Count unique combinations of elements in a 3D matrix

Hi all,

I was wondering if there was a way to count a unique combination of numbers within a 3D Matrix. The best way I can describe this is with an example:

Suppose I have a 3D Matrix which is laid out as such

A(:,:,1)
1 2
3 1
A(:,:,2)
1 2
3 1
A(:,:,3)
1 3
3 1

So if I wanted to know the count of the combination (1,1,1) it would be 2, as the combination of the 3 numbers (1, 1, 1) appears twice in the matrix, once at (1,1,:) and once at (2,1,:). Another example might be, if I wanted to know the count of (3,3,3) within the matrix, it would be 1, as the combination only appears once in the matrix, at (2,1,:)

I hope I explained this well. Again, I'd like the count of these unique combinations, rather than any indexing information. I've tried count and/or sum as well as unique, but they did not give me the results I've hoped for, however I probably utilized them wrong

A loop of this, so that I could get the counts of all unique combinations of the elements would also be much appreciated, but I understand if this is harder.

This is my first time posting so I apologize if this isn't formulated right.

Thanks in advance for any help you can give!

Answer 1

[Star Strider]

The only way I can see to do this is first to reshape ‘A’ and then use the unique function on the resulting rows, and do the counting with accumarray:

A(:,:,1) = [...
1 2
3 1];
A(:,:,2) = [...
1 2
3 1];
A(:,:,3) = [...
1 3
3 1];

Ar = reshape(A, [],3);
[Aru,~,ix] = unique(Ar,'rows','stable') 
Count = accumarray(ix,1);
Out = [Aru, Count]

producing:

Out = 
     1     1     1     2
     3     3     3     1
     2     2     3     1

I am not certain how robust this approach would be for other matrices, or for other matrices with additional dimensions.

[Adam Danz]

My solution was very similiar to Star Strider's,

A(:,:,1) = [1 2
    3 1];
A(:,:,2) = [1 2
    3 1];
A(:,:,3) = [1 3
    3 1];


Am = reshape(A,[],3);
[AmUnq, ~, group] = unique(Am,'rows','stable'); 
T = table(AmUnq, groupcounts(group), 'VariableNames', {'UniqueSeq','Counts'})

T = 3×2 table
     UniqueSeq     Counts
    ___________    ______

    1    1    1      2   
    3    3    3      1   
    2    2    3      1   

[Tommy Carter]

Hi both,

These answers work great, thank you so much!

I was curious if either of you know how to reverse index the resulting Aru matrix from your answers?

I want to be able to access the Count for a given row combination in Aru.

In essence, if I want to find the count of the combination 3,3,3 (which is 1) i could search something like :

idx = idx(Aru where each col is 3);

and then use that index to search through Count:

myAnswer = Count(idx,1);

Hope I explained that well,

Thanks so much, you've been a great help.

[Star Strider]

My pleasure!

Try this:

[~,idx2] = ismember([3 3 3], Aru, 'rows');                      % Row # In ‘Aru’
MyAnswer = Count(idx2);                                         % Corresponding Value Of ‘Count’

.

[Tommy Carter]

Thanks, these both work fab!

[Star Strider]

As always, my pleasure!