Overlapping Community Detection in Networks via Sparse Spectral Decomposition

Jesús Arroyo () and Elizaveta Levina ()
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Jesús Arroyo: University of Maryland
Elizaveta Levina: University of Michigan

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 1, No 1, 35 pages

Abstract: Abstract We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on sparse node membership vectors. Our algorithm is based on sparse principal subspace estimation with iterative thresholding. The method is computationally efficient, with computational cost equivalent to estimating the leading eigenvectors of the adjacency matrix, and does not require an additional clustering step, unlike spectral clustering methods. We show that a fixed point of the algorithm corresponds to correct node memberships under a version of the stochastic block model. The methods are evaluated empirically on simulated and real-world networks, showing good statistical performance and computational efficiency.

Keywords: Sparse principal component analysis; Stochastic blockmodel; Mixed memberships; Primary: 62H30; Secondary: 91C20; 68T10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13171-021-00245-4

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