Clustering by hypergraphs and dimensionality of cluster systems

TL;DR

This paper explores hypergraph-based clustering with multiple metrics, introduces hyperedge dimension definitions, and applies the approach to phylogenetic graph construction, linking hyperedge dimension to genetic diversity sources.

Contribution

It introduces a hypergraph clustering framework with new hyperedge dimension concepts and demonstrates their application to biological phylogenetic analysis.

Findings

Hypergraph clustering extends traditional tree-based methods.

Hyperedge dimensions relate to p-adic parameters in multidimensional cases.

Application to biology links hyperedge dimension to genetic diversity sources.

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.