期刊
ELECTRONIC JOURNAL OF STATISTICS
卷 16, 期 1, 页码 3135-3175出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/22-EJS2018
关键词
EM algorithm; random graph; curved exponential family; estimating equations; mixture model
资金
- D3M program of the Defense Advanced Research Projects Agency (DARPA)
The stochastic blockmodel plays an important role in modeling connectivity within and between nodes in networks. Utilizing curved Gaussian mixture models for clustering graph nodes can better take advantage of curved structures. Using the ES algorithm can achieve better clustering results.
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.
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