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Estimation and clustering in popularity adjusted block model

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  • Majid Noroozi
  • Ramchandra Rimal
  • Marianna Pensky

Abstract

The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (Journal of the Royal Statistical Society Series B, 2018, 80, 365–386). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modelling networks that appear in biological sciences. We expand the theory of PABM to the case of an arbitrary number of communities which possibly grows with a number of nodes in the network and is not assumed to be known. We produce estimators of the probability matrix and of the community structure and, in addition, provide non‐asymptotic upper bounds for the estimation and the clustering errors. We use the Sparse Subspace Clustering (SSC) approach for partitioning the network into communities, the approach that, to the best of our knowledge, has not been used for the clustering network data. The theory is supplemented by a simulation study. In addition, we show advantages of the PABM for modelling a butterfly similarity network and a human brain functional network.

Suggested Citation

  • Majid Noroozi & Ramchandra Rimal & Marianna Pensky, 2021. "Estimation and clustering in popularity adjusted block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 293-317, April.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:2:p:293-317
    DOI: 10.1111/rssb.12410
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    References listed on IDEAS

    as
    1. Srijan Sengupta & Yuguo Chen, 2018. "A block model for node popularity in networks with community structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 365-386, March.
    2. Bo Wang & Armin Pourshafeie & Marinka Zitnik & Junjie Zhu & Carlos D. Bustamante & Serafim Batzoglou & Jure Leskovec, 2018. "Network enhancement as a general method to denoise weighted biological networks," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
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    Cited by:

    1. Majid Noroozi & Marianna Pensky, 2022. "The Hierarchy of Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 64-107, June.

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