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Overlapping Community Detection in Networks via Sparse Spectral Decomposition

Author

Listed:
  • Jesús Arroyo

    (University of Maryland
    Johns Hopkins University)

  • Elizaveta Levina

    (University of Michigan)

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.

Suggested Citation

  • Jesús Arroyo & Elizaveta Levina, 2022. "Overlapping Community Detection in Networks via Sparse Spectral Decomposition," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 1-35, June.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-021-00245-4
    DOI: 10.1007/s13171-021-00245-4
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Tianxi Li & Elizaveta Levina & Ji Zhu, 2020. "Network cross-validation by edge sampling," Biometrika, Biometrika Trust, vol. 107(2), pages 257-276.
    3. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    4. Cape, Joshua & Tang, Minh & Priebe, Carey E., 2019. "On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs," Network Science, Cambridge University Press, vol. 7(3), pages 269-291, September.
    5. Andrea Lancichinetti & Filippo Radicchi & José J Ramasco & Santo Fortunato, 2011. "Finding Statistically Significant Communities in Networks," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-18, April.
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