Find the best combination of each pair of entries in a matrix
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Hello, I would like to find the best combination (max probability)of each (row, column) pair in my probability matrix, such that I shall get at the end each row is associated with only one column , in other words a bijection. here is an example to clarify more the task:
my_Probability_Matrix =[0.0192 0.0152 0.0246 0.0235;
0.2521 0.0135 0.475 0.0278;
0.0141 0.0175 0.0257 0.106;
0.0226 0.0026 0.0155 0.0165];
and I should get the following combinations: Best_Probabilities(row,column)={(1,2);(2,3);(3,4);(4,1)} any ideas how to implement this without too many iterations?! Thank you!
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Roger Stafford
2016-3-18
The number of possible bijections for an n-by-n matrix, M, would be n factorial. Use 'perms' to generate all possible permutations of 1:n and for each, compute the corresponding product from your matrix.
P = perms(1:n);
q = zeros(size(P,1),1);
for k = 1:size(P,1)
q(k) = prod(M((1:n)+n*(P(k,:)-1)));
end
[~,b] = max(q);
Your best combination is then P(b,:);
3 个评论
Roger Stafford
2016-3-24
编辑:Roger Stafford
2016-3-24
It's the standard formula used to transform subscripts into linear indices in Matlab. In the case of a two-dimensional matrix, 'M', if 'ix' is the row (first) subscript and 'iy' the column (second) subscript, and if there are 'n' rows, then the corresponding linear index is:
L = ix + n*(iy-1)
The element M(ix,iy) is equally well referenced by just M(L).
In the case of (1:n)+n*(P(k,:)-1) it is an entire vector of subscript pairs that is being transformed into a corresponding vector of linear indices:
[1+n*(P(k,1)-1) , 2+n*(P(k,2)-1) , 3+n*(P(k,3)-1) , ... ]
See
http://www.mathworks.com/help/matlab/ref/ind2sub.html
and
http://www.mathworks.com/help/matlab/ref/sub2ind.html
for an explanation of the correspondence between subscripts and linear indices.
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Guillaume
2016-3-18
I'm not sure I've understood your question correctly since for me the highest value in the first row is column 3, but if I have, then:
[~, col] = max(my_Probability_Matrix, [], 2); %position of the max in each row
Best_Probabilities = [(1:size(my_Probability_Matrix, 1))', col]
2 个评论
Guillaume
2016-3-18
Yes, as I said, I don't understand why you've selected (1, 2) for the first pair. Can you explain what the criteria for choosing pairs is.
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