Totally Balanced Dissimilarities

We show in this paper a bijection between totally balanced hypergraphs and so-called totally balanced dissimilarities. We give an efficient way ( O ( n 3 ) where n is the number of elements) to (i) recognize if a given dissimilarity is totally balanced and (ii) approximate it if it is not the case. We also introduce a new kind of dissimilarity which generalizes chordal graphs and allows a polynomial number of clusters that can be easily computed and interpreted.

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