Grouping matched data by row and column

I have a matrix attached, Rows_col.mat. This gives the Row and column of some other matrix that has matched a condition I have imposed. So for example, 6 has matched with 1, 19 has matched with 7. However there are occasions where there are more matches, for example 9 has matched with 3, but 17 has also matched with 3. In this instance I would like the output to be [9, 17, 3] (the order is not important). I think the output in a cell array would be the most suitable since there is a varying matrix column size for each "match". I hope this is clear, This for example would be the desired output:

[6,1];[9,3,17 (any order would be fine)];[19,7];[15,10,23];[12,11,18];[21,13];[20,14], this would be a 7x1 cell.

Thankyou.

[Matlab User]

So far I have something like this

D=accumarray(Rows_col_(:,1),Rows_col_(:,2),[],@(v){v});

However this doesnt give me the desired outcome!!

[Guillaume]

In your example you have several rows matching the same column. Could you also have several columns matching the same row, i.e:

6   1
6   2

Or even a mixture of two:

6  1
6  2
5  2

which would give a permutation of [1 2 5 6]?

In your output example of [9 3 17] are you sure you don't care anymore if a number comes from a row or column?

[Matlab User]

I'm not sure that my explanation was good enough. I would like, for example you see in my matrix that there is a [9, 3] pair and also a [17, 3]. They both share a common value, 3, so I would like to concatenate the elements, so now [9,3,17] are all in one. When it comes to the order, I meant that it would be fine to have [3 9 17],[9 ,3,17 ],[17,3,9]...ETC, so long as all three (in this case) elements are there.

Answer 1

[Guillaume]

I don't think that there is any other way than using loops to solve this. This works:

Rows_col_ = [6 1; 9 3; 17 3; 19 7; 17 9; 15 10; 23 10; 12 11; 18 11; 18 12; 21 13; 20 14; 23 15];
sequences = {};
for row = Rows_col_'  %iterate over the rows of Rows_Cols
   hascommonvalue = cellfun(@(s) any(ismember(row, s)), sequences); %check if current row has any value common to a stored sequence
   if any(hascommonvalue)
      %current row has a common value with one or more sequence already stored, group all together
      newmatch = unique([sequences{hascommonvalue}, row']); %concatenate all matching sequences and current row
      sequences(hascommonvalue) = []; %remove matching sequences since they've been concatenated as a new sequence
      sequences{end+1} = newmatch; %and add new sequence
   else
      %current did not match any previous sequence, add as new
      sequences{end+1} = row';
   end
end

[Matlab User]

Thankyou, I was trying to avoid loops but this works very well so thanks again.