MATLAB Answers

## correlation for multi-dimensional arrays

Asked by Niko

### Niko (view profile)

on 14 Sep 2011
Latest activity Answered by Mustapha Adamu

### Mustapha Adamu (view profile)

on 10 Dec 2018
Accepted Answer by David Young

### David Young (view profile)

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!

Raj

### Raj (view profile)

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

Sign in to comment.

## 2 Answers

Answer by David Young

### David Young (view profile)

on 15 Sep 2011
Accepted Answer

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));

Niko

### Niko (view profile)

on 15 Sep 2011
Thank you so much David! Works like a charm and runs in no time.
André Gadêlha

### André Gadêlha (view profile)

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!

Sign in to comment.

Answer by Mustapha Adamu

### Mustapha Adamu (view profile)

on 10 Dec 2018

Dear David,
How do you go about this if you have nans,
Kind regards;
mustapha

#### 0 Comments

Sign in to comment.