IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v152y2020ics0167947320301353.html
   My bibliography  Save this article

Bayesian nonparametric clustering as a community detection problem

Author

Listed:
  • Tonellato, Stefano F.

Abstract

A wide class of Bayesian nonparametric priors leads to the representation of the distribution of the observable variables as a mixture density with an infinite number of components. Such a representation induces a clustering structure in the data. However, due to label switching, cluster identification is not straightforward a posteriori and some post-processing of the MCMC output is usually required. Alternatively, observations can be mapped on a weighted undirected graph, where each node represents a sample item and edge weights are given by the posterior pairwise similarities. It is shown how, after building a particular random walk on such a graph, it is possible to apply a community detection algorithm, known as map equation, leading to the minimisation of the expected description length of the partition. A relevant feature of this method is that it allows for the quantification of the posterior uncertainty of the classification.

Suggested Citation

  • Tonellato, Stefano F., 2020. "Bayesian nonparametric clustering as a community detection problem," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:csdana:v:152:y:2020:i:c:s0167947320301353
    DOI: 10.1016/j.csda.2020.107044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320301353
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.107044?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. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Azzalini, Adelchi & Menardi, Giovanna, 2014. "Clustering via Nonparametric Density Estimation: The R Package pdfCluster," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i11).
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Jara, Alejandro & Hanson, Timothy & Quintana, Fernando A. & Müller, Peter & Rosner, Gary L., 2011. "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i05).
    5. Rastelli, Riccardo & Latouche, Pierre & Friel, Nial, 2018. "Choosing the number of groups in a latent stochastic blockmodel for dynamic networks," Network Science, Cambridge University Press, vol. 6(4), pages 469-493, December.
    6. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    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. Stefano Tonellato, 2019. "Bayesian nonparametric clustering as a community detection problem," Working Papers 2019: 20, Department of Economics, University of Venice "Ca' Foscari".
    2. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    3. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 33-64, March.
    4. Dolnicar, Sara & Grün, Bettina & Leisch, Friedrich, 2016. "Increasing sample size compensates for data problems in segmentation studies," Journal of Business Research, Elsevier, vol. 69(2), pages 992-999.
    5. Paul Riverain & Simon Fossier & Mohamed Nadif, 2023. "Poisson degree corrected dynamic stochastic block model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 135-162, March.
    6. Scrucca, Luca, 2016. "Identifying connected components in Gaussian finite mixture models for clustering," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 5-17.
    7. Jerzy Korzeniewski, 2016. "New Method Of Variable Selection For Binary Data Cluster Analysis," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 295-304, June.
    8. Sun Jiehuan & Warren Joshua L. & Zhao Hongyu, 2017. "A Bayesian semiparametric factor analysis model for subtype identification," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(2), pages 145-158, April.
    9. Kemmawadee Preedalikit & Daniel Fernández & Ivy Liu & Louise McMillan & Marta Nai Ruscone & Roy Costilla, 2024. "Row mixture-based clustering with covariates for ordinal responses," Computational Statistics, Springer, vol. 39(5), pages 2511-2555, July.
    10. Crook Oliver M. & Gatto Laurent & Kirk Paul D. W., 2019. "Fast approximate inference for variable selection in Dirichlet process mixtures, with an application to pan-cancer proteomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(6), pages 1-20, December.
    11. Thierry Chekouo & Alejandro Murua, 2018. "High-dimensional variable selection with the plaid mixture model for clustering," Computational Statistics, Springer, vol. 33(3), pages 1475-1496, September.
    12. Melnykov, Volodymyr, 2016. "Model-based biclustering of clickstream data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 31-45.
    13. Tsai, Chieh-Yuan & Chiu, Chuang-Cheng, 2008. "Developing a feature weight self-adjustment mechanism for a K-means clustering algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4658-4672, June.
    14. Monia Ranalli & Roberto Rocci, 2017. "A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1007-1034, December.
    15. Giovanna Menardi, 2016. "A Review on Modal Clustering," International Statistical Review, International Statistical Institute, vol. 84(3), pages 413-433, December.
    16. Susan Brudvig & Michael J. Brusco & J. Dennis Cradit, 2019. "Joint selection of variables and clusters: recovering the underlying structure of marketing data," Journal of Marketing Analytics, Palgrave Macmillan, vol. 7(1), pages 1-12, March.
    17. Morris, Katherine & McNicholas, Paul D., 2013. "Dimension reduction for model-based clustering via mixtures of shifted asymmetric Laplace distributions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2088-2093.
    18. Jerzy Korzeniewski, 2016. "New Method Of Variable Selection For Binary Data Cluster Analysis," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 295-304, June.
    19. Zhao, Yanyun & Ausín Olivera, María Concepción & Wiper, Michael Peter, 2013. "Bayesian multivariate Bernstein polynomial density estimation," DES - Working Papers. Statistics and Econometrics. WS ws131211, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.

    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:eee:csdana:v:152:y:2020:i:c:s0167947320301353. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.