文章基本信息

标题：Spectral graph clustering via the expectation-solution algorithm
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作者：Zachary M. Pisano ; Joshua S. Agterberg ; Carey E. Priebe 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：3135-3175
DOI：10.1214/22-EJS2018
语种：English
出版社：Institute of Mathematical Statistics
摘要：The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM’s adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE) both converge in law to Gaussian mixtures where the components are curved exponential families. Maximum likelihood estimation via the Expectation-Maximization (EM) algorithm for a full Gaussian mixture model (GMM) can then perform the task of clustering graph nodes, albeit without appealing to the components’ curvature. Noting that EM is a special case of the Expectation-Solution (ES) algorithm, we propose two ES algorithms that allow us to take full advantage of these curved structures. After presenting the ES algorithm for the general curved-Gaussian mixture, we develop those corresponding to the ASE and LSE limiting distributions. Simulating from artificial SBMs and a brain connectome SBM reveals that clustering graph nodes via our ES algorithms can improve upon that of EM for a full GMM for a wide range of settings.
关键词：60B20;62H30;62P10;curved exponential family;EM algorithm;estimating equations;mixture model;random graph