Componentwise classification and clustering of functional data

Biometrika

Volumn 99, Issue 2, 2012, Pages 299-313

  Delaigle, A ^a   Hall, P ^a   Bathia, N ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Bandwidth; Classification error rate; Kernel method; Statistical smoothing; Tightness of clusters

Indexed keywords

EID: 84861623629     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/ass003     Document Type: Article

References (33)

1. ARAKI, Y., KONISHI, S., KAWANO, S. & MATSUI, H. (2009). Functional logistic discrimination via regularized basis expansions. Commun. Statist. A 38, 2944-57.
2. BERLINET, A., BIAU, G. & ROUVÌERE, L. (2008) Functional classification with wavelets. Ann. Inst. Statist. Univ. Paris 52, 61-80.
3. BIAU, G.,BUNEA, F. & WEGKAMP, M. H. (2005). Functional classification in Hilbert spaces. IEEE Trans. Info. Theory 51, 2163-72.
4. CHAMROUKHI, F., SAME, A.,GOVAERT, G. & AKNIN, P. (2010). A hidden process regression model for functional data description. Application to curve discrimination. Neurocomputing 73, 1210-21.
5. CHIOU, J.-M. & LI, P.-L. (2007). Functional clustering and identifying substructures of longitudinal data. J. R. Statist. Soc. B 69, 679-99.
6. CUEVAS, A., FEBRERO, M. & FRAIMAN, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Comp. Statist. 22, 481-96.
7. DELAIGLE, A. & HALL, P. (2010). Defining probability density for a distribution of random functions. Ann. Statist. 38, 1171-93.
8. DELAIGLE, A. & HALL, P. (2012). Achieving near-perfect classification for functional data. J. R. Statist. Soc. B 74, 267-86.
9. EPIFANIO, I. (2008). Shape descriptors for classification of functional data. Technometrics 50, 284-94.
10. ESCABIAS, M.,AGUILERA, A. M. & VALDERRAMA, M. J. (2007). Functional PLS logit regression model. Comp. Statist. Data Anal. 51, 4891-902.
11. FERRATY, F. & VIEU, P. (2003). Curves discrimination: a nonparametric functional approach. Comp. Statist. Data Anal. 4, 161-73.
12. FERRATY, F. & VIEU, P. (2006). Nonparametric Functional Data Analysis. New York: Springer.
13. FERRATY, F. & VIEU, P. (2009). Additive prediction and boosting for functional data. Comp. Statist. Data Anal. 53, 1400-13.
14. FERRATY, F.,HALL, P. & VIEU, P. (2010). Most-predictive design points for functional data predictors. Biometrika 97, 807-24.
15. FROMONT, M. & TULEAU, C. (2006). Functional classification with margin conditions. In Proc. 19th Annual Conf. Learn. Theory, Pittsburgh, PA, USA, June 22-25, 2006, Ed. J. G. Carbonell and J. Siekmann. New York: Springer.
16. GLENDINNING, R. H. & HERBERT, R. A. (2003). Shape classification using smooth principal components. Pat. Recog. Lett. 24, 2021-30.
17. HALL, P. & HOSSEINI-NASSAB, M. (2006). On properties of functional principal components analysis. J. R. Statist. Soc. B 68, 109-26.
18. HALL, P., POSKITT, D. & PRESNELL, B. (2001). A functional data-Analytic approach to signal discrimination. Technometrics 43, 1-9.
19. HUANG, D.-S. & ZHENG, C.-H. (2006). Independent component analysis-based penalized discriminant method for tumor classification using gene expression data. Bioinformatics 22, 1855-62.
20. JAMES, G. & HASTIE, T. (2001). Functional linear discriminant analysis for irregularly sampled curves. J. R. Statist. Soc. B 63, 533-50.
21. JAMES, G. & SUGAR, C. (2003). Clustering for sparsely sampled functional data. J. Am. Statist. Assoc. 98, 397-408.
22. LENG, X. & MÜLLER, H.-G. (2006). Classification using functional data analysis for temporal gene expression data. Bioinformatics 22, 68-76.
23. LÓPEZ-PINTADO, S. & ROMO, J. (2006). Depth-based classification for functional data. In DIMACS Ser. Discrete Math. Theor. Comp. Sci., vol. 72, 103-20.
24. PENG, J. & MÜLLER, H.-G. (2008). Distance-based clustering of sparsely observed stochastic processes, with applications to online auctions. Ann. Appl. Statist. 2, 1056-77.
25. PREDA, C., SAPORTA, G. & LEVEDER, C. (2007). PLS classification of functional data. Comp. Statist. 22, 223-35.
26. R DEVELOPMENT CORE TEAM (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0, http://www.R-project.org.
27. RAMSAY, J. O. & SILVERMAN, B. W. (2005). Functional Data Analysis, 2nd ed. New York: Springer.
28. ROSSI, F. & VILLA, N. (2006). Support vector machine for functional data classification. Neurocomputing 69, 730-42.
29. SHIN, H. (2008). An extension of Fisher's discriminant analysis for stochastic processes. J. Mult. Anal. 99, 1191-216.
30. SONG, J. J., DENG, W., LEE, H.-J. & KWON, D. (2008). Optimal classification for time-course gene expression data using functional data analysis. Comp. Biol. Chem. 32, 426-32.
31. VILAR, J. A. & PERTEGA, S. (2004). Discriminant and cluster analysis for Gaussian stationary processes: local linear fitting approach. J. Nonparam. Statist. 16, 443-62.
32. WAND, M. P. & JONES, M. C. (1995). Kernel Smoothing. London: Chapman & Hall.
33. WANG, X. H., RAY, S. & MALLICK, B. K. (2007). Bayesian curve classification using wavelets. J. Am. Statist. Assoc. 102, 962-73.