Question

For example [2 , 5] dominates [3 , 8] cause (2 < 3) and (5 < 8)

but [2 , 5] does not dominates [3 , 1] cause though (2 < 3) but (5 > 1) so these two vectors are non dominated

now for example assume that I have a matrix like this :

a =[ 1 8;
    2 6;
    3 5;
    4 6];

here the first three are non dominated but the last one is dominated by (3,5), I need a code which can omit it and give me this output:

ans =

    [ 1 8;
    2 6;
    3 5]

note that there may be lots of non dominated elements in a Nx2 matrix

Answer 1

1. Compare one row with other rows using bsxfun
2. Do this for every row using arrayfun (or a loop if you prefer that) and transform the output back to a matrix with cell2mat
3. use any and all to check which rows are dominated
4. remove these rows

code:

a=[1 8;2 6;3 5;4 6];
dominated_idxs = any(cell2mat(arrayfun(@(ii) all(bsxfun(@(x,y) x>y,a,a(ii,:)),2),1:size(a,1),'uni',false)),2);

a(dominated_idxs,:) = [];

edit

If you want to use >= instead of > comparison, each row will dominate itself and will be removed, so you’ll end up with an empty matrix. Filter these false-positives out by adjusting the code as follows:

a=[1 8;2 6;3 5;4 6];
N = size(a,1);

compare_matrix = cell2mat(arrayfun(@(ii) all(bsxfun(@(x,y) x>=y,a,a(ii,:)),2),1:N,'uni',false));
compare_matrix(1:N+1:N^2)=false; % set diagonal to false
dominated_idxs = any(compare_matrix,2);

a(dominated_idxs ,:) = [];