Rethinking Variational Bayes in Community Detection from Graph Signal Perspective

Methods based on variational bayes theory are widely used to detect community structures in networks. In recent years, many related methods have emerged that provide valuable insights into variational bayes theory. Remarkably, a fundamental assumption remains incomprehensible. Variational bayes-based methods typically employ a posterior distribution that follows a gaussian distribution to approximate the unknown prior distribution. However, the complexity and irregularity of node distributions in real-world networks prompt us to consider what characteristics of network information are suitable for the posterior distribution. Mathematically, inappropriate low- and high-frequency signals in expectation inference and variance inference can intensify the adverse effects of community distortion and ambiguity. To analysis these two phenomena and propose reasonable countermeasures, we conduct an empirical study. It is found that appropriately compressing low-frequency signals during expectation inference and amplifying high-frequency signals during variance inference are effective strategies. Based on these two strategies, this paper proposes a novel variational bayes plug-in, namely VBPG, to boost the performance of existing variational bayes-based community detection methods. Specifically, we modulate the frequency signals during expectation and variance inference to generate a new gaussian distribution. This strategy improves the fitting accuracy between the posterior distribution and the unknown true distribution without altering the modules of existing methods. The comprehensive experimental results validate that methods using VBPG achieve competitive performance improvements in most cases. The code is available at https://github.com/GDM-SCNU/VBPG.