Spectral and matrix factorization methods for consistent community detection in multi-layer networks (Q2176617)

The aim of the article is to investigate consistency properties of different methods applied to community detection under data generated from a multi-layer stochastic block model, MLSBM. Two methods for consensus clustering in multi-layer networks: the orthogonal LMF, (OLMF) which is an adoption to the linked matrix factorization (LMF) and the co-regularization based approach to multi-layer spectral clustering from Kumar, Rai und Daume and two baseline procedures: the spectral clustering on mean adjacency matrix and the aggregate spectral kernel and module allegiance matrix are considered. The authors introduce the multi-layer stochastic model, define the mis-clustering rate and prove the correct recovery in the noiseless case. They investigate the asymptotic consistency of consensus community detection using the considered methods. Consistency results for co-regularized spectral clustering, for orthogonal linked matrix factorization and for mean adjacency matrix, are proved. Simulation results are presented and conclusions are largely discussed.