Variational graph filter autoencoder for uncovering community structure in multiplex networks

Multiplex networks can model multiple types of interaction relationships in the real-world complex systems, and community detection is one of important research topics for them. Variational bayes-based methods, known for their unsupervised learning capabilities, have become prominent in this field. Although low-pass filters, which are used in variational bayes methods, have proven to be beneficial for learning node representations in attributed networks, their weaknesses are highlighted when applied to multiplex networks. That is, low-pass filtering strategy results in node representations that are less discriminative across all network layers. Furthermore, a viable strategy is needed to extract associations information among the layers. To this end, this paper proposes a novel method based on variational bayes theory, named VGFA, for community detection in multiplex networks. Specifically, we design a general graph filter that adaptively fuses high-frequency and low-frequency signals. This filter is employed for variance inference, enabling node representations to incorporate layer distinctive structural information. Furthermore, we note that the attributes and community affiliations remain unchanged in multiplex networks. Based on these findings, we construct a K-Nearest Neighbors layer based on attribute similarity to explicitly extract homogeneity information from the network. In parallel, we introduce a shared Gaussian Mixture Model across layers to guide node representations at each layer to incorporate as much consistent community structure information as possible. The comprehensive experimental results on three benchmark multiplex networks validate that our method performs better in most cases. The code is available at https://github.com/GDM-SCNU/VGFA.