Find Nearest Location in Two Matrix MATLAB

Question

I have two matrices:

A = [  76  159
      112  143
      153  159];

and

B = [  77   159
      114   143
      153   159
      173   236];

How can I get the nearest location with the result is the index of nearest location from another matrix without looping if possible.

For the above example, the result would look like this:

iA = 1 2 3;
iB = 1 2 3 3;

I have no idea what you are trying to achieve here. How dus iA and iB follow from A and B? — Bernhard, May 26 '15 at 11:32

Luis Mendo · Accepted Answer · 2015-05-26T13:59:49.437

4

You can compute the distances between pairs of rows using pdist2 (Statistics Toolbox), and then find the minimizing index along each dimension:

d = pdist2(A,B);     % // default is Euclidean distance. You can specify other metrics
[~, iB] = min(d);    % // arg min along each column
[~, iA] = min(d.');  %'// arg min along each row

If you don't have the Statistics Toolbx, you can replace pdist2 with bsxfun to compute squared Euclidean distance:

d = squeeze(sum(bsxfun(@minus, A, permute(B,[3 2 1])).^2, 2));

edited May 26 '15 at 13:59

answered May 26 '15 at 11:36

Luis Mendo

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@Adiel http://www.offbeatoregon.com/Images/H128-hank-vaughn/ppl-390319pmo-ralph-lee-hank-vaughan-gunfight-1500.gif :-D – Luis Mendo May 26 '15 at 11:43
ooh this is what i search, sorry but can you explain how pdist2 can get the value? i dont realy understand it – Brilian Aringga May 26 '15 at 11:45
oh and 1 more, what is (d.') mean? – Brilian Aringga May 26 '15 at 11:47
@LuisMendo I would prefer to keep it here in SO... :)) – Adiel May 26 '15 at 11:50
from documentation: `D = pdist2(X,Y) returns a matrix D containing the Euclidean distances between each pair of observations` – Adiel May 26 '15 at 12:09
2

@LuisMendo I think it would be good if you added that `pdist2` requires Statistics toolbox. – kkuilla May 26 '15 at 12:25
@BrilianAringga - `d.'` means to transpose the matrix `d`. Luis Mendo will argue with you that `d.'` is the proper way to transpose a matrix over `'` :). See a fruitful discussion here: http://stackoverflow.com/questions/25150027/using-transpose-versus-ctranspose-in-matlab – rayryeng May 26 '15 at 13:59
@rayryeng Exactly! :-D – Luis Mendo May 26 '15 at 14:00
@LuisMendo both results are giving different results.. could you check on that? – Santhan Salai May 26 '15 at 14:08
@SanthanSalai They give the same `iA` and `iB`. `d` in the second approach is `d.^2` in the first, to save time – Luis Mendo May 26 '15 at 14:14

Santhan Salai · Answer 2 · 2015-05-26T13:59:40.190

Using bsxfun, permute and calculating Euclidean distance based on native approach

This may not look elegant, but its very faster than pdist2 for small data sizes

d = sqrt(sum((bsxfun(@minus,permute(A,[1 3 2]),permute(B,[3 1 2]))).^2,3));

[~, iB] = min(d);    %// from Luis's answer
[~, iA] = min(d.');

Bechmarking (performed after warming up several times)

tic
out = sqrt(sum((bsxfun(@minus,permute(A,[1 3 2]),permute(B,[3 1 2]))).^2,3));
toc

tic
d = pdist2(A,B); 
toc

Elapsed time is 0.000080 seconds.
Elapsed time is 0.000453 seconds.

Bench Marking performed (using timeit())for Different data sizes of A keeping Datasize of B constant at 20.

enter image description here

Conclusion: pdist2 is significantly efficient with large datasizes while bsxfun+permute could be used for very small data sizes.

aah, this is what i need too, thank you for help, this is helping me so much too — Brilian Aringga, May 26 '15 at 14:47

Find Nearest Location in Two Matrix MATLAB

2 Answers2