how to get the intersection of many different length cell vectors in matlab

Question

I have n different length cell vectors, call it c{i}, i=1,2,...,n.

I wanna know if there any c{j} is the subset of c{i}, for example:

c{1}=[1 2 3 4 5 6]; c{2}=[1 3 5 7];c{3}=[2 4 6 8];
c{4}=[1 4 6];c{5}=[3 7];

then I hope I can find that c{4} is subset of c{1}, c{5} is subset of c{2}.

I used two for loops with intersect function can process it, but I hope I can use at most one loop to process it, is there any way can achieve it?

Answer 1

Building on the other answers, you can also use ismember:

sets = {[1 2 3 4 5 6], [1 3 5 7], [2 4 6 8], [1 4 6], [3 7]};

N = numel(sets);          % number of sets
idx = nchoosek(1:N,2);    % indices of combinations
subsets = false(N,N);
for i = 1:size(idx,1)
    a = idx(i,1); b = idx(i,2);

    % check that set A is a subset of B, and the other way around as well
    subsets(a,b) = all(ismember(sets{a},sets{b}));
    subsets(b,a) = all(ismember(sets{b},sets{a}));
end

We get a logical matrix:

>> subsets
subsets =
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     1     0     0     0     0
     0     1     0     0     0

where non-zeros indicate subset relationship:

>> [i,j] = find(subsets)
i =
     4
     5
j =
     1
     2

i.e c{4} is a subset of c{1}, and c{5} is a subset of c{2}

Note: it is obvious that any set is a subset of itself, so the diagonals of subsets matrix should also be made 1. You could add that if you want using:

subsets(1:N+1:end) = true;