MATLAB: One/zero Matrix, merge subset of columns

matrixmatrix manipulationvector

Say I have this matrix of ones and zeros, 10×6:
x= [    0	0	0	1	0	0
        0	1	1	1	1	1
        0	1	1	0	1	1
        0	0	0	0	0	0
        0	0	0	0	0	0
        1	0	0	0	0	0
        0	0	1	1	1	1
        0	0	0	0	0	1
        0	0	0	0	0	1
        0	0	0	0	1	1];
I would like to remove the columns that are a subset of any other column. For instance, column 2 is a subset of column 3 (because all ones in column 2 are in the same rows of column 3). Similarly column 3 is a subset of column 6, then columns 3 should be eliminated. At the end only the columns are not "subset" of other should remain only. So in the example, I should get:
0	1	0
0	1	1
0	0	1
0	0	0
0	0	0
1	0	0
0	1	1
0	0	1
0	0	1
0	0	1
The order of te columns is not importan, but the speed.
Any hint will be very much appreciatted. Thanks!

Best Answer

x0 = [  0,	0,	0,	1,	0,	0; ...
	0,	1,	1,	1,	1,	1; ...
	0,	1,	1,	0,	1,	1; ...
	0,	0,	0,	0,	0,	0; ...
	0,	0,	0,	0,	0,	0; ...
	1,	0,	0,	0,	0,	0; ...
	0,	0,	1,	1,	1,	1; ...
	0,	0,	0,	0,	0,	1; ...
	0,	0,	0,	0,	0,	1; ...
	0,	0,	0,	0,	1,	1];
% Save memory:
x = logical(x0);
for Iter = 1:2  % From left to right and right to left
    nCol = size(x, 2);
    del  = false(1, nCol);
    for iCol = 1:nCol
        col = x(:, iCol);
        for jCol = iCol + 1:nCol
            if all(and(col, x(:, jCol)) == col)
                del(iCol) = true;
                break
            end
        end
    end
    x(:, del) = [];
    x         = x(:, end:-1:1);  % Change order
end
Another apporach:
x    = logical(x0);  % Save memory
nCol = size(x, 2);
del  = false(1, nCol);
for iCol = 1:nCol
    if ~del(iCol)
        col = x(:, iCol);
        for jCol = iCol + 1:nCol
            if ~del(jCol)
                both = and(col, x(:, jCol));
                if all(both == x(:, jCol))
                    del(jCol) = true;
                elseif all(both == col)
                    del(iCol) = true;
                    break
                end
            end
        end
    end
end
x(:, del) = [];
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