arXiv Machine Learning By Zhongyuan Lyu, Ting Li, Dong Xia

Optimal Clustering of Multi-layer Networks under Mixture Block Models

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The paper investigates clustering of multi‑layer networks generated under a mixture multi‑layer stochastic block model (MMSBM). It derives the minimax optimal clustering error rate, expressed via Chernoff information between component edge‑probability distributions, and introduces a two‑stage estimator that achieves this rate even under extreme sparsity. The method is extended to count‑weighted networks using a mixture multi‑layer Poisson block model, with numerical experiments and real‑data analyses demonstrating its practical performance.

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arXiv Machine Learning
Oct 3

Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection

The paper introduces a degree‑corrected joint matrix factorization technique for detecting communities in multilayer networks. It uses a nonnegative symmetric matrix trifactorization that enforces disjoint, shared communities across layers while allowing each layer to have distinct connectivity patterns and node degrees. An efficient algorithm is presented and evaluated on a multilayer degree‑corrected stochastic block model, showing superior performance compared to existing methods.

By Alexandra Dache, Manon Rustin, Arnaud Vandaele, Nicolas Gillis
arXiv Machine Learning
4d ago

Dual-Corrected Stochastic Block Model ($\text{DC}^2\text{SBM}$): A Generalized Structure Detection Method for Attributed Networks

The paper introduces the Dual-Corrected Stochastic Block Model (DC²SBM), a generative framework for community detection in attributed networks that decouples node activity into independent topological and attribute correction factors. By incorporating these factors into link‑generation and attribute‑generation channels and adding a global scaling parameter, the model preserves computational efficiency while improving detection accuracy, especially when topological signals are weak. Experiments on synthetic and real datasets demonstrate that DC²SBM outperforms existing methods and that a single shared activity factor is insufficient when topology and attributes are decoupled.

By Zhenhai Chang, Shuo Wang, Yumeng Liu, Wei Liu