IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v8y2014i1p27-43.html
   My bibliography  Save this article

A constrained robust proposal for mixture modeling avoiding spurious solutions

Author

Listed:
  • L. García-Escudero
  • A. Gordaliza
  • A. Mayo-Iscar

Abstract

The high prevalence of spurious solutions and the disturbing effect of outlying observations in mixture modeling are well known problems that pose serious difficulties for non-expert practitioners of this kind of models in different applied areas. An approach which combines the use of Trimmed Maximum Likelihood ideas and the imposition of restrictions on the maximization problem will be presented and studied in this paper. The proposed methodology is shown to have nice mathematical properties as well as good performance in avoiding the appearance of spurious solutions in a quite automatic manner. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • L. García-Escudero & A. Gordaliza & A. Mayo-Iscar, 2014. "A constrained robust proposal for mixture modeling avoiding spurious solutions," 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(1), pages 27-43, March.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:1:p:27-43
    DOI: 10.1007/s11634-013-0153-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11634-013-0153-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11634-013-0153-3?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. Fritz, Heinrich & García-Escudero, Luis A. & Mayo-Iscar, Agustín, 2013. "A fast algorithm for robust constrained clustering," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 124-136.
    2. Pietro Coretto & Christian Hennig, 2010. "A simulation study to compare robust clustering methods based on mixtures," 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. 4(2), pages 111-135, September.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. 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.
    5. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
    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. García-Escudero, Luis Angel & Gordaliza, Alfonso & Greselin, Francesca & Ingrassia, Salvatore & Mayo-Iscar, Agustín, 2016. "The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 131-147.
    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. Amparo Baíllo & Javier Cárcamo & Konstantin Getman, 2019. "New distance measures for classifying X-ray astronomy data into stellar classes," 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 531-557, June.
    4. Andrea Cappozzo & Francesca Greselin & Thomas Brendan Murphy, 2020. "A robust approach to model-based classification based on trimming and constraints," 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 327-354, June.
    5. 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.
    6. Diego Rivera-García & Luis A. García-Escudero & Agustín Mayo-Iscar & Joaquín Ortega, 2019. "Robust clustering for functional data based on trimming and constraints," 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 201-225, March.
    7. Marco Riani & Andrea Cerioli & Domenico Perrotta & Francesca Torti, 2015. "Simulating mixtures of multivariate data with fixed cluster overlap in FSDA library," 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 461-481, December.

    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. Pietro Coretto & Christian Hennig, 2016. "Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1648-1659, October.
    2. 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.
    3. L. García-Escudero & A. Gordaliza & A. Mayo-Iscar, 2013. "Comments on: model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 459-461, November.
    4. García-Escudero, Luis Angel & Gordaliza, Alfonso & Greselin, Francesca & Ingrassia, Salvatore & Mayo-Iscar, Agustín, 2016. "The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 131-147.
    5. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    6. Andrea Cerioli & Domenico Perrotta, 2014. "Robust clustering around regression lines with high density regions," 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(1), pages 5-26, March.
    7. Luca De Angelis, 2013. "Latent class models for financial data analysis: some statistical developments," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 227-242, June.
    8. Ingrassia, Salvatore & Rocci, Roberto, 2011. "Degeneracy of the EM algorithm for the MLE of multivariate Gaussian mixtures and dynamic constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1715-1725, April.
    9. Andrea Cappozzo & Francesca Greselin & Thomas Brendan Murphy, 2020. "A robust approach to model-based classification based on trimming and constraints," 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 327-354, June.
    10. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    11. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    12. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    13. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    14. Francesca Torti & Domenico Perrotta & Marco Riani & Andrea Cerioli, 2019. "Assessing trimming methodologies for clustering linear regression 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. 13(1), pages 227-257, March.
    15. Luca Greco, 2022. "Robust fitting of mixtures of GLMs by weighted likelihood," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 25-48, March.
    16. Cong, Lin & Yao, Weixin, 2021. "A Likelihood Ratio Test of a Homoscedastic Multivariate Normal Mixture Against a Heteroscedastic Multivariate Normal Mixture," Econometrics and Statistics, Elsevier, vol. 18(C), pages 79-88.
    17. 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.
    18. Luca Greco & Antonio Lucadamo & Claudio Agostinelli, 2021. "Weighted likelihood latent class linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 711-746, June.
    19. 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.
    20. Fritz, Heinrich & García-Escudero, Luis A. & Mayo-Iscar, Agustín, 2013. "A fast algorithm for robust constrained clustering," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 124-136.

    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:8:y:2014:i:1:p:27-43. 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.