IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v16y2022i2d10.1007_s11634-021-00483-2.html
   My bibliography  Save this article

Factor and hybrid components for model-based clustering

Author

Listed:
  • Jason Hou-Liu

    (University of Waterloo)

  • Ryan P. Browne

    (University of Waterloo)

Abstract

A major challenge when performing model-based clustering is a large increase in the number of free parameters as the data dimensionality increases. To combat this issue, parsimonious methods such allow component covariance matrices to share parameters by exploiting geometric redundancies. The present work considers an additional level of intracluster structure that also captures hybridisation of mean and covariance parameters between components for the multivariate normal distribution. We posit components with heterogeneous parameterisation; a subset are considered factor components and have explicit mean and covariance parameters, and the remainder are considered hybrid components that have means and covariances implied by a set of factor loadings that weight factor component parameters. An estimation procedure is provided using the Expectation-Maximization algorithm, and comparison to Gaussian mixture models with parsimonious covariances is made by evaluation on a collection of datasets.

Suggested Citation

  • Jason Hou-Liu & Ryan P. Browne, 2022. "Factor and hybrid components for 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. 16(2), pages 373-398, June.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00483-2
    DOI: 10.1007/s11634-021-00483-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-021-00483-2
    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/s11634-021-00483-2?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. Hajo Holzmann & Axel Munk & Tilmann Gneiting, 2006. "Identifiability of Finite Mixtures of Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 753-763, December.
    2. Jian Zhang, 2013. "Epistatic Clustering: A Model-Based Approach for Identifying Links Between Clusters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1366-1384, December.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    5. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    6. Ryan Browne & Paul McNicholas, 2014. "Estimating common principal components in high dimensions," 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 217-226, June.
    7. McNicholas, P.D. & Murphy, T.B. & McDaid, A.F. & Frost, D., 2010. "Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 711-723, 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. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    2. Jason Hou-Liu & Ryan P. Browne, 2022. "Chimeral Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 171-190, March.
    3. 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.
    4. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    5. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    6. Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.
    7. Paolo Berta & Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini, 2016. "Multilevel cluster-weighted models for the evaluation of hospitals," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 275-292, December.
    8. Shaikh Mateen & McNicholas Paul D & Desmond Anthony F, 2010. "A Pseudo-EM Algorithm for Clustering Incomplete Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-17, March.
    9. Tyler Roick & Dimitris Karlis & Paul D. McNicholas, 2021. "Clustering discrete-valued time series," 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. 15(1), pages 209-229, March.
    10. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    11. Tang, Yang & Browne, Ryan P. & McNicholas, Paul D., 2015. "Model based clustering of high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 84-101.
    12. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    13. Ryan P. Browne & Luca Bagnato & Antonio Punzo, 2024. "Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal 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. 18(3), pages 597-625, September.
    14. 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.
    15. Sanjeena Subedi & Antonio Punzo & Salvatore Ingrassia & Paul McNicholas, 2013. "Clustering and classification via cluster-weighted 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. 7(1), pages 5-40, March.
    16. Naderi, Mehrdad & Hung, Wen-Liang & Lin, Tsung-I & Jamalizadeh, Ahad, 2019. "A novel mixture model using the multivariate normal mean–variance mixture of Birnbaum–Saunders distributions and its application to extrasolar planets," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 126-138.
    17. 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.
    18. Alex Sharp & Glen Chalatov & Ryan P. Browne, 2023. "A dual subspace parsimonious mixture of matrix normal 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. 17(3), pages 801-822, September.
    19. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    20. Browne, Ryan P., 2022. "Revitalizing the multivariate elliptical leptokurtic-normal distribution and its application in model-based clustering," Statistics & Probability Letters, Elsevier, vol. 190(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:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00483-2. 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.