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Estimating mixed-memberships using the symmetric laplacian inverse matrix

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Abstract

Mixed membership community detection is a challenging problem. In this paper, to detect mixed memberships, we propose a new method Mixed-SLIM which is a spectral clustering method on the symmetrized Laplacian inverse matrix under the degree-corrected mixed membership model. We provide theoretical bounds for the estimation error on the proposed algorithm and its regularized version under mild conditions. Meanwhile, we provide some extensions of the proposed method to deal with large networks in practice. These Mixed-SLIM methods outperform state-of-art methods in simulations and substantial empirical datasets for both community detection and mixed membership community detection problems.

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Funding

Qing’s work was supported by High level personal project of Jiangsu Province (JSSCBS20211218). Wang’s work was supported by the Fundamental Research Funds for the Central Universities, Nankai University, 63221044 and the National Natural Science Foundation of China (Grant 12001295).

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Huan Qing

  2. School of Statistics and Data Science, KLMDASR, LEBPS, and LPMC, Nankai University, Tianjin, 30071, Tianjin, China

    Jingli Wang

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  1. Huan Qing
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  2. Jingli Wang
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Authors’ contributions. Qing mainly worked on the algorithm and theoretical properties. Wang mainly worked on the algorithm and whole paper organization.

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Correspondence to Jingli Wang.

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The proofs of lemmas and theorem are provided in the Supplementary. (pdf 251KB)

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Qing, H., Wang, J. Estimating mixed-memberships using the symmetric laplacian inverse matrix. J. Korean Stat. Soc. 52, 248–264 (2023). https://doi.org/10.1007/s42952-022-00199-9

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