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Network Cross-Validation for Determining the Number of Communities in Network Data

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  • Kehui Chen
  • Jing Lei

Abstract

The stochastic block model (SBM) and its variants have been a popular tool for analyzing large network data with community structures. In this article, we develop an efficient network cross-validation (NCV) approach to determine the number of communities, as well as to choose between the regular stochastic block model and the degree corrected block model (DCBM). The proposed NCV method is based on a block-wise node-pair splitting technique, combined with an integrated step of community recovery using sub-blocks of the adjacency matrix. We prove that the probability of under-selection vanishes as the number of nodes increases, under mild conditions satisfied by a wide range of popular community recovery algorithms. The solid performance of our method is also demonstrated in extensive simulations and two data examples. Supplementary materials for this article are available online.

Suggested Citation

  • Kehui Chen & Jing Lei, 2018. "Network Cross-Validation for Determining the Number of Communities in Network Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 241-251, January.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:521:p:241-251
    DOI: 10.1080/01621459.2016.1246365
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    Citations

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    Cited by:

    1. Lu, Hong & Sang, Xiaoshuang & Zhao, Qinghua & Lu, Jianfeng, 2020. "Community detection algorithm based on nonnegative matrix factorization and pairwise constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Jianqing Fan & Yingying Fan & Xiao Han & Jinchi Lv, 2022. "SIMPLE: Statistical inference on membership profiles in large networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 630-653, April.
    3. Wu, Qianyong & Hu, Jiang, 2024. "Two-sample test of stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    4. Momin M. Malik, 2020. "A Hierarchy of Limitations in Machine Learning," Papers 2002.05193, arXiv.org, revised Feb 2020.
    5. Can M. Le & Tianxi Li, 2022. "Linear regression and its inference on noisy network‐linked data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1851-1885, November.
    6. Mingyang Ren & Sanguo Zhang & Junhui Wang, 2023. "Consistent estimation of the number of communities via regularized network embedding," Biometrics, The International Biometric Society, vol. 79(3), pages 2404-2416, September.
    7. Thorben Funke & Till Becker, 2019. "Stochastic block models: A comparison of variants and inference methods," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-40, April.
    8. Watanabe, Chihiro & Suzuki, Taiji, 2021. "Goodness-of-fit test for latent block models," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    9. Tidarat Luangrungruang & Urachart Kokaew, 2022. "Adapting Fleming-Type Learning Style Classifications to Deaf Student Behavior," Sustainability, MDPI, vol. 14(8), pages 1-16, April.
    10. Vainora, J., 2024. "Latent Position-Based Modeling of Parameter Heterogeneity," Cambridge Working Papers in Economics 2455, Faculty of Economics, University of Cambridge.

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