IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v11y2017i4d10.1007_s11634-016-0271-9.html
   My bibliography  Save this article

A fuzzy approach to robust regression clustering

Author

Listed:
  • Francesco Dotto

    (Università di Roma “La Sapienza”)

  • Alessio Farcomeni

    (Università di Roma “La Sapienza”)

  • Luis Angel García-Escudero

    (Universidad de Valladolid)

  • Agustín Mayo-Iscar

    (Universidad de Valladolid)

Abstract

A new robust fuzzy regression clustering method is proposed. We estimate coefficients of a linear regression model in each unknown cluster. Our method aims to achieve robustness by trimming a fixed proportion of observations. Assignments to clusters are fuzzy: observations contribute to estimates in more than one single cluster. We describe general criteria for tuning the method. The proposed method seems to be robust with respect to different types of contamination.

Suggested Citation

  • Francesco Dotto & Alessio Farcomeni & Luis Angel García-Escudero & Agustín Mayo-Iscar, 2017. "A fuzzy approach to robust regression 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. 11(4), pages 691-710, December.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:4:d:10.1007_s11634-016-0271-9
    DOI: 10.1007/s11634-016-0271-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-016-0271-9
    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/s11634-016-0271-9?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. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.
    2. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    3. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    4. Peter Bryant, 1991. "Large-sample results for optimization-based clustering methods," Journal of Classification, Springer;The Classification Society, vol. 8(1), pages 31-44, January.
    5. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    6. 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.
    7. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    8. Ingrassia, Salvatore & Minotti, Simona C. & Punzo, Antonio, 2014. "Model-based clustering via linear cluster-weighted models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 159-182.
    9. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    10. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    11. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    12. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    13. Christian Hennig & Tim F. Liao, 2013. "How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 309-369, May.
    14. Rousseeuw, P. J. & Kaufman, L. & Trauwaert, E., 1996. "Fuzzy clustering using scatter matrices," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 135-151, November.
    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. Gordon Anderson & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "Rectangular latent Markov models for time‐specific clustering, with an analysis of the wellbeing of nations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 603-621, April.
    2. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    3. Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2017. "Rectangular latent Markov models for time-specific clustering," Working Papers tecipa-589, University of Toronto, Department of Economics.

    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. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    2. 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.
    3. 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.
    4. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    5. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    7. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    8. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    9. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    10. Teague R. Henry & Kathleen M. Gates & Mitchell J. Prinstein & Douglas Steinley, 2020. "Modeling Heterogeneous Peer Assortment Effects Using Finite Mixture Exponential Random Graph Models," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 8-34, March.
    11. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    12. 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.
    13. Mirfarah, Elham & Naderi, Mehrdad & Chen, Ding-Geng, 2021. "Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    14. Joki, Kaisa & Bagirov, Adil M. & Karmitsa, Napsu & Mäkelä, Marko M. & Taheri, Sona, 2020. "Clusterwise support vector linear regression," European Journal of Operational Research, Elsevier, vol. 287(1), pages 19-35.
    15. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    16. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.
    17. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    18. Elvira Pelle & Roberta Pappadà, 2021. "A clustering procedure for mixed-type data to explore ego network typologies: an application to elderly people living alone in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1507-1533, December.
    19. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    20. 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.

    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:11:y:2017:i:4:d:10.1007_s11634-016-0271-9. 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.