Abstract
In fuzzy clustering, data elements can belong to more than one cluster , and membership levels are associated with each element, to indicate the strength of the association between that data element and a particular cluster. Unfortunately, fuzzy clustering is not robust, while in real applications the data is contaminated by outliers and noise, and the assumed underlying Gaussian distributions could be unrealistic. Here we propose a robust fuzzy estimator for clustering through Factor Analyzers, by introducing the joint usage of trimming and of constrained estimation of noise matrices in the classic Maximum Likelihood approach.
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References
Cattell R (1944) A note on correlation clusters and cluster search methods. Psychometrika 9(3):169–184
Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J Cybern 3:32–57
Fritz H, García-Escudero LA, Mayo-Iscar A (2013) A fast algorithm for robust constrained clustering. Comput Stat Data Anal 61:124–136
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(3):1324–1345
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
Greselin F, Ingrassia S (2015) Maximum likelihood estimation in constrained parameter spaces for mixtures of factor analyzers. Stat Comput 25:215–226
Gustafson EE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE lnternational conference on fuzzy systems, San Diego, pp 761–766
Hathaway R (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13(2):795–800
Huber PJ (1981) Robust statistics. Wiley, New York
Ingrassia S, Rocci R (2007) Constrained monotone EM algorithms for finite mixture of multivariate Gaussians. Comput Stat Data Anal 51:5339–5351
MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of 5-th Berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, Berkeley, pp 281–297
McLachlan GJ, Peel D (2000) Finite mixture models. Wiley, New York
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 (IFSA97), vol 2, pp 86–92
Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41:212–223
Wee WG, Fu KS (1969) A formulation of fuzzy automata and its application as a model of learning systems. IEEE Trans Syst Sci Cybern 5(3):215–223. doi:10.1109/TSSC.1969.300263
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García-Escudero, L.A., Greselin, F., Mayo Iscar, A. (2017). Fuzzy Clustering Through Robust Factor Analyzers. 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_29
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DOI: https://doi.org/10.1007/978-3-319-42972-4_29
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