Hi

I'm struggling with something that is probably trivially taken care of by the math community, but I don't know where to start!

Given a symmetric matrix, namely a correlation matrix but any would do. I am looking for an algorithm to cluster the elements of the matrix just with permutations, while keeping the symmetry of the matrix.

What I mean by "clustering the elements of the matrix" is moving the higher number of the matrix close together and do the same with the lower numbers.

Regarding the use of "permutations respecting the matrix symmetry", I mean that if you exchange column i (resp. row i) with column j (row j), you have to permute row i (resp. column i) with row j (column j) so that the symmetry of the matrix is respected.

The reason behind this problem is a bit superficial actually. When you get a correlation matrix you obviously look for the the highest (in absolute value) coefficients and a good way to do it is to "heat map" the matrix. And what you get is a patchwork of various colours scattered on your map! What I would like is to "get the colours together" to make the map much more readable without losing the symmetry of the map - it needs to stay a correlation matrix after all.

Thanks