svkernel(ker,X(i0,:),X(j,:));
    end
        
    n1=size(Xt,1);
    for i=1:n1
        f=0;
        for j=1:n
            f=f-svkernel(ker,Xt(i,:),X(j,:));
        end
        if f<f0
            Yt(i,1)=1;
        else
            Yt(i,1)=-1;
        end
    end
    
    y1=find(Yt==1);
    figure(2);
    hold on
    plot(Xt(y1,1),Xt(y1,2),'k+');
    plot(X(:,1),X(:,2),'*');