Abstract
Three different approaches for robust fuzzy clusterwise regression are reviewed. They are all based on the simultaneous application of trimming and constraints. The first one follows from the joint modeling of the response and explanatory variables through a normal component fitted in each cluster. The second one assumes normally distributed error terms conditional on the explanatory variables while the third approach is an extension of the Cluster Weighted Model. A fixed proportion of “most outlying” observations are trimmed. The use of appropriate constraints turns these problem into mathematically well-defined ones and, additionally, serves to avoid the detection of non-interesting or “spurious” linear clusters. The third proposal is specially appealing because it is able to protect us against outliers in the explanatory variables which may act as “bad leverage” points. Feasible and practical algorithms are outlined. Their performances, in terms of robustness, are illustrated in some simple simulated examples.
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References
Banerjee A, Davé RN (2012) Robust clustering. WIREs Data Min Know Discov 2:29–59
Bezdek JC (1981) Pattern recognition with fuzzy objective function algoritms. Plenum Press, New York
Davé RN, Krishnapuram R (1997) Robust clustering methods: a unified view. IEEE Trans Fuzzy Syst 5:270–293
DeSarbo WS, Cron WL (1988) A maximum likelihood methodology for clusterwise linear regression. J Classif 5:249–282
Dotto F, Farcomeni A, García-Escudero LA, Mayo-Iscar A (2017) A fuzzy approach to robust clusterwise regression. Adv Data Anal Classif 11(4):691–710
Farcomeni A, Greco L (2015) Robust methods for data reduction. Chapman & Hall/CRC, London
Fritz H, García-Escudero LA, Mayo-Iscar A (2013) Robust constrained fuzzy clustering. Inf Sci 245:38–52
Fritz H, García-Escudero LA, Mayo-Iscar A (2013) A fast algorithm for robust constrained clustering. Comput Stat Data Anal 61:124–136
García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2008) A general trimming approach to robust cluster analysis. Ann Stat 36:1324–1345
García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2010) A review of robust clustering methods. Adv Data Anal Classif 4:89–109
García-Escudero LA, Gordaliza A, San Martín R, Mayo-Iscar A (2010) Robust clusterwise linear regresssion through trimming. Comput Stat Data Anal 54:3057–3069
García-Escudero LA, Gordaliza A, Greselin F, Ingrassia S, Mayo-Iscar A (2016) The joint role of trimming and constraints in robust estimation for mixtures of gaussian factor analyzers. Comput Stat Data Anal 99:131–147
García-Escudero LA, Greselin F, Mayo-Iscar A (2017) Robust fuzzy cluster weighted modeling. Submitted
Gershenfeld N, Schoner B, Metois E (1999) Cluster-weighted modelling for time-series analysis. Nature 397:329–332
Gustafson EE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of 1978 IEEE conference on decision and control including the 17th symposium on adaptive processes. IEEE, Piscataway
Hathaway R (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13:795–800
Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1:195–204
Honda K, Ohyama T, Ichihashi H, Hotsu A (2008) FCM-type switching regression with alternating least square method. In: Proceedings of 2008 IEEE international conference on Fuzzy systems (IEEE World congress on computational intelligence). IEEE, Piscataway
Hosmer DW Jr (1974) Maximum likelihood estimates of the parameters of a mixture of two regression lines. Commun Stat 3:995–1006
Ingrassia S, Rocci R (2007) Constrained monotone EM algorithms for finite mixture of multivariate gaussians. Comput Stat Data Anal 51:5339–5351
Lenstra AK, Lenstra JK, Rinnoy Kan AHG, Wansbeek TJ (1982) Two lines least squares. Ann Discr Math 16:201–211
Ritter G (2015) Robust cluster analysis and variable selection. Monographs on statistics and applied probability. Chapman & Hall/CRC, London
Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41:212–223
Rousseeuw PJ, Kaufman L, Trauwaert E (1996) Fuzzy clustering using scatter matrices. Comp Stat Data Anal 23:135–151
Ruspini E (1969) A new approach to clustering. Inf Control 15:22–32
Späth H (1982) A fast algorithm for clusterwise regression. Computing 29:175–181
Trauwaert E, Kaufman L, Rousseeuw PJ (1991) Fuzzy clustering algorithms based on the maximum likelihood principle. Fuzzy Sets Syst 42:213–227
Yang M-S (1993) On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets Syst 57:365–375
Wu WL, Yang MS, Hsieh NJ (2009) Alternative fuzzy switching regression. In: Proceedings of international multiconference of engineers and computer scientists, IMECS 2009, vol I. IAENG, Hong Kong
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García-Escudero, L.A., Gordaliza, A., Greselin, F., Mayo-Iscar, A. (2018). Robust Approaches for Fuzzy Clusterwise Regression Based on Trimming and Constraints. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_15
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