Higher order learning with graphs
ICML '06 Proceedings of the 23rd international conference on Machine learning
Spectral Embedding of Feature Hypergraphs
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Hypergraphs, Characteristic Polynomials and the Ihara Zeta Function
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Multi-way clustering using super-symmetric non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
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The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we propose a novel hypergraph characterization method by using the Ihara coefficients, i.e. the characteristic polynomial coefficients extracted from the Ihara zeta function. We investigate the flexibility of the Ihara coefficients for learning relational structures with different relational orders. Furthermore, we introduce an efficient method for computing the coefficients. 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 in the hypergraph Laplacian. In experiments we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.