Impact of contamination on training and test error rates in statistical clustering

Communications in Statistics: Simulation and Computation

Volumn 40, Issue 3, 2011, Pages 394-411

  Ruwet, C ^a   Haesbroeck, G ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Clustering analysis; Error rate; Generalized k means; Influence function; Principal points; Robustness

Indexed keywords

CLUSTERING ANALYSIS; ERROR RATE; GENERALIZED K-MEANS; INFLUENCE FUNCTION; PRINCIPAL POINTS; ROBUSTNESS;

METHOD OF MOMENTS; SUBSIDENCE;

CLUSTER ANALYSIS;

EID: 79751511557     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918.2010.542847     Document Type: Article

References (23)

1. Brøns, H. K., Brunk, H. D., Franck, W. E., Hanson, D. L. (1969). Generalized means and associated families of distributions. The Annals of Mathematical Statistics 40:339-355.
2. Croux, C., Dehon, C. (2001). Robust linear discriminant analysis using S-estimators. The Canadian Journal of Statistics 29:473-492.
3. Croux, C., Filzmoser, P., Joossens, K. (2008). Classification efficiencies for robust linear discriminant analysis. Statistica Sinica 18:581-599.
4. Cuesta-Albertos, J. A., Gordaliza, A., Matran, C. (1997). Trimmed k-means: an attempt to robustify quantizers. The Annals of Statistics 25:553-576.
5. Cuesta-Albertos, J. A., Matran, C. (1988). The strong law of large numbers for k-means and best possible nets of Banach valued random variables. Probability Theory and Related Fields 78:523-534.
6. Donoho, D. L., Huber, P. J. (1983). The notion of breakdown point. In: Bickel, P. J., Doksum, K. A., Hodges, J. L. Jr., eds. A Festschrift for Erich L. Lehmann. Belmont, CA: Wadsworth, pp. 157-184.
7. Dučinskas, K. (1995). Optimal training sample allocation and asymptotic expansions for error rates in discriminant analysis. Acta Applicandae Mathematicae 38:3-11.
8. Flury, B. A. (1990). Principal points. Biometrika 77:33-41.
9. Fraley, C., Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631.
10. Gallegos, M. T., Ritter, G. (2005). A robust method for cluster analysis. The Annals of Statistics 33:347-380. (Pubitemid 40653793)
11. Garcia-Escudero, L. A., Gordaliza, A. (1999). Robustness properties of k-means and trimmed k-means. Journal of the American Statistical Association 94:956-969.
12. Garcia-Escudero, L. A., Gordaliza, A., Matran, C., Mayo-Iscar, A. (2008). A general trimming approach to robust cluster analysis. The Annals of Statistics 36:1324-1345.
13. Genton, M. G., Lucas, A. (2003). Comprehensive definitions of breakdown points for independent and dependent observations. Journal of the Royal Statistical Society Series B 65:81-94. (Pubitemid 37155337)
14. Hampel, F. R. (1971). A general qualitative definition of robustness. The Annals of Statistics 42:1887-1896.
15. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. New-York: John Wiley and Sons.
16. He, X., Simpson, D. G. (1992). Robust direction estimation. The Annals of Statistics 20:351-369.
17. Johnson, R. A., Wichern, D. W. (2007). Applied Multivariate Statistical Analysis. 6th ed. Upper Saddle River, NJ: Pearson Prentice Hall.
18. Mansour, Y., McAllester, D. (2002). Boosting using branching programs. Journal of Computer and System Sciences 64:103-112. (Pubitemid 34473698)
19. Pollard, D. (1981). Strong consistency of k-means clustering. The Annals of Statistics 9:135-140.
20. Pollard, D. (1982). A central limit theorem for k-means clustering. The Annals of Probability 10:919-926.
21. Qiu, D., Tamhane, A. C. (2007). A comparative study of the k-means algorithm and the normal mixture model for clustering: univariate case. Journal of Statistical Planning and Inference 137:3722-3740.
22. Ruwet, C., Haesbroeck, G. (2010). Classification performance of k-means. Preprint of the University of Liege. Available online at: http://orbi.ulg.ac.be/ handle/2268/81354
23. Symons, M. J. (1981). Clustering criteria and multivariate normal mixtures. Biometrics 37:35-43