correlation for multi-dimensional arrays

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]

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

Answer 1

[David Young]

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]

Thank you so much David! Works like a charm and runs in no time.

[André Gadêlha]

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!

Answer 2

[Mustapha Adamu]

Dear David,

How do you go about this if you have nans,

Kind regards;

mustapha