Find set intersection of multiple arrays in MATLAB

Question

I tried to solve this problem, but I could not implement. Could you help me anything for this?

Problem

Mat1 | Mat2 | Mat3

 1 2 | 1 3  |         


        

Answer 1

If I understand correctly, you have a number of sets of pairs: Mat1,Mat2, Mat3, ... MatN. Now you want to find the unique pairs and then find out in which set every unique pair appears.

If you have a large number of sets, I suggest you start using a cell array to hold them all, makes things a lot easier:

N = 3; % total number of data sets
Mat = cell(N,1);
Mat{1} = [1 2;
          1 3;
          2 4;
          3 1;
          4 5];
Mat{2} = [1 3;
          2 6;
          3 1;
          3 5];
Mat{3} = [2 6;
          2 5;
          3 1;
          5 2];
% etc.

First let's find the unique pairs:

uniq_pairs = unique(cat(1,Mat{:}),'rows');
M = size(uniq_pairs ,1);

Then use ismember to check which sets contain which pairs:

matcontpair = false(M,N); %preallocate
for ii=1:N % unavoidable loop
    matcontpair(:,ii) = ismember(uniq_pairs,Mat{ii},'rows');
end

To translate this intersection matrix to a set of matrix numbers for each pair, loop through it again and store the final result in a cell array (you can't use an array, because they might not be of same size (some pairs only found once, other twice, other three times ...)

pair_occurence= cell(M,1);
d=1:N;
for jj=1:M
    pair_occurence{jj} = d(matcontpair(jj,:));
end

Now you have a matrix uniq_pairs of size Mx2 containing the unique pairs, and a occurence cell array pair_occurence of size Mx1: each cell corresponds to a pair and contains a list of matrices where the pair is present.

If you want to remove pairs from the list which are only present in one matrix, use the following:

% find them
lonely_pairs = cellfun(@numel,pair_occurence)<2;
% and destroy them
uniq_pairs(lonely_pairs,:) = [];
pair_occurence(lonely_pairs) = [];