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Consistency of Spectral Clustering on Hierarchical Stochastic Block Models
时间:2026年07月01日 10:28 点击数:

报告人:李晓东

报告地点:人民大街校区惟真楼523报告厅

报告时间:2026年07月02日星期四16:00-17:00

邀请人:郑术蓉

报告摘要:

Hierarchical community structure appears naturally in many networks, but the multiscale edge heterogeneity it creates can make standard spectral perturbation arguments misleading. This talk studies spectral clustering based on the unnormalized graph Laplacian for hierarchical stochastic block models, with emphasis on recovering the first split of the hierarchy. We first characterize the population Fiedler vector and show that, under weak assortativity, its signs encode the root partition independently of lower-level connection probabilities. We then explain why dense small communities can help, rather than hurt, root-level recovery, even when within-leaf probabilities are much larger than root-scale probabilities. The main results establish weak and strong sign consistency for the empirical Fiedler vector under multiscale heterogeneity, including a refined balanced strong-leaf regime proved through direct nodewise and leave-one-out analysis. Synthetic and real-network experiments compare unnormalized, adjacency-based, and normalized spectral methods, illustrating when the Laplacian captures the top-level hierarchy and when degree heterogeneity changes the picture.

主讲人简介:

Dr. Xiaodong Li is an Associate Professor in the Department of Statistics at the University of California, Davis. His research interests lie mainly in statistical learning and high-dimensional statistics. He has received several honors, including the NSF CAREER Award, the 2019 Information Theory Paper Award, and the 2022–23 UC Davis Chancellor’s Fellow award. He currently serves as an Associate Editor for the Journal of Multivariate Analysis, Sankhya A, and ASA Discoveries.

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