finding Bias in dual form SVM using mean of support vector

Hi , here i am trying to implement Soft margin SVM using CVX

After getting the set of alpha using CVX i try to set the constrain of alpha to a set of support vector as S , then calculate the weight (w)

Now my problem is i want to calculate the bias b by using the mean of support vector but dont actually know how to implement that formula into matlab code

function dual = svm_train_dual(X_train, y_train, C)
%r = 800 , l = 200
[r,l] = size(X_train);
H = zeros(r,r);
q = ones(r,1);
for a = 1:r
    for b = 1:r
          H(a,b) = X_train(a,:)*X_train(b,:)';
    end
end
cvx_begin
    variable alp(r);
    % minimize((1/2)*alp'*H*alp - q'*alp);
    minimize(0.5*quad_form(y_train'.*alp,H) - q'*alp);
    subject to 
        alp >= 0;
        alp <= C/r; 
        y_train * alp == 0;
cvx_end

     w = zeros(1,l);
     b = 0;
        %constraint alp to  1*10^-2 < alp < (C/r) - 1*10^-5 as a support vector
        %S is set of support vector
     S = alp(alp > 1*10^-5 | alp< (C/r) - 1*10^-5);  
     w = (S'.*y_train)*(X_train);
%      S = alp(alp > 1*10^-5 | alp < (C/r) - 1*10^-5)
     b = ?????????????;
    dual.w = w;
    dual.b = b;
    dual.alp = alp;
    dual.S = S;
end

Answer 1

[Shubham Rawat]

Hi Kien,

Here Bias will be :

b = mean(y_train - w'*X_train);
% here you have already calculated weight vector