Event Date
SPEAKER: Xiaodong Li; Statistics, UC Davis
TITLE: “Spectral methods in networks: hierarchical structures and risk estimation”
ABSTRACT: Hierarchical structures are common in real world data sets, and diverse clustering methods have been proposed to explore such structures. In the first part of this talk, we focus on the top-down hierarchical clustering based on the Fiedler vectors of graph-Laplacians. In particular, we show that Fiedler vector based hierarchical clustering is consistent under general tree structures and broad ranges of connectivity probabilities. Our analysis relies on careful exploiting the algebraic properties of graph Laplacian, as well as recently-developed probabilisitic tools in controlling the L-infinity norm perturbation of eigenvectors of random matrices.
The second part of this talk is motivated by a basic question in network analysis: How to determine the number of communities in a network dataset. The spectrum of the adjacency matrix is widely used in practice, but the cut-off is usually difficult to determine. We formulate this problem as evaluation of graphon estimation via spectral hard thresholding. Based on Efron's approximate GSURE framework for independent binary data, we derive GSURE formulas for spectral graphon estimation. The key of this derivation is to calculate the divergence of spectral functions. The performance of the proposed methods is illustrated by numerical simulations and real world data.
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DATE: Thursday, October 31st, 4:10pm
LOCATION: MSB 1147, Colloquium Room
REFRESHMENTS: 3:30pm MSB 4110 (4th floor lounge)