Clustering by hypergraphs and dimensionality of cluster systems |
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Authors: | S Albeverio S V Kozyrev |
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Institution: | 1.University of Bonn,Bonn,Germany;2.Steklov Mathematical Institute,Moscow,Russia |
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Abstract: | In the present paper we discuss a new clustering procedure in the case where instead of a single metric we have a family of metrics. In this case we can obtain a partially ordered graph of clusters which is not necessarily a tree. We discuss a structure of a hypergraph above this graph. We propose two definitions of dimension for hyperedges of this hypergraph and show that for the multidimensional p-adic case both dimensions are reduced to the number of p-adic parameters.We discuss the application of the hypergraph clustering procedure to the construction of phylogenetic graphs in biology. In this case the dimension of a hyperedge will describe the number of sources of genetic diversity. |
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