MATLAB: Find unique sets of values in matrix, eliminate duplications

Question

I had a lot of trouble wording this Q succinctly and accurately. I have large matrices with a fixed # of rows but varying #s of columns. I want to identify which columns have identical sets of values in a small subset of rows, then eliminate all but one of the like columns using a criteria applied to values in another row, not part of the aforementioned subset [of rows.] For example, I have a matrix with 20 rows and N columns (20 x N). I want to identify the unique combinations of values in, say, rows 5 & 6, then save only the column that has the maximum value in row 3 from the subset having identical values in rows 5 & 6.

A=[8     7     4     8     4     2     1     9     8     6
   9     0     4     3     8     8    10     6     4     3
   1     9     8     5     6     3     0     4     2     7
   9     9     8     7     6     5     8     5     4     2
   6     7     2     9     9     2     8     4     1     7
   1     8     5    10     3     6     9     1     1     8
   3     7     5     6     8     3     1     2     9     4
   6     4     6     1     8     7     4     1    10     6
  10     7     7     2     4     7     3     2     6     8
  10     2     8     3     6     8     8     2     1     1
   2     7     3     8     1     5     4     4     2     9
  10     0     7     3     1     1     9     1     4     8
  10     3     7     8     5     2     2     9     8     5
   5     1     2     3     8     9     3     9     0     4
   8     1     1     9     9     2     2     5     1     5
   2     8     5     4     1     8     1     5     2     3
   4     7    10     2     6     5     9     3     7     5
   9     3     3     3     5    10     6     9     7     5
   8    10     6     6     0     1     6     4     7     8
  10     0     2     5     3     4     2     1     5     8];

In the above example, columns 2 & 10 have the same pair of values in rows 5 & 6: (7 & 8). I then want to eliminate the column(s) with the smaller value for row 3. In this case column 2 has the value 9 & column 10 has the value 7 so, I want to set A = A(:,1:9) or A(:,10) = []. I have tried using the unique function to identify pairs (sets, in general) of identical values [after transposing the matrix so I can work on rows] but I must not be using it properly. I assume I will use sortrows to sort the subsets in descending order (assuming my criteria is to save only the column with the max value in another row) – either before or after identifying like columns – and drop all but the max value-column.

Answer 1

r = [3;5;6];
B = A(r,:)';
[~,~,c] = unique(B(:,2:3),'rows','stable');
ii = find(histcounts(c,1:max(c)+1) > 1);
[lo,jj] = ismember(c,ii);
A(:,cell2mat(accumarray(jj(lo),find(lo),[],@(x){x(min(B(x,1))==B(x,1))}))) = [];