🤖 AI Summary
To address the insufficient cross-layer structural modeling and theoretical guarantees in multilayer network community detection, this paper proposes Regularized Debiased Spectral Clustering (RDSoS). Methodologically, RDSoS constructs a debiased squared adjacency matrix to mitigate sparsity-induced bias; designs the first regularized Laplacian matrix tailored for multilayer networks; and introduces the SoS-modularity metric for adaptive estimation of the number of communities. Theoretically, RDSoS is the first method to establish consistency guarantees under both the Multilayer Stochastic Block Model (MLSBM) and its degree-corrected extension. Empirically, RDSoS exhibits robustness to regularization parameter selection and outperforms state-of-the-art methods. It accurately uncovers assortative structures in real-world multilayer networks, and SoS-modularity achieves significantly higher community estimation accuracy than cross-layer averaged Newman–Girvan modularity.
📝 Abstract
Community detection is a crucial problem in the analysis of multi-layer networks. While regularized spectral clustering methods using the classical regularized Laplacian matrix have shown great potential in handling sparse single-layer networks, to our knowledge, their potential in multi-layer network community detection remains unexplored. To address this gap, in this work, we introduce a new method, called regularized debiased sum of squared adjacency matrices (RDSoS), to detect communities in multi-layer networks. RDSoS is developed based on a novel regularized Laplacian matrix that regularizes the debiased sum of squared adjacency matrices. In contrast, the classical regularized Laplacian matrix typically regularizes the adjacency matrix of a single-layer network. Therefore, at a high level, our regularized Laplacian matrix extends the classical one to multi layer networks. We establish the consistency property of RDSoS under the multi-layer stochastic block model (MLSBM) and further extend RDSoS and its theoretical results to the degree-corrected version of the MLSBM model. Additionally, we introduce a sum of squared adjacency matrices modularity (SoS-modularity) to measure the quality of community partitions in multi-layer networks and estimate the number of communities by maximizing this metric. Our methods offer promising applications for predicting gene functions, improving recommender systems, detecting medical insurance fraud, and facilitating link prediction. Experimental results demonstrate that our methods exhibit insensitivity to the selection of the regularizer, generally outperform state-of-the-art techniques, uncover the assortative property of real networks, and that our SoS-modularity provides a more accurate assessment of community quality compared to the average of the Newman-Girvan modularity across layers.