Community Detection: A Statistical Approach

• Main Authors: Chung-Yi Lin, 林宗毅
• Other Authors: 王奕翔
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/2aq2j5

碩士 === 國立臺灣大學 === 電信工程學研究所 === 106 === The problem of community detection in the Stochastic Block Model SBM is considered. The first half of this thesis is devoted to the community detection problem extended from graphs to hypergraphs. We propose a more general hypergraph generative model termed d-hSBM, and characterize the asymptotic misclassification ratio in the minimax sense under it. Achievability part is settled first information-theoretically with the Maximum Likelihood Estimator (MLE) under 3-hSBM and then computation-efficientlly with a two-step algorithm for any order d-hSBM. The converse lower bound is set by finding a smaller parameter space which contains the most dominant error events. The second half of this thesis considers the problem of estimating the number of communities itself apart from the clustering task. As an attempt to characterize the fundamental limit in such formulation, we demonstrate that the MLE, which is optimal under a Bayesian perspective, is consistent, whose form might further endorse a sparser connectivity level. In addition, an efficient spectral method EigenGap is proposed along with a theoretical guarantee. Experimental results on both synthetic data and real-world data consolidate our theoretical finding.