Dual-learning Multi-hop Nonnegative Matrix Factorization for community detection.

As an important branch of network science, community detection has garnered significant attention. Among various community detection methods, nonnegative matrix factorization (NMF)-based community detection approaches have become a popular research topic. However, most NMF-based methods overlook the network's multi-hop information, let alone the community detection results specific to each hop of the network. In this paper, we propose Dual-learning Multi-hop NMF (DL-MHNMF), a method that considers not only the multi-hop connectivity between two nodes but also factors in the shared results across multiple hops and the impact of differences in the specific results at each hop on the shared outcomes. An efficient iterative optimization algorithm with guaranteed theoretical convergence is proposed for solving DL-MHNMF. Methodologically, by iteratively removing the specific results during the optimization process of DL-MHNMF, we achieve enhanced detection accuracy, which is also verified by subsequent experiments. Specifically, we compare fourteen algorithms on eleven publicly available datasets, and experimental results show that our algorithm outperforms most state-of-the-art methods. The source code is availiable at https://github.com/bx20000827/DL-MHNMF.git.