GHOC: A generative model for hybrid-order community detection

Recently, hybrid-order community detection has been proposed for addressing the hypergraph fragmentation issue suffered by the motif-based higher-order community detection. However, the existing attempts of hybrid-order community detection inadvertently damage the lower-order connectivity pattern and the higher-order connectivity pattern when constructing the fusion model. Additionally, like the higher-order community detection approaches, they also adopt a two-phase strategy that separately applies the existing graph node clustering methods to the proximity matrix derived from the lower-order connectivity pattern and the higher-order connectivity pattern. Therefore, the higher-order connectivity pattern is only utilized for constructing proximity matrix and hence has no direct effect on the final community results. In this paper, to address the above issues, we propose a Generative model for Hybrid-Order Community detection (GHOC). The main idea lies in defining a likelihood function of a generative model that finds the optimal community membership strength vectors of nodes, based on which the original lower-order connectivity pattern and the higher-order connectivity pattern can be directly reconstructed simultaneously. From the community membership strength vectors, the final community structure can be derived. Extensive experiments have been conducted on several data sets, and the results have confirmed the superiority of the proposed GHOC method.