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Covariate-assisted spectral clustering

Author

Listed:
  • N. Binkiewicz
  • J. T. Vogelstein
  • K. Rohe

Abstract

SummaryBiological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanied by contextualizing measures on each node. We utilize these node covariates to help uncover latent communities in a graph, using a modification of spectral clustering. Statistical guarantees are provided under a joint mixture model that we call the node-contextualized stochastic blockmodel, including a bound on the misclustering rate. The bound is used to derive conditions for achieving perfect clustering. For most simulated cases, covariate-assisted spectral clustering yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis. We apply our clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates. In both cases, covariate-assisted spectral clustering yields clusters that are easier to interpret neurologically.

Suggested Citation

  • N. Binkiewicz & J. T. Vogelstein & K. Rohe, 2017. "Covariate-assisted spectral clustering," Biometrika, Biometrika Trust, vol. 104(2), pages 361-377.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:2:p:361-377.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx008
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    Citations

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    Cited by:

    1. Fengqin Tang & Xuejing Zhao & Cuixia Li, 2023. "Community Detection in Multilayer Networks Based on Matrix Factorization and Spectral Embedding Method," Mathematics, MDPI, vol. 11(7), pages 1-19, March.
    2. Heather Mathews & Alexander Volfovsky, 2023. "Community informed experimental design," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1141-1166, October.
    3. Junlong Zhao & Xiumin Liu & Hansheng Wang & Chenlei Leng, 2022. "Dimension reduction for covariates in network data [On semidefinite relaxations for the block model]," Biometrika, Biometrika Trust, vol. 109(1), pages 85-102.
    4. Fengqin Tang & Chunning Wang & Jinxia Su & Yuanyuan Wang, 2020. "Spectral clustering-based community detection using graph distance and node attributes," Computational Statistics, Springer, vol. 35(1), pages 69-94, March.
    5. Guo, Li & Tao, Yubo & Härdle, Wolfgang Karl, 2019. "Dynamic Network Perspective of Cryptocurrencies," IRTG 1792 Discussion Papers 2019-009, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Qiuping Wang & Yuan Zhang & Ting Yan, 2023. "Asymptotic theory in network models with covariates and a growing number of node parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 369-392, April.
    7. Ma, Shujie & Su, Liangjun & Zhang, Yichong, 2020. "Detecting Latent Communities in Network Formation Models," Economics and Statistics Working Papers 12-2020, Singapore Management University, School of Economics.
    8. Li Guo & Wolfgang Karl Hardle & Yubo Tao, 2018. "A Time-Varying Network for Cryptocurrencies," Papers 1802.03708, arXiv.org, revised Nov 2022.
    9. Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.
    10. Lucy L. Gao & Daniela Witten & Jacob Bien, 2022. "Testing for association in multiview network data," Biometrics, The International Biometric Society, vol. 78(3), pages 1018-1030, September.
    11. S Chandna & S C Olhede & P J Wolfe, 2022. "Local linear graphon estimation using covariates [Representations for partially exchangeable arrays of random variables]," Biometrika, Biometrika Trust, vol. 109(3), pages 721-734.
    12. Babkin, Sergii & Stewart, Jonathan R. & Long, Xiaochen & Schweinberger, Michael, 2020. "Large-scale estimation of random graph models with local dependence," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

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