pdist2 equivalent in MATLAB version 7

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Here is vectorized implementation for computing the euclidean distance that is much faster than what you have (even significantly faster than PDIST2 on my machine):

D = sqrt( bsxfun(@plus,sum(A.^2,2),sum(B.^2,2)') - 2*(A*B') );

It is based on the fact that: ||u-v||^2 = ||u||^2 + ||v||^2 - 2*u.v

Consider below a crude comparison between the two methods:

A = rand(4754,1024);
B = rand(6800,1024);

tic
D = pdist2(A,B,'euclidean');
toc

tic
DD = sqrt( bsxfun(@plus,sum(A.^2,2),sum(B.^2,2)') - 2*(A*B') );
toc

On my WinXP laptop running R2011b, we can see a 10x times improvement in time:

Elapsed time is 70.939146 seconds.        %# PDIST2
Elapsed time is 7.879438 seconds.         %# vectorized solution

You should be aware that it does not give exactly the same results as PDIST2 down to the smallest precision.. By comparing the results, you will see small differences (usually close to eps the floating-point relative accuracy):

>> max( abs(D(:)-DD(:)) )
ans =
  1.0658e-013

On a side note, I’ve collected around 10 different implementations (some are just small variations of each other) for this distance computation, and have been comparing them. You would be surprised how fast simple loops can be (thanks to the JIT), compared to other vectorized solutions…

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