2020/12/07 by Sihan Huang, Huang, Sihan, Haolei Weng +3 · 2 citations
Computer Science · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST) #cs.LG #cs.SI #math.ST #stat.CO #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.2012.04646
74 pages
arxiv created 2022/10/06 · arxiv updated 2022/10/07
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream k-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the mis-clustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used k-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods.