## A simulation study to compare robust clustering methods based on mixtures.(English)Zbl 1284.62366

Summary: The following mixture model-based clustering methods are compared in a simulation study with one-dimensional data, fixed number of clusters and a focus on outliers and uniform “noise”: an ML-estimator (MLE) for Gaussian mixtures, an MLE for a mixture of Gaussians and a uniform distribution (interpreted as “noise component” to catch outliers), an MLE for a mixture of Gaussian distributions where a uniform distribution over the range of the data is fixed, a pseudo-MLE for a Gaussian mixture with improper fixed constant over the real line to catch “noise”, and MLEs for mixtures of $$t$$-distributions with and without estimation of the degrees of freedom. The RIMLE is the best method in some, and acceptable in all, simulation setups, and can therefore be recommended.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62F35 Robustness and adaptive procedures (parametric inference) 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators

mclust
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### References:

 [1] Banfield J, Raftery AE (1993) Model-based gaussian and non-gaussian clustering. Biometrics 49: 803–821 · Zbl 0794.62034 [2] Coretto P (2008) The noise component in model-based clustering. PhD thesis, Department of Statistical Science, University College London. http://www.ontherubicon.com/pietro/docs/phdthesis.pdf [3] Cuesta-Albertos JA, Gordaliza A, Matrán C (1997) Trimmed k-means: an attempt to robustify quantizers. Ann Stat 25: 553–576 · Zbl 0878.62045 [4] Fraley C, Raftery AE (1998) How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput J 41: 578–588 · Zbl 0920.68038 [5] Fraley C, Raftery AE (2006) Mclust version 3 for r: normal mixture modeling and model-based clustering. Technical report 504, Department of Statistics, University of Washington [6] Gallegos MT, Ritter G (2005) A robust method for cluster analysis. Ann Stat 33(5): 347–380 · Zbl 1064.62074 [7] García-Escudero LA, Gordaliza A, Matrán C, Mayo-Iscar A (2008) A general trimming approach to robust cluster analysis. Ann Stat 38(3): 1324–1345 · Zbl 1360.62328 [8] Hathaway RJ (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13: 795–800 · Zbl 0576.62039 [9] Hennig C (2004) Breakdown points for maximum likelihood estimators of location-scale mixtures. Ann Stat 32(4): 1313–1340 · Zbl 1047.62063 [10] Hennig C (2005) Robustness of ML estimators of location-scale mixtures. In: Baier D, Wernecke KD (eds) Innovations in classification. Data science, and information systems. Springer, Heidelberg, pp 128–137 · Zbl 05243397 [11] Hennig C, Coretto P (2008) The noise component in model-based cluster analysis. In: Preisach C, Burkhardt H, Schmidt-Thieme L, Decker R (eds) Data analysis, machine learning and applications. Springer, Berlin, , pp 127–138 [12] Hosmer DW (1978) Comment on ”Estimating mixtures of normal distributions and switching regressions” by R. Quandt and J.B. Ramsey. J Am Stat Assoc 73(364): 730–752 · Zbl 0401.62024 [13] Karlis D, Xekalaki E (2003) Choosing initial values for the EM algorithm for finite mixtures. Comput Stat Data Anal 41(3–4): 577–590 · Zbl 1429.62082 [14] Liu C (1997) ML estimation of the multivariate t distribution and the EM algorithms. J Multivar Anal 63: 296–312 · Zbl 0884.62059 [15] McLachlan G, Krishnan T (1997) The EM algorithm and extensions. Wiley, New York · Zbl 0882.62012 [16] McLachlan G, Peel D (2000) Robust mixture modelling using the t-distribution. Stat Comput 10(4): 339–348 [17] Neykov N, Filzmoser P, Dimova R, Neytchev P (2007) Robust fitting of mixtures using the trimmed likelihood estimator. Comput Stat Data Anal 17(3): 299–308 · Zbl 1328.62033 [18] Redner R, Walker HF (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev 26: 195–239 · Zbl 0536.62021
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