The Department of
Statistics and Operations Research
The University of North Carolina at Chapel Hill
Graduate Student Seminar
Friday, September 1st, 2023 125 Hanes Hall 3:30-4:00pm
or via Zoom:
https://unc.zoom.us/j/92731259806?pwd=eTc3Ylo0SWNFOHV4eERvSjRrUmlKQT09
Meeting ID: 927 3125 9806
Passcode: 100210
UNC Chapel Hill – Statistics & Operations Research Semi-Supervised Community Detection via Eigenvector Analyses of Random Matrices with Low Expected Rank Abstract: Given an underlying stochastic block model on n nodes with two communities, spectral methods for community detection use eigenvectors of network structures such as the adjacency matrix to efficiently estimate community membership. Previously, Abbé et al. (2019) provided a tight bound for the difference between the empirical eigenvector and a linear transformation of the eigenvector of the mean through an entrywise eigenvector analysis for the first-order approximation under the sup norm. We extend the analysis to the case of a previously labelled k-fraction of one or both communities by considering the corresponding quasi-stationary distributions generated by random walks. We provide bounds for the difference between the empirical and mean eigenvectors of the normalized adjacency submatrix under the sup norm, showing that exact recovery is still possible under a wider range of parameters.

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