dualmax3sparsecovariance.m

a function inside machine learning

function b = dualMax3SparseCovariance(K, Kj, Y, Yj)
%A function to compute the maximum 3 sparse covariance vector between matrix
%K and vector y

%We need to go through all combinations of 3 examples, so this might be
%quite slow. 

numExamples = size(K, 1); 
sparsity = 3; 
maxCovariance = -1; 
alpha = 0.0001;

b = zeros(numExamples, 1); 
Ky = Kj'*Y;
I = alpha*eye(sparsity, sparsity); 

KySub = zeros(sparsity, 1); 
KSub = zeros(sparsity, sparsity); 

for i=1:numExamples
    for j=1:numExamples
        for k=1:numExamples

            KySub = Ky([i, j, k]);
            KSub = K([i, j, k], [i, j, k]);
            
            %Very slightly faster with inv3 
            %bSub = inv3(KSub)*KySub; 
            bSub = (KSub+I)\KySub;
            bSub = bSub/sqrt(bSub'*KSub*bSub);

            covariance = bSub'*KySub;

            if covariance > maxCovariance
                b = zeros(numExamples, 1);
                b([i, j, k]) = bSub;
                maxCovariance = covariance;
            end

        end
    end
end

maxCovariance;