Jul 12, 2020

Learning community structures in graphs that are randomly generated by stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the problem of exactly recovering the communities in a binary symmetric SBM, where a graph of n vertices is partitioned into two equal-sized communities and the vertices are connected with probability p = αlog(n)/n within communities and q = βlog(n)/n across communities for some α>β>0. We propose a two-stage iterative algorithm for solving this problem, which employs the power method with a random starting point in the first-stage and turns to a generalized power method that can identify the communities in a finite number of iterations in the second-stage. It is shown that for any fixed α and β such that √(α) - √(β) > √(2), which is known to be the information-theoretical limit for exact recovery, the proposed algorithm exactly identifies the underlying communities in Õ(n) running time with probability tending to one as n→∞. As far as we know, this is the first algorithm with nearly-linear running time that achieves exact recovery at the information-theoretical limit. We also present numerical results of the proposed algorithm to support and complement our theoretical development.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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