Community detection in multiplex networks by deep structure-preserving non-negative matrix factorization - Zhou, Qinli; Zhu, Wenjie; Chen, Hao; Peng, Bo (Applied intelligence (Dordrecht, Netherlands), 2025)
Multiplex networks convey more valuable information than single-layer networks; thus, performing the community detection task involving these networks has become a subject of extensive research on the exploration of latent community structures. The non-negative matrix factorization (NMF) algorithm has proven successful in community detection scenarios by offering good interpretations of community structures. However, directly obtaining consensus community assignments using the traditional NMF algorithm poses a challenge due to the presence of complex structures spanning across different layers in the multiplex network. In this paper, we propose a novel algorithm called Deep Structure-Preserving Non-negative Matrix Factorization (DSP-NMF) to perform community detection in multiplex networks. Specifically, DSP-NMF constructs a deep autoencoder-like NMF model to generate meaningful network embeddings that are represented by multiple basis matrices and reconstructed by corresponding transposed basis matrices. By integrating the similarity relationships of nodes into the proposed DSP-NMF algorithm, the corresponding Laplacian matrices in each network layer are regularized to preserve the community structure during the learning process. Simultaneously, a consensus network embedding can be learned to obtain the final community partition. In this manner, the proposed DSP-NMF algorithm not only uncovers robust community structures in multiplex networks but also maintains the coherence between layers without losing complementary features. The experimental results obtained on five multiplex network datasets show that our proposed DSP-NMF algorithm outperforms other competitive methods in community detection tasks involving multiplex networks.