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A fast algorithm for robust constrained clustering

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  • Fritz, Heinrich
  • García-Escudero, Luis A.
  • Mayo-Iscar, Agustín

Abstract

The application of “concentration” steps is the main principle behind Forgy’s k-means algorithm and the fast-MCD algorithm. Despite this coincidence, it is not completely straightforward to combine both algorithms for developing a clustering method which is not severely affected by few outlying observations and being able to cope with non spherical clusters. A sensible way of combining them relies on controlling the relative cluster scatters through constrained concentration steps. With this idea in mind, a new algorithm for the TCLUST robust clustering procedure is proposed which implements such constrained concentration steps in a computationally efficient fashion.

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  • 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.
    • Handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:124-136
    DOI: 10.1016/j.csda.2012.11.018
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    6. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," 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 89-109, September.
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.

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