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On Clustering Detection Based on a Quadratic Program in Hypergraphs

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  • Qingsong Tang

Abstract

A proper cluster is usually defined as maximally coherent groups from a set of objects using pairwise or more complicated similarities. In general hypergraphs, clustering problem refers to extraction of subhypergraphs with a higher internal density, for instance, maximal cliques in hypergraphs. The determination of clustering structure within hypergraphs is a significant problem in the area of data mining. Various works of detecting clusters on graphs and uniform hypergraphs have been published in the past decades. Recently, it has been shown that the maximum {1,2}‐clique size in {1,2}‐hypergraphs is related to the global maxima of a certain quadratic program based on the structure of the given nonuniform hypergraphs. In this paper, we first extend this result to relate strict local maxima of this program to certain maximal cliques including 2‐cliques or {1,2}‐cliques. We also explore the connection between edge‐weighted clusters and strictly local optimum solutions of a class of polynomials resulting from nonuniform {1,2}‐hypergraphs.

Suggested Citation

  • Qingsong Tang, 2022. "On Clustering Detection Based on a Quadratic Program in Hypergraphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4840964
    DOI: 10.1155/2022/4840964
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    References listed on IDEAS

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    1. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
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