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arXiv · 1204.5952

Clustering by hypergraphs and dimensionality of cluster systems

S. Albeverio·S. V. Kozyrev
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Abstract

In the present paper we discuss the 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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S. Albeverio, S. V. Kozyrev. 2012-04-26. Clustering by hypergraphs and dimensionality of cluster systems. https://arxiv.org/abs/1204.5952

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