A proposal for robust curve clustering

Journal of Classification

Volumn 22, Issue 2, 2005, Pages 185-201

  Garcia Escudero, Luis Angel ^a   Gordaliza, Alfonso ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Clustering; Functional data; K means; Robustness; Trimmed k means

Indexed keywords

EID: 33744726447     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-005-0013-8     Document Type: Article

References (30)

1. ABRAHAM, C., CORMLLON, P.A., MATZNER-LØBER, E., and MOLINARI, N. (2003), "Unsupervised Curve Clustering Using B-splines," Scandinavian Journal of Statistics, 30, 1-15.
2. CADEZ, I., GAFFNEY, S., and SMYTH, P. (2000), "A General Probabilistic Framework for Clustering Individuals", Proceedings of the sixth ACMSIGKDD International Conference on Knowledge Discovery and Data Mining, 140-149.
3. CRELLIN, N., HASTIE, T., and JOHNSTONE, I.M. (1997), "Statistical Models for Image Sequences," in L. Billard, N. I. Fisher (Eds.), Computing Science and Statistics. Interface '96. Proceedings of the 28th Symposium on the Interface. Fairfax Station, VA: The Interface Foundation of North America, Inc.
4. CUESTA-ALBERTOS, J.A., and FRAIMAN, R. (2005), To appear in "Data Depth: Robust Multivariate Statistical Analysis, Computational Geometry & Applications" in R. Liu, R. Serfling and D. Souvaine (Eds.), American Mathematical Society in DIMACS Series.
5. CUESTA-ALBERTOS, J.A., GORDALIZA, A., and MATRÁN, C. (1997), "Trimmed k-means: An Attempt to Robustify Quantizers," The Annals of Statistics, 25, 553-576.
6. CUESTA, J.A., and MATRÁN, C. (1988), "The Strong Law of Large Numbers and Best Possible Nets of Banach Valued Random Variables," Probability Theory and Related Fields, 78, 523-534.
7. DE BOOR, C. (1978). A Practical Guide to Splines, New York: Springer-Verlag.
8. DE SOETE, G. (1993), "Hierarchical Clustering of Sampled Functions," in O. Opitz, B. Lausen amd R. Klar (Eds.), Information and Classification. Berlin: Springer-Verlag.
9. EUBANK, R.L. (1988). Spline Smoothing and Nonparametric Regression. New York: Marcel Dekker.
10. FRAIMAN, R., and MUNIZ, G. (2001), "Trimmed Means for Functional Data," TEST, 10, 419-440.
11. FLURY, B., and TARPEY, T. (1993), "Representing a Large Collection of Curves: A Case for Principal Points "American Statistician, 47, 305-306.
12. FRIEDMAN, J.H., and SILVERMAN, B.W. (1989), "Flexible Parsimonious Smoothing and Additive Modelling (With Discussion and Report)," Technometrics, 31, 1-39.
13. GARCÍA-ESCUDERO, L.A., and GORDALIZA, A. (1999), "Robustness Properties of k-means and Trimmed k-means" Journal of the American Statistical Association, 94, 956-969.
14. GARCÍA-ESCUDERO, L.A., GORDALIZA, A.c and MATRÁN, C. (1999), "A Central Limit Theorem for Multivariate Generalized Trimmed k-means," The Annals of Statistics, 27, 1061-1079.
15. GARCÍA-ESCUDERO, L.A., GORDALIZA, A., and MATRÁN, C. (2003), "Trimming Tools in Exploratory Data Analysis," Journal of Computational and Graphical Statistics, 12, 434-449.
16. GREEN, P.J, and SILVERMAN, B.W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. London: Chapman and Hall.
17. HARTIGAN, J.A. (1975), Clustering Algorithms. New York: Wiley.
18. HECKMAN, N., and ZAMAR, R.H. (1999), "The Shape of Regression Curves," Biometrika, 87, 135-144.
19. HUHTALA, I., KÄRKKÄINEN, J., and TOIVONEN, H. (1999), "Mining for Similarities in Aligned Time Series Using Wavelets," Data Mining and Knowledge Discovery: Theory, Tools, and Technology. SPIE Proceedings Series, 3695, 150-160.
20. JAMES, G.M., and SUGAR, C.A. (2003), "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, 98, 397-408.
21. JONES, M.C., and RICE, J.A. (1992), "Displaying the Important Data Features of a Large Collection of Similar Curves," The American Statistician, 46, 140-145.
22. KAUFMAN, L., and ROUSSEEUW, P.J. (1990), Finding Groups in Data. New York: Wiley.
23. LOCANTORE, N., MARRON, J.S., SIMPSON, D.G., ZHANG, J.T, and COHEN, K.L. (1999), "Robust Principal Component Analysis for Functional Data," TEST, 8, 1-73.
24. th Berkeley Symposium on Mathematics, Statistics, and Probability. Vol 1, 281-298.
25. RAMSAY, J., and SILVERMAN, B. (1997). Functional Data Analysis. New York: Springer.
26. ROUSSEEUW, P.J., and LEROY, A.M. (1987), Robust Regression and Outlier Detection. New York: Wiley-Interscience.
27. ROUSSEEUW, P.J., and VAN DRIESSEN, K. (1999), "A Fast Algorithm for the Minimum Covariance Determinant Estimator," Technometrics, 41, 212-223.
28. SCHUMAKER, L.L. (1981). Spline Functions: Basic Theory, New York: Wiley.
29. TARPEY, T., and KINATEDER, K.K. J. (2003), "Clustering Functional Data," Journal of Classification, 20, 93-114.
30. TARPEY, T., PETKOVA, E., and OGDEN, R.T. (2003), "Profiling Placebo Responders by Selfconsistent Partitioning of Functional Data," Journal of the American Statistical Association, 98, 850-858.