# Speed up Matrix Subtraction for Euclidean Distance calculation

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TYS on 30 Dec 2016
Commented: Walter Roberson on 31 Dec 2016
I have 2 matrices, both of them are feature matrices, M1 is 9216x26310, M2 is 9216x34000. each column represents 9216x1 represents one feature for a particular image, in this case 26310 images for the M1, 34000 for M2. I want to speed up the time for it to calculate euclidean distance, my current code takes average 1.3 secs or 1.4 secs per calculation.
tic;
for idx = 1:Number_of_Test_Images
for TrnIdx = 1 : Number_of_Train_Images
E_distance(TrnIdx) = sqrt(sum(abs((ftest(:,idx)-ftrain(:,TrnIdx)).^2)));
end
%
%[smallest_value, Idx_smallest] = min(E_distance);
%
Esimate_Test_labels(idx,1) = TrnLabels(Idx_smallest,1);
toc;
end
even if I replace the nested for loop with this
[smallest_value,Idx_smallest] = min(sum(abs(bsxfun(@minus,ftest(:,idx),ftrain))));
it still takes roughly the same time, although this one doesn't calculate sqrt.
Is there other way to speed this up to about 0.2 secs per calculation?
I have a i7 6700k CPU sadly no Nvidia GPU, owning AMD GPU. Else I can use gpuarray to speed things up.
Any ideas guys?
Both matrices are type double, I've tried to use sparse double on the my original code, my computer hangs every time after it reaches maximum memory usage, had to restart. and Sparse double matrices actually takes longer to compute.
Update! I've tried convert both matrices into single precision, and it runs faster, average of 0.63 secs per calculation by using the formula below, which runs the fastest compare to others.
I still need it to run faster, preferably under 0.2 secs if that's possible.
for TrnIdx = 1 : Number_of_Train_Images
E_distance(TrnIdx) = norm(ftest(:,idx)-ftrain(:,TrnIdx));
end
% runs averagely of 0.63secs which is the best at the moment, after converting both matrices from double to single, double runs at 1.05secs
Walter Roberson on 31 Dec 2016
My testing with parfor and norm indicated it was about 7 times slower than a straight forward norm loop.

Ahmet Cecen on 30 Dec 2016
If you have the stats & ML toolbox:
NS = createns(M1'); % Create Search Object for The Train Set
Idx = knnsearch(NS,M2'); % Search Nearest Element of M1 for Each Element in M2
This should be lightning fast compared to your original code, probably would take around 20-30 minutes for the entire task. If you run out of memory, chunk the test matrix into smaller groups, and provide that as input, instead of looping over them one-by-one with i.
TYS on 31 Dec 2016
Thanks so much, now from from 4h30min+ to 38 minutes!!! Thanks so so much.

### More Answers (1)

Matt J on 30 Dec 2016
Edited: Matt J on 30 Dec 2016
You could try DNORM2( Download ), as applied to
E_distance = DNorm2( bsxfun(@minus,ftest(:,idx),ftrain) ,1) ; %Equation (*)
You could also try parallelizing the outer loop with parfor and maybe even the computation of E_distance as well (break ftrain into smaller parallel chunks and perform pieces of Equation (*) above on different workers).
Finally, if ftest and ftrain are type double, you might try moving to type single.
TYS on 31 Dec 2016
Edited: TYS on 31 Dec 2016
2.1 Secs using DNorm2. Running out of ideas now.