Spectral graph clustering via the expectation-solution algorithm

The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that rows an SBM’s adjacency spectral embedding (ASE) Laplacian (LSE) both converge law to Gaussian mixtures where components are curved exponential families. Maximum likelihood estimation via Expectation-Maximization (EM) algorithm for a full mixture model (GMM) can then perform task clustering graph nodes, albeit without appealing components’ curvature. Noting EM is special case Expectation-Solution (ES) algorithm, we propose two ES algorithms allow us take advantage these structures. After presenting general curved-Gaussian mixture, develop those corresponding ASE LSE limiting distributions. Simulating from artificial SBMs brain connectome SBM reveals our improve upon GMM wide range settings.