Nonnegative matrix factorization with mixed hypergraph regularization for community detection

Community structure is the most significant attribute of networks, which is often identified to help discover the underlying organization of networks. Currently, nonnegative matrix factorization (NMF) based community detection method makes use of the related topology information and assumes that networks are able to be projected onto a latent low-dimensional space, in which the nodes can be efficiently clustered. In this paper, we propose a novel framework named mixed hypergraph regularized nonnegative matrix factorization (MHGNMF), which takes higher-order information among the nodes into consideration to enhance the clustering performance. The hypergraph regularization term forces the nodes within the identical hyperedge to be projected onto the same latent subspace, so that a more discriminative representation is achieved. In the proposed framework, we generate a set of hyperedges by mixing two kinds of neighbors for each centroid, which makes full use of topological connection information and structural similarity information. By testing on two artificial benchmarks and eight real-world networks, the proposed framework demonstrates better detection results than the other state-of-the-art methods.