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Variable selection in model-based clustering: A general variable role modeling

Author

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  • Maugis, C.
  • Celeux, G.
  • Martin-Magniette, M.-L.

Abstract

The currently available variable selection procedures in model-based clustering assume that the irrelevant clustering variables are all independent or are all linked with the relevant clustering variables. A more versatile variable selection model is proposed, taking into account three possible roles for each variable: The relevant clustering variables, the irrelevant clustering variables dependent on a part of the relevant clustering variables and the irrelevant clustering variables totally independent of all the relevant variables. A model selection criterion and a variable selection algorithm are derived for this new variable role modeling. The model identifiability and the consistency of the variable selection criterion are also established. Numerical experiments highlight the interest of this new modeling.

Suggested Citation

  • Maugis, C. & Celeux, G. & Martin-Magniette, M.-L., 2009. "Variable selection in model-based clustering: A general variable role modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3872-3882, September.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3872-3882
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    References listed on IDEAS

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    1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard & Langrognet, Florent, 2006. "Model-based cluster and discriminant analysis with the MIXMOD software," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 587-600, November.
    2. Tadesse, Mahlet G. & Sha, Naijun & Vannucci, Marina, 2005. "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 602-617, June.
    3. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
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    2. C. Biernacki & J. Jacques & C. Keribin, 2023. "A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 332-381, July.
    3. Jinsun Kim & Jiyeon Choi & Minji Park & Joong-Hyuk Min & Jong Mun Lee & Jimin Lee & Eun Hye Na & Heeseon Jang, 2022. "A Study on Identifying Priority Management Areas and Implementing Best Management Practice for Effective Management of Nonpoint Source Pollution in a Rural Watershed, Korea," Sustainability, MDPI, vol. 14(21), pages 1-22, October.
    4. Maugis, C. & Celeux, G. & Martin-Magniette, M.-L., 2011. "Variable selection in model-based discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1374-1387, November.
    5. Nema Dean & Rebecca Nugent, 2013. "Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas," 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(3), pages 339-357, September.
    6. Anzanello, Michel J. & Fogliatto, Flavio S., 2011. "Selecting the best clustering variables for grouping mass-customized products involving workers' learning," International Journal of Production Economics, Elsevier, vol. 130(2), pages 268-276, April.
    7. Peña, Daniel & Prieto Fernández, Francisco Javier & Rendon Aguirre, Janeth Carolina, 2017. "Clustering Big Data by Extreme Kurtosis Projections," DES - Working Papers. Statistics and Econometrics. WS 24522, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Melnykov, Volodymyr, 2016. "Model-based biclustering of clickstream data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 31-45.
    9. Matthieu Marbac & Christophe Biernacki & Vincent Vandewalle, 2015. "Model-Based Clustering for Conditionally Correlated Categorical Data," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 145-175, July.
    10. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    11. Matthieu Marbac & Mohammed Sedki & Tienne Patin, 2020. "Variable Selection for Mixed Data Clustering: Application in Human Population Genomics," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 124-142, April.
    12. Léna CAREL & Pierre ALQUIER, 2017. "Simultaneous Dimension Reduction and Clustering via the NMF-EM Algorithm," Working Papers 2017-38, Center for Research in Economics and Statistics.
    13. 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.
    14. Cappozzo, Andrea & Greselin, Francesca & Murphy, Thomas Brendan, 2021. "Robust variable selection for model-based learning in presence of adulteration," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    15. Dolnicar, Sara & Grün, Bettina & Leisch, Friedrich, 2016. "Increasing sample size compensates for data problems in segmentation studies," Journal of Business Research, Elsevier, vol. 69(2), pages 992-999.

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