Matlab matrix operations without loops

Hello. I have an issue with a code performing some matrix operations. It is getting to slow, because I am using loops. I am trying for some time to optimize this code and to re-write it with less or without loops. Until now unsuccessful. Can you please help me solve this:

    pb = rand(10,15);
    data = rand(10000,15);
    [rP, cP] = size(pb);
    [r, c] = size(data);
    dist=zeros(r, rP);
    C = zeros(r,1);
    for h=1:r
        min=inf;
        for w=1:rP
            dist(h,w)= sum((data(h,:) - pb(w,:)).^2);
            if min > dist(h,w)
                min= dist(h,w);
                near_clust=w;
            end
        end
        C(h) = near_clust   ;
    end

For large dimension the execution time of these two loops is very high. How can I optimize this?

Thank you,

Answer 1

[Joseph Cheng]

you can get rid of the second for loop;

    tic
    for h=1:r
        dist1(h,:)= sum((repmat(data(h,:),rP,1) - pb).^2,2)';
        [mindist near_clust] = min(dist1(h,:));
        C1(h) = near_clust;
    end
    toc

here i'm performing all of what you're doing in the for loop and looking for the minimum. as the second loop does distance calculations of one point vs all pb points and replace min value. here using repmat i can perform a matrix subtraction and find all the distances then use min() to find the minimum distance.

there is a question of what if two clusters have the same min distance?

[kusum bharti]

Thank you so much for ur quick response.

Answer 2

[Guillaume]

First of all, don't use min as the name of a variable as you can't then matlab's min function which you actually want.

Secondly, using matlab's min function you can calculate C in one go, outside both for loop:

[~, C] = min(dist, [], 2); %won't work if you have a variable called min

Finally, you can eliminate the inner loop entirely:

for h=1:r
  dist(h, :) = sum(bsxfun(@minus, data(h,:), pb).^2, 2)';
end
[~, C] = min(dist, [], 2);

[kusum bharti]

Thank you so much for ur quick response.