A fuzzy approach to robust regression clustering
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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.
KeywordsRobustness Fuzzy clustering Trimming Regression clustering
Mathematics Subject Classification62H30
The authors are grateful to three referees and the Associated Editor for several constructive suggestions. Research partially supported by the Spanish Ministerio de Economía y Competitividad, Grant MTM2014-56235-C2-1-P, and by Consejería de Educación de la Junta de Castilla y León, Grant VA212U13.
- Ali AM, Karmakar GC, Dooley LS (2008) Review on fuzzy clustering algorithms. J Adv Comput 2:169–181Google Scholar
- Bock HH (1969) The equivalence of two extremal problems and its application to the iterative classification of multivariate data. Paper presented at the Workshop “Medizinische Statistik”, Forschungsinstitut OberwolfachGoogle Scholar
- Coretto P, Hennig C (2016) Robust improper maximum likelihood: tuning, computation and a comparison with other methods for robust Gaussian clustering. J Am Stat Assoc (in press)Google Scholar
- Gustafson DE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE international conference on fuzzy systems, vol 25, pp 761–766Google Scholar
- Honda K, Ohyama T, Ichihashi H, Notsu A (2008) FCM-type switching regression with alternating least square method. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ 2008), pp 122–127Google Scholar
- Perry PO (2009) Cross-validation for unsupervised learning. arXiv:0909.3052
- Sadaaki M, Masao M (1997) Fuzzy \(c\)-means as a regularization and maximum entropy approach. In: Proceedings of the 7th international fuzzy systems association world congress (IFSA’97), vol 2. University of Economics, Prague, pp 86–92Google Scholar
- Wu KL, Yang MS, Hsieh, JN (2009) Alternative fuzzy switching regression. In: Proceedings of the international multiconference of engineers and computer scientists 2009 (IMECS 2009), 18–20 Mar, vol 1. Newswood Limited, Hong KongGoogle Scholar