Abstract
A methodology for robust fuzzy clustering is proposed. This methodology can be widely applied in very different statistical problems given that it is based on probability likelihoods. Robustness is achieved by trimming a fixed proportion of “most outlying” observations which are indeed self-determined by the data set at hand. Constraints on the clusters’ scatters are also needed to get mathematically well-defined problems and to avoid the detection of non-interesting spurious clusters. The main lines for computationally feasible algorithms are provided and some simple guidelines about how to choose tuning parameters are briefly outlined. The proposed methodology is illustrated through two applications. The first one is aimed at heterogeneously clustering under multivariate normal assumptions and the second one might be useful in fuzzy clusterwise linear regression problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Banerjee A, Davé RN (2012) Robust clustering. Wires Data Min Knowl 2:29–59
Bezdek JC (1981) Pattern recognition with fuzzy objective function algoritms. Plenum Press, New York
Davé RN (1991) Characterization and detection of noise in clustering. Pattern Recogn Lett 12:657–664
Davé RN, Krishnapuram R (1997) Robust clustering methods: a unified view. IEEE Trans Fuzzy Syst 5:270–293
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39:1–38
Dotto F, Farcomeni A, García-Escudero LA, Mayo-Iscar A (2016) A fuzzy approach to robust regression clustering. Submitted manuscript
Farcomeni A, Greco L (2015) Robust methods for data reduction. Chapman and Hall/CRC, Boca Raton, Florida
Fritz H, García-Escudero LA, Mayo-Iscar A (2013) Robust constrained fuzzy clustering. Inf Sci 245:38–52
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 regresin through trimming. Comput Stat data Anal 54:3057–3069
Gath I, Geva AB (1989) Unsupervised optimal fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 11:773–781
Gustafson EE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. Proceedings of the IEEE lnternational conference on fuzzy systems, San Diego, pp 761–766 (1979)
Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1:195–204
Hosmer DW (1974) Maximun likelihood estimates of the parameters of a mixture of two regression lines. Commun Stat Theory Methods 3:995–1006
Kuo-Lung W, Miin-Shen Y, June-Nan H (2009) Alternative fuzzy switching regression. In: Proceedings of the international multiconference of engineers and computer scientist
Kim J, Krishnapuram R, Davé R (1996) Application of the least trimmed squares technique to prototype-based clustering. Pattern Recogn Lett 17:633–641
Klawonn F (2004) Noise clustering with a fixed fraction of noise. In: Lotfi A, Garibaldi JM (eds) Applications and science in soft computing. Springer, Berlin-Heidelberg, pp 133–138
Krishnapuram R, Keller JM (1993) A possibilistic approach to clustering. IEEE Trans Fuzzy Syst 1:98–110
Krishnapuram R, Keller JM (1996) The possibilistic \(C\)-means algorithm: Insights and recommandations. IEEE Trans Fuzzy Syst 4:385–393
Lenstra AK, Lenstra JK, Rinnoy Kan AHG, Wansbeek TJ (1982) Two lines least squares. Ann Discrete Math 16:201–211
Łeski J (2003) Towards a robust fuzzy clustering. Fuzzy Set Syst 137:215–233
Miyamoto S, Mukaidono 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), pp 86–92
Ritter G (2015) Robust cluster analysis and variable selection. Monographs on statistics and applied probability. Chapman & Hall/CRC, Boca Raton, Florida
Rousseeuw PJ, Trauwaert E, Kaufman L (1995) Fuzzy clustering with high contrast. J Comput Appl Math 64:81–90
Rousseeuw PJ, Kaufman L, Trauwaert E (1996) Fuzzy clustering using scatter matrices. Comput Stat Data Anal 23:135–151
Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41:212–223
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
Wu KL, Yang MS (2002) Alternative \(c\)-means clustering algorithms. Pattern Recogn 35:2267–2278
Yang MS (1993) On a class of fuzzy classification maximum likelihood procedures. Fuzzy Set Syst 57:365–337
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Dotto, F., Farcomeni, A., García-Escudero, L.A., Mayo-Iscar, A. (2017). Robust Fuzzy Clustering via Trimming and Constraints. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-42972-4_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42971-7
Online ISBN: 978-3-319-42972-4
eBook Packages: EngineeringEngineering (R0)