I have a random array of 10000 7-letter strings. I have a simple algorithm that assesses how similar each element is to all others. For example, SESTINA and SESTINE would have a high similarity, but ZYZZYVA and NEROLIS would have low similarity. The result is a 10000x10000 symetric matrix.
I want to group/sort the strings based on similarity, where proximity of similar strings is important and order is irrelevant. The higher the similarity of two strings, the more important it is for them to be together. I've imagined some sort of least squares technique?
Anyone have a clue for me?
EDIT: The end goal is a 1d array, and not looking for a graphic solution.
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Your problem looks like a variation of the Traveling Salesman Problem where the strings play the role of the "cities" with distances between them defined by your 10000x10000 similarity matrix. The TSP is NP-hard, so I don't know how much hope you have of solving it rapidly for 10000 cities. However, there are a number of different TSP solvers offered on the FEX which you could look at. The following one looks more relevant to you than some since it doesn't require a return to the starting point
There are probably also some hard-core optimized non-MATLAB TSP sovers out there somewhere.
Another thing that might help is to try to optimize the way you initialize your current algorithm. If anagrams have lower separation distances than substitutions, for example, I would expect that doing a dictionary sort, but one which groups anagrams together, would provide a pretty good initial guess, e.g.,
AA AB BA AC CA BB BC CB CC