matlab remove for loop in matrix computation

Question

I'm working on a problem on Matlab according to Matrix. I think my code could be improved by remove the for loop. But I really don't know how to fix this one. Can anyone help me, please? the code is:

K = 3;
X = [1 2; 3 4; 5 6; 7 8];
idx = [1;2;3;1];
for i = 1:K
    ids = (idx == i);
    centroids(i,:) = sum(bsxfun(@times, X, ids))./ sum(ids);
end

in this code, data points X is 4x2. There are K=3 centroids, so the centroids is a matrix of 3x2. This code is part of a K-mean function, which is using data points and their closest centroids to find new position of centroids. I want to make the code as something without the FOR loop, maybe beginning like this:

ids = bsxfun(@eq, idx, 1:K);
centroids = ..............

Answer 1

You can avoid the bsxfun by using logical indexing, this seems to be a worthwhile performance increase, at least for small matrices X. It is best for small K, and for a small number of rows of X.

K = 3;
X = [1 2; 3 4; 5 6; 7 8];
idx = [1;2;3;1];
centroids=zeros(K,2);
for i = 1:K
    ids = (idx == i);
    centroids(i,:) = sum(X(ids,:),1)./sum(ids);
end

If X has a large number of rows, this method is fastest:

K = 3;
X = [1 2; 3 4; 5 6; 7 8];
idx = [1;2;3;1];
centroids=zeros(K,2);
t=bsxfun(@eq,idx,1:K);
centroids=bsxfun(@rdivide,t.'*X,sum(t).');

And if K is very large, Luis' accumarray method is fastest.