IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v10y2016i4d10.1007_s11634-016-0262-x.html
   My bibliography  Save this article

The determination of uncertainty levels in robust clustering of subjects with longitudinal observations using the Dirichlet process mixture

Author

Listed:
  • Reyhaneh Rikhtehgaran

    (Isfahan University of Technology)

  • Iraj Kazemi

    (University of Isfahan)

Abstract

In this paper we introduce a new method to the cluster analysis of longitudinal data focusing on the determination of uncertainty levels for cluster memberships. The method uses the Dirichlet-t distribution which notably utilizes the robustness feature of the student-t distribution in the framework of a Bayesian semi-parametric approach together with robust clustering of subjects evaluates the uncertainty level of subjects memberships to their clusters. We let the number of clusters and the uncertainty levels be unknown while fitting Dirichlet process mixture models. Two simulation studies are conducted to demonstrate the proposed methodology. The method is applied to cluster a real data set taken from gene expression studies.

Suggested Citation

  • Reyhaneh Rikhtehgaran & Iraj Kazemi, 2016. "The determination of uncertainty levels in robust clustering of subjects with longitudinal observations using the Dirichlet process mixture," 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. 10(4), pages 541-562, December.
    • Handle: RePEc:spr:advdac:v:10:y:2016:i:4:d:10.1007_s11634-016-0262-x
    DOI: 10.1007/s11634-016-0262-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-016-0262-x
    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/s11634-016-0262-x?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. Felix Heinzl & Ludwig Fahrmeir & Thomas Kneib, 2012. "Additive mixed models with Dirichlet process mixture and P-spline priors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 47-68, January.
    2. Wan-Lun Wang & Tsung-I Lin, 2015. "Robust model-based clustering via mixtures of skew-t distributions with missing information," 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. 9(4), pages 423-445, December.
    3. 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.
    4. Lin, Tsung-I & McNicholas, Paul D. & Ho, Hsiu J., 2014. "Capturing patterns via parsimonious t mixture models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 80-87.
    5. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    6. Katherine Morris & Paul McNicholas & Luca Scrucca, 2013. "Dimension reduction for model-based clustering via mixtures of multivariate $$t$$ t -distributions," 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. 7(3), pages 321-338, September.
    7. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    8. Lin, Tsung-I, 2014. "Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 183-195.
    9. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    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. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
    2. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.
    3. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    4. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic factor analyzers," 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. 10(4), pages 423-440, December.
    5. Hung Tong & Cristina Tortora, 2022. "Model-based clustering and outlier detection with missing data," 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. 16(1), pages 5-30, March.
    6. Marek Śmieja & Magdalena Wiercioch, 2017. "Constrained clustering with a complex cluster structure," 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. 11(3), pages 493-518, September.
    7. Nicola Loperfido, 2019. "Finite mixtures, projection pursuit and tensor rank: a triangulation," 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 145-173, March.
    8. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," 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(2), pages 167-193, June.
    9. Francisco H. C. Alencar & Larissa A Matos & Víctor H. Lachos, 2022. "Finite Mixture of Censored Linear Mixed Models for Irregularly Observed Longitudinal Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 463-486, November.
    10. Mazucheli, Josmar & Louzada-Neto, Francisco & Achcar, Jorge A., 2001. "Bayesian inference for polyhazard models in the presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 1-14, November.
    11. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2014. "Mixtures of skew-t factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 326-335.
    12. Michael P. B. Gallaugher & Paul D. McNicholas, 2020. "Mixtures of skewed matrix variate bilinear factor analyzers," 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. 14(2), pages 415-434, June.
    13. Lachos, Víctor H. & Moreno, Edgar J. López & Chen, Kun & Cabral, Celso Rômulo Barbosa, 2017. "Finite mixture modeling of censored data using the multivariate Student-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 151-167.
    14. Wang, Wan-Lun & Lin, Tsung-I, 2016. "Maximum likelihood inference for the multivariate t mixture model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 54-64.
    15. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    16. Pang, W. K. & Yang, Z. H. & Hou, S. H. & Leung, P. K., 2002. "Non-uniform random variate generation by the vertical strip method," European Journal of Operational Research, Elsevier, vol. 142(3), pages 595-609, November.
    17. Samantha Leorato & Maura Mezzetti, 2015. "Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach," CEIS Research Paper 338, Tor Vergata University, CEIS, revised 09 Apr 2015.
    18. Z. Rezaei Ghahroodi & M. Ganjali, 2013. "A Bayesian approach for analysing longitudinal nominal outcomes using random coefficients transitional generalized logit model: an application to the labour force survey data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1425-1445, July.
    19. Stephen G. Walker, 2006. "Sampling the Dirichlet Mixture Model with Slices," ICER Working Papers - Applied Mathematics Series 16-2006, ICER - International Centre for Economic Research.
    20. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, 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:advdac:v:10:y:2016:i:4:d:10.1007_s11634-016-0262-x. 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.