dualmax3sparsealignment.m

a function inside machine learning

function b = dualMax3SparseAlignment(K, Kj, Y, Yj)
%A function to compute the maximum 3 sparse alignment vector between matrix
%K and vector y

%We need to go through all combinations of 3 examples, so is really
%quite slow. 

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

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

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

for i=1:numExamples
    for j=1:numExamples
        for k=1:numExamples
            KySub = Ky([i, j, k]);
            ySub = Y([i, j, k]);

            KjSub = Kj([i, j, k], [i, j, k]);
            KjKjSub(1, 1) = Kj(:, i)'*Kj(:, i);
            KjKjSub(1, 2) = Kj(:, i)'*Kj(:, j);
            KjKjSub(1, 3) = Kj(:, i)'*Kj(:, k);
            KjKjSub(2, 2) = Kj(:, j)'*Kj(:, j);
            KjKjSub(2, 3) = Kj(:, j)'*Kj(:, k);
            KjKjSub(3, 3) = Kj(:, k)'*Kj(:, k);

            KjKjSub(2, 1) = KjKjSub(1, 2);
            KjKjSub(3, 1) = KjKjSub(1, 3);
            KjKjSub(3, 2) = KjKjSub(2, 3);

            KjKjSub = KjKjSub + I;

            bSub = KjKjSub\KySub;
            bSub = bSub/sqrt(KySub'*bSub);
            
            %Note: not really the alignment - but proportional to it 
            alignment = bSub'*KySub;

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