How do I correlate elements from two different cell array files?

Dear community,

I have two cell array files. They are "distances_head_lefthand_windows" and "distances_head_righthand_windows".

They both look like this (in reality they are much larger with many more cells):

distances_head_lefthand_windows =

19×1 cell array

{512×54 double}

{512×50 double}

...

distances_head_righthand_windows =

19×1 cell array

{512×53 double}

{512×49 double}

...

Inside of each cell is a matrix with columns that are all 512 elements in length. What I want to do is correlate each of these columns with the matching column in the other file and save it in a cell array file called "correlations".

Example:

X1 = distances_head_lefthand_windows{1,1}(:,1);

Y1 = distances_head_righthand_windows{1,1}(:,1);

corr( X1 , Y1 )

X2 = distances_head_lefthand_windows{1,1}(:,2);

X2 = distances_head_righthand_windows{1,1}(:,2);

corr( X2 , Y2 )

... and so on.

Basically, I want to do that until all the columns in the cells of "distances_head_lefthand_windows" are correlated with all the columns of the cells in "distances_head_righthand_windows".

How would I do this?

(Sorry if this is overly complicated but I hope it makes sense. And sorry for the long names)

Thanks for your help!

[the cyclist]

A few clarifying questions:

For the first cell in left & right, you have a 512x54 and a 512x53. Do you want to ignore the last column in the "left" matrix? Is the "left" matrix always the one with more columns, and is it always exactly one more?

How do you want the output stored? Keeping with the same example of the first cell, it seems that you will generate 53 correlation coefficients. Do you want correlations{1} to be a 1x53 vector of those coefficents, or something else?

[lil brain]

Hi @the cyclist thanks for the response!

1) Yes I would like to ingnore the last column. And yes, the "left" matrix is always one column bigger.

2) And yes, the output, using that example, should ideally be a 1x53 vector with 53 columns. in correlations each cell represents a participant. And in that case each participant should ideally have a 1xn vector of coefficients.

Thanks!

Answer 1

[the cyclist]

This is done straightforwardly with loops. If this is fast enough, I would not bother trying to optimize for speed, since it is better to understand what the code is doing.

% Made up inputs. (Use your actual data instead, and rename everywhere)
L = {rand(4,3); rand(5,7)};
R = {rand(4,2); rand(5,6)};

% Preallocate memory for output
correlations = cell(size(L));

% Loop over each cell
for ncell = 1:size(L,1)

    % Define the number of correlation coefficients in this cell
    ncorr = size(R{ncell},2);
    
    % Preallocate the correlation vector
    correlations{ncell} = zeros(1,ncorr);

    % Loop over each pair of columns
    for ncoeff = 1:ncorr
        % Calculate the correlation coefficient
        correlations{ncell}(ncoeff) = corr(L{ncell}(:,ncoeff),R{ncell}(:,ncoeff));
    end

end

[lil brain]

Works like a charm! Thanks for the additional comments. Those make quite a difference.

[lil brain]

Speed is not too much of a issue here so no worries!