arXiv Machine Learning
Oct 23

Optimal Clustering of Multi-layer Networks under Mixture Block Models

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.

By Zhongyuan Lyu, Ting Li, Dong Xia
arXiv Machine Learning
Oct 2

T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models

The paper introduces T-ARC, a clustering algorithm that integrates topological information into the K‑means objective by coupling a data‑fidelity term with a graph‑cut penalty. The latent graph is modeled as a random realization from a Stochastic Block Model, whose parameter is optimized via Distributionally Robust Optimization, using a persistence‑based similarity matrix derived from zero‑dimensional persistent homology. Experiments on synthetic non‑convex data and Fashion‑MNIST subsets demonstrate that T‑ARC recovers latent topological structures and outperforms K‑means on curved and interleaved clusters while remaining competitive and more stable on real data.

By Serena Grazia De Benedictis, Andersen Ang, Nicoletta Del Buono, Flavia Esposito, Laura Selicato