2017/09/01 by Xueyu Mao, Mao, Xueyu, Purnamrita Sarkar +3 · 1 citation
Computer Science · Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Human Mobility and Location-Based Analysis #Machine Learning (stat.ML) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1709.00407
openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require strong assumptions about the population, are computationally expensive, and only provide an overall error bound for the whole community membership matrix. This paper provides uniform rates of convergence for the inferred community membership vector of each node in a network generated from the Mixed Membership Stochastic Blockmodel (MMSB); to our knowledge, this is the first work to establish per-node rates for overlapping community detection in networks. We achieve this by establishing sharp row-wise eigenvector deviation bounds for MMSB. Based on the simplex structure inherent in the eigen-decomposition of the population matrix, we build on established corner-finding algorithms from the optimization community to infer the community membership vectors. Our results hold over a broad parameter regime where the average degree only grows poly-logarithmically with the number of nodes. Using experiments with simulated and real datasets, we show that our method achieves better error with lower variability over competing methods, and processes real world networks of up to 100,000 nodes within tens of seconds.