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correlation for multi-dimensional arrays

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Niko
Niko on 14 Sep 2011
Answered: Mustapha Adamu on 10 Dec 2018
Hi everyone,
I need to compute correlation coefficients - lots of them. I have two three-dimensional arrays (frequency x time x observations) and I want to compute correlations between the two arrays along the third dimension. The result I need is a two-dimensional array of correlation coefficients (frequency x time). If I understand the corr function correctly, corr is only for column vectors. If I loop over my other two dimensions, I can of course compute the correlation for each time-frequency point separately, but this is very slow.
Is there a way to compute correlation coefficients for multi-dimensional arrays along an arbitrary dimension, or any other way to speed up the computation of correlations?
Thanks!

  1 Comment

Raj
Raj on 27 Aug 2014
Can you please provide formulas (math models) for the multi-dimensional correlation?

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Accepted Answer

David Young
David Young on 15 Sep 2011
If you don't have NaNs in the data, and you want the standard Pearson coefficient, then you could try applying the formula for correlation directly, like this:
% Synthetic data for testing
a = rand(10, 10, 100);
b = rand(10, 10, 100);
b(1, 1, :) = 3 * a(1, 1, :) - 2; % r(1,1) should be + 1;
b(1, 2, :) = -17 * a(1, 2, :) + 8; % r(1,2) should be - 1;
% rest of r should be random between +1 and -1
% Compute correlations on third dimension
% Remove means
az = bsxfun(@minus, a, mean(a,3));
bz = bsxfun(@minus, b, mean(b,3));
% Standard Pearson correlation coefficient formula
a2 = az .^ 2;
b2 = bz .^ 2;
ab = az .* bz;
r = sum(ab, 3) ./ sqrt(sum(a2, 3) .* sum(b2, 3));

  2 Comments

Niko
Niko on 15 Sep 2011
Thank you so much David! Works like a charm and runs in no time.
André Gadêlha
André Gadêlha on 10 Oct 2017
Dear David Young,
.
Why did you use this formulas to calculate the correlation:
.
b(1, 1, :) = 3 * a(1, 1, :) - 2; % r(1,1) should be + 1;
b(1, 2, :) = -17 * a(1, 2, :) + 8; % r(1,2) should be - 1;
.
and why did you removed means?
.
Best Regards!

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More Answers (1)

Mustapha Adamu
Mustapha Adamu on 10 Dec 2018
Dear David,
How do you go about this if you have nans,
Kind regards;
mustapha

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