IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v13y2019i3d10.1007_s11634-018-0333-2.html
   My bibliography  Save this article

Subspace clustering for the finite mixture of generalized hyperbolic distributions

Author

Listed:
  • Nam-Hwui Kim

    (University of Waterloo)

  • Ryan Browne

    (University of Waterloo)

Abstract

The finite mixture of generalized hyperbolic distributions is a flexible model for clustering, but its large number of parameters for estimation, especially in high dimensions, can make it computationally expensive to work with. In light of this issue, we provide an extension of the subspace clustering technique developed for finite Gaussian mixtures to that of generalized hyperbolic distribution. The methodology will be demonstrated with numerical experiments.

Suggested Citation

  • Nam-Hwui Kim & Ryan Browne, 2019. "Subspace clustering for the finite mixture of generalized hyperbolic 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. 13(3), pages 641-661, September.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:3:d:10.1007_s11634-018-0333-2
    DOI: 10.1007/s11634-018-0333-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-018-0333-2
    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/s11634-018-0333-2?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. 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.
    2. Bouveyron, C. & Girard, S. & Schmid, C., 2007. "High-dimensional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 502-519, September.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    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. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael P. B. Gallaugher & Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2022. "Multivariate cluster weighted models using skewed 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. 16(1), pages 93-124, March.
    2. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).

    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. 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.
    3. 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.
    4. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wan-Lun Wang & Luis M. Castro & Yen-Ting Chang & Tsung-I Lin, 2019. "Mixtures of restricted skew-t factor analyzers with common factor loadings," 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(2), pages 445-480, June.
    10. 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.
    11. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    12. 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.
    13. 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.
    14. Semhar Michael & Volodymyr Melnykov, 2016. "An effective strategy for initializing the EM algorithm in finite mixture models," 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 563-583, December.
    15. 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.
    16. Chaofeng Yuan & Wensheng Zhu & Xuming He & Jianhua Guo, 2019. "A mixture factor model with applications to microarray data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 60-76, March.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:13:y:2019:i:3:d:10.1007_s11634-018-0333-2. 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.