Compute Average Matrix from Cell Array of Matrices

I have a cell array of matrices of different sizes and constant length:

ABC = [(122x21) (124x21) (117x21)....]

I would like to create a new matrix, where each element contains the average of each element from each of my array matrices.

NewMat = (124x21)

where element (1,1) = mean of all of the 1,1 elements in my primary matrices element (1,2) = the mean of all of the 1,2 elements in my primary matrices

Edited to upload starting cell array

[Azzi Abdelmalek]

your matrices are not the same size

[Guillaume]

Please show a concrete example, so we can understand what you want to do.

For example, given:

ABC = {[1 2;3 4;5 6; 7 8], [10 11; 12 13], [20 21; 22 23; 24 25]};

What would NewMat be?

[Thorsten]

How are missing values treated? In your example, if there is only a single value for 124, 21, say 8. Would you like the mean to be 8 or mean([0 8 0])=8/3?

[Mat]

Thorsten.... Would like the mean to be 8... Thanks.

Trying to incorporate your proposed code into my own atm, some teething issues. Also for Anzi's

[Thorsten]

Then you need to modify Azzi's solution, I think, that would return 8/3 in the above example.

Answer 1

[Azzi Abdelmalek]

If you fill your missing data with zeros

a={rand(122,21), rand(124,21) , rand(117,21)} % Example
n=max(cellfun(@(x)  size(x,1),a))
b=cellfun(@(x) [x ; zeros(n-size(x,1),21)],a,'un',0)
out=mean(cat(3,b{:}),3)

[Mat]

HI Azzi, thanks, I have some trouble converting into my script... supplied additional info below...

Error received is

??? Error using ==> vertcat CAT arguments dimensions are not consistent.

Error in ==> run>@(x)[x;zeros(n-size(x,1),21)]

Error in ==> FindGoldenBatchesAz at 23 b=cellfun(@(x) [x ; zeros(n-size(x,1),21)],ABC2,'un',0)

Error in ==> run at 57 evalin('caller', [s ';']);

Answer 2

[Thorsten]

The idea is to create a 124x21xN matrix 'Anew' with missing values filled with NaNs, and then take the nanmean along the third dimension of 'Anew':

 A = {rand(122,21), rand(124,21),  rand(117,21)};
[nrows ncols] = cellfun(@size, A);
if any(ncols - 21)
  error('Not all arrays have 21 columns.')
end
maxrows = max(nrows);
for i = 1:numel(A)
  X = A{i};
  if size(X, 1) < maxrows
    X(maxrows, 21) = NaN;
  end
  Anew(:,:,i) = X;
end
M = nanmean(Anew, 3);

[Mat]

??? Conversion to cell from double is not possible.

Error in ==> FindGoldenBatches at 30 X(maxrows, 21) = 0;

I get this error when converting into my code, I've posted below for further details on my data that might be the issue.

Answer 3

[Guillaume]

You don't have a cell array of matrices, but a cell array of cell arrays that should be matrices:

This will work (based on Azzi's answer):

maxrows = max(cellfun(@(c) size(c, 1), ABC3));
numcols = cellfun(@(c) size(c, 2), ABC3);
assert(all(diff(numcols) == 0)) %just make sure
resized = cellfun(@(c) [cell2mat(c); NaN(maxrows-size(c, 1), numcols(1))], ABC3, 'UniformOutput', false);
out = nanmean(cat(3, resized{:}), 3)

[Mat]

BIG thanks!!

See, I had tried to ensure ABC3 was cell array of matrices using ABC4=cell2mat(ABC3)

This returned an error so I assumed it wouldn't work.

I am trying to see how this code works around that- any pointers or advice much appreciated!

[Guillaume]

ABC4 = cellfun(@(c) cell2mat(c), 'UniformOutput', false);

It's the individual cells in the main cell array that you want to convert to matrices, not the main cell array.

My code does just the above ( cell2mat) when it comes to resize the matrix to match the maximum height.

Answer 4

[Mat]

Both of these codes work great, but am struggling to fit both to my code.

Matrices in my array will have strings in the first two columns. E.g.

Timestamp   ID   Var1    Var2   Var3   Var4

Could this be impacting when I try to use on my own code?

[Thorsten]

You should get rid of the first two columns in my example when you create the Anew matrix.

[Mat]

I've done this, but still can't get either working... I'm loading my ABC matrix so that folk can have a closer look.

Racked my brains on this and can't see where the difference is between my cell array and the ones you've provided in the examples; I'm clearly missing something though