finding Bias in dual form SVM using mean of support vector

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Kien Tang
Kien Tang 2020-9-3
回答： Shubham Rawat 2020-9-14
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

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回答（1 个）

Shubham Rawat
Shubham Rawat 2020-9-14
Hi Kien,
Here Bias will be :
b = mean(y_train - w'*X_train);
% here you have already calculated weight vector

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