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Abstract:
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Although spectral clustering has been extensively studied in network analysis, some important issues, such as hierarchical clustering via eigenvectors and determining the number of communities via eigenvalues, have been far less investigated thus far. The first part of the talk is about the theoretical analysis of hierarchical community detection. We show that graph-Laplacian based spectral hierarchical clustering is consistent under general tree structures and broad ranges of connectivity probabilities. Our analysis relies on a careful exploitation of the algebraic properties of graph Laplacian and statistical properties of hierarchical SBM.
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