Efficiently calculating weighted distance in MATLAB

Question

Several posts exist about efficiently calculating pairwise distances in MATLAB. These posts tend to concern quickly calculating euclidean distance between large numbers of p

Answer 1

For r = 1 ("cityblock" case), you can use bsxfun to get elementwise subtractions and then use matrix-multiplication, which must speed up things. The implementation would look something like this -

%// Calculate absolute elementiwse subtractions
absm = abs(bsxfun(@minus,permute(A,[1 3 2]),permute(B,[3 1 2])));

%// Perform matrix multiplications with the given weights and reshape
D = reshape(reshape(absm,[],size(A,2))*wts(:),size(A,1),[]);

Answer 2

You can replace repmat by bsxfun. Doing so avoids explicit repetition, therefore it's more memory-efficient, and probably faster:

function D = pairdist1(A, B, wts, distancemetric)

    if strcmp(distancemetric,'cityblock')
        r=1;
    elseif strcmp(distancemetric,'euclidean')
        r=2;
    else
        error('Function only accepts "cityblock" and "euclidean" distance')
    end

    differences  = abs(bsxfun(@minus, A, permute(B, [3 2 1]))).^r;
    differences = bsxfun(@times, differences, wts).^(1/r);
    D = permute(sum(differences,2),[1,3,2]);

end