PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A polynomial characterization of hypergraphs using the Ihara zeta function
Peng Ren, Tatjana Aleksić, Edwin Hancock and Richard Wilson
Pattern Recognition 2011.

Abstract

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we develop a polynomial characterization for hypergraphs based on the Ihara zeta function. We investigate the flexibility of the polynomial coefficients for learning relational structures with different relational orders. Furthermore, we develop an efficient method for computing the coefficient set. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity if the hypergraph Laplacian is used. In our experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Machine Vision
Learning/Statistics & Optimisation
ID Code:7391
Deposited By:Edwin Hancock
Deposited On:17 March 2011