Count all pairwise interactions in a matrix

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Luis Cascao
Luis Cascao 2023-4-23
评论： Luis Cascao 2023-4-23
Suppose I have the following matrix:
[23 51 42; 42 23 18]
how can I count all pairwise terms occurring per row where order is not important? In this case, for row 1 the pairwise terms are (23,51),(23,42),(42,51) and for the second row (23,42),(18,42),(18,23).
Therefore the answer is:
{(23,51),1}, {(23,42),2}, {(42,51),1}, {(18,42),1}, {(18,23),1}
Many thanks

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采纳的回答

John D'Errico
John D'Errico 2023-4-23
编辑：John D'Errico 2023-4-23
Ran in:
If you have only one row, then it is trivial. Just use nchoosek.
Row = [2 3 5 7];
Row(nchoosek(1:4,2))
ans = 6×2
2 3 2 5 2 7 3 5 3 7 5 7
But you have multiple rows. We can still use nchoosek. But now we need to be a little more creative. For example:
Rows = [1 2 4 8;2 3 5 7]
Rows = 2×4
1 2 4 8 2 3 5 7
[nrows,ncols] = size(Rows);
combs = nchoosek(ncols,2)
combs = 6
permute(reshape(Rows(:,nchoosek(1:ncols,2)),nrows,combs,2),[2 3 1])
ans =
ans(:,:,1) = 1 2 1 4 1 8 2 4 2 8 4 8 ans(:,:,2) = 2 3 2 5 2 7 3 5 3 7 5 7
The result is a 3-dimensional array, as it arguably should be.
As you can see, no loops were needed.

更多回答（1 个）

LeoAiE
LeoAiE 2023-4-23
Hi,
great question! Here is my attempt to solve this problem and if you find it helpful please accept the answer.. Thanks
% Input matrix
matrix = [23 51 42; 42 23 18];
% Number of rows
nrows = size(matrix, 1);
% Initialize an empty cell array to store the result
pairwise_terms = {};
% Iterate through each row
for row = 1:nrows
% Get all unique pairs in the current row
pairs = nchoosek(matrix(row, :), 2);
% Iterate through each pair
for i = 1:size(pairs, 1)
% Sort the pair to ignore order
sorted_pair = sort(pairs(i, :));
if isempty(pairwise_terms)
% If pairwise_terms is empty, add the first pair with a count of 1
pairwise_terms(end + 1, :) = {sorted_pair, 1};
else
% Create a logical index array to check if the sorted_pair exists in pairwise_terms
logical_index = cellfun(@(x) isequal(x, sorted_pair), pairwise_terms(:, 1));
% Find the index of the existing pair in pairwise_terms
idx = find(logical_index, 1);
if isempty(idx)
% If the pair does not exist, add it to pairwise_terms with a count of 1
pairwise_terms(end + 1, :) = {sorted_pair, 1};
else
% If the pair exists, increment the count
pairwise_terms{idx, 2} = pairwise_terms{idx, 2} + 1;
end
end
end
end
% Display the result
pairwise_terms

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