IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v38y2021i2d10.1007_s00357-020-09363-4.html
   My bibliography  Save this article

Model-based Clustering of Count Processes

Author

Listed:
  • Tin Lok James Ng

    (University of Wollongong)

  • Thomas Brendan Murphy

    (University College Dublin)

Abstract

A model-based clustering method based on Gaussian Cox process is proposed to address the problem of clustering of count process data. The model allows for nonparametric estimation of intensity functions of Poisson processes, while simultaneous clustering count process observations. A logistic Gaussian process transformation is imposed on the intensity functions to enforce smoothness. Maximum likelihood parameter estimation is carried out via the EM algorithm, while model selection is addressed using a cross-validated likelihood approach. The proposed model and methodology are applied to two datasets.

Suggested Citation

  • Tin Lok James Ng & Thomas Brendan Murphy, 2021. "Model-based Clustering of Count Processes," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 188-211, July.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09363-4
    DOI: 10.1007/s00357-020-09363-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-020-09363-4
    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/s00357-020-09363-4?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. M. Giacofci & S. Lambert-Lacroix & G. Marot & F. Picard, 2013. "Wavelet-Based Clustering for Mixed-Effects Functional Models in High Dimension," Biometrics, The International Biometric Society, vol. 69(1), pages 31-40, March.
    2. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    3. R. C. H. Cheng & W. B. Liu, 2001. "The Consistency of Estimators in Finite Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 603-616, December.
    4. Adrian O’Hagan & Thomas Brendan Murphy & Luca Scrucca & Isobel Claire Gormley, 2019. "Investigation of parameter uncertainty in clustering using a Gaussian mixture model via jackknife, bootstrap and weighted likelihood bootstrap," Computational Statistics, Springer, vol. 34(4), pages 1779-1813, December.
    5. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 297-302, October.
    6. Theofanis Sapatinas, 1995. "Identifiability of mixtures of power-series distributions and related characterizations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 447-459, September.
    7. Gabriela Ciuperca & Andrea Ridolfi & Jérôme Idier, 2003. "Penalized Maximum Likelihood Estimator for Normal Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 45-59, March.
    8. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    9. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
    10. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    11. Zhang, Yongli & Yang, Yuhong, 2015. "Cross-validation for selecting a model selection procedure," Journal of Econometrics, Elsevier, vol. 187(1), pages 95-112.
    12. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," LSE Research Online Documents on Economics 16375, London School of Economics and Political Science, LSE Library.
    13. Chris Fraley & Adrian E. Raftery, 2007. "Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 155-181, September.
    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. Adriano Zanin Zambom & Julian A. A. Collazos & Ronaldo Dias, 2019. "Functional data clustering via hypothesis testing k-means," Computational Statistics, Springer, vol. 34(2), pages 527-549, June.
    2. Kim, Daeyoung & Seo, Byungtae, 2014. "Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 100-120.
    3. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," 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. 12(2), pages 235-260, June.
    4. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    5. Seo, Byungtae & Kim, Daeyoung, 2012. "Root selection in normal mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2454-2470.
    6. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
    7. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    8. Ja‐Yoon Jang & Hee‐Seok Oh & Yaeji Lim & Ying Kuen Cheung, 2021. "Ensemble clustering for step data via binning," Biometrics, The International Biometric Society, vol. 77(1), pages 293-304, March.
    9. Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
    10. Yiqing Chen, 2019. "A Renewal Shot Noise Process with Subexponential Shot Marks," Risks, MDPI, vol. 7(2), pages 1-8, June.
    11. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," 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. 8(3), pages 257-285, September.
    12. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    13. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    14. Alan Genaro & Adilson Simonis, 2015. "Estimating doubly stochastic Poisson process with affine intensities by Kalman filter," Statistical Papers, Springer, vol. 56(3), pages 723-748, August.
    15. Luis Angel García-Escudero & Alfonso Gordaliza & Francesca Greselin & Salvatore Ingrassia & Agustín Mayo-Iscar, 2018. "Eigenvalues and constraints in mixture modeling: geometric and computational issues," 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. 12(2), pages 203-233, June.
    16. Li, Zehang & Elías, Antonio & Morales, Juan M., 2024. "Clustering and forecasting of day-ahead electricity supply curves using a market-based distance," DES - Working Papers. Statistics and Econometrics. WS 43805, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Alan De Genaro Dario & Adilson Simonis, 2011. "Properties of Doubly Stochastic Poisson Process with affine intensity," Papers 1109.2884, arXiv.org, revised Sep 2011.
    18. Mario Teixeira Parente & Georg Brandl & Christian Franz & Uwe Stuhr & Marina Ganeva & Astrid Schneidewind, 2023. "Active learning-assisted neutron spectroscopy with log-Gaussian processes," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    19. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
    20. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

    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:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09363-4. 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.