IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v84y2022i1d10.1007_s13171-021-00247-2.html
   My bibliography  Save this article

The Hierarchy of Block Models

Author

Listed:
  • Majid Noroozi

    (Washington University in St. Louis)

  • Marianna Pensky

    (University of Central Florida)

Abstract

There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions. We propose a Nested Block Model (NBM) that treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values, and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing, to see which block model is really true.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-021-00247-2
    DOI: 10.1007/s13171-021-00247-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-021-00247-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-021-00247-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. P. Tseng, 2000. "Nearest q-Flat to m Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 249-252, April.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.
    3. Markovič, Rene & Gosak, Marko & Grubelnik, Vladimir & Marhl, Marko & Virtič, Peter, 2019. "Data-driven classification of residential energy consumption patterns by means of functional connectivity networks," Applied Energy, Elsevier, vol. 242(C), pages 506-515.
    4. Avanti Athreya & Joshua Cape & Minh Tang, 2022. "Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with Low-Rank Edge Probability Matrices," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 36-63, June.
    5. Renli Liang & Yanqin Bai & Hai Xiang Lin, 2019. "An inexact splitting method for the subspace segmentation from incomplete and noisy observations," Journal of Global Optimization, Springer, vol. 73(2), pages 411-429, February.
    6. Anirban Dasgupta & Srijan Sengupta, 2022. "Scalable Estimation of Epidemic Thresholds via Node Sampling," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 321-344, June.
    7. Xinjun Li & Fan Feng & Hongxi Pu & Wai Yan Leung & Jie Liu, 2021. "scHiCTools: A computational toolbox for analyzing single-cell Hi-C data," PLOS Computational Biology, Public Library of Science, vol. 17(5), pages 1-14, May.
    8. Vincent Miele & Catherine Matias & Stéphane Robin & Stéphane Dray, 2019. "Nine quick tips for analyzing network data," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-10, December.
    9. Wang, Zhixiao & Rui, Xiaobin & Yuan, Guan & Cui, Jingjing & Hadzibeganovic, Tarik, 2021. "Endemic information-contagion outbreaks in complex networks with potential spreaders based recurrent-state transmission dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    10. Yu, Jiating & Leng, Jiacheng & Sun, Duanchen & Wu, Ling-Yun, 2023. "Network Refinement: Denoising complex networks for better community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    11. Yuan-Hai Shao & Nai-Yang Deng, 2015. "The Equivalence Between Principal Component Analysis and Nearest Flat in the Least Square Sense," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 278-284, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-021-00247-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.