Achieving near perfect classification for functional data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 74, Issue 2, 2012, Pages 267-286

  Delaigle, Aurore ^a   Hall, Peter ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Bayes classifier; Centroid method classifier; Cross validation; Dimension reduction; Error rate; Gaussian process; Linear model; Projection

Indexed keywords

EID: 84858298016     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2011.01003.x     Document Type: Article

References (33)

1. Araki, Y., Konishi, S., Kawano, S. and Matsui, H. (2009) Functional logistic discrimination via regularized basis expansions. Communs Statist. Theor. Meth., 38, 2944-2957.
2. Berlinet, A., Biau, G. and Rouvière, L. (2008) Functional classification with wavelets. Ann. Inst. Statist. Univ. Par., 52, 61-80.
3. Biau, G., Bunea, F. and Wegkamp, M. H. (2005) Functional classification in Hilbert spaces. IEEE Trans. Inform. Theor., 51, 2163-2172.
4. Chamroukhi, F., Same, A., Govaert, G. and Aknin, P. (2010) A hidden process regression model for functional data description: application to curve discrimination. Neurocomputing, 73, 1210-1221.
5. Cook, R. D. (2007) Dimension reduction in regression. Statist. Sci., 22, 1-26.
6. Cox, D. R. (1968) Notes on some aspects of regression analysis. J. R. Statist. Soc. A, 131, 265-279.
7. Cuevas, A., Febrero, M. and Fraiman, R. (2007) Robust estimation and classification for functional data via projection-based depth notions. Comput. Statist., 22, 481-496.
8. Delaigle, A. and Hall, P. (2010) Defining probability density for a distribution of random functions. Ann. Statist., 38, 1171-1193.
9. Epifanio, I. (2008) Shape descriptors for classification of functional data. Technometrics, 50, 284-294.
10. Ferraty, F. and Vieu, P. (2003) Curves discrimination: a nonparametric functional approach. Comput. Statist. Data Anal., 4, 161-173.
11. Ferraty, F. and Vieu, P. (2006) Nonparametric Functional Data Analysis. New York: Springer.
12. Fromont, M. and Tuleau, C. (2006) Functional classification with margin conditions. In Learning Theory: Proc. 19th A. Conf. Learning Theory, Pittsburgh, June 22nd-25th(eds J. G. Carbonell and J. Siekmann). New York: Springer.
13. Glendinning, R. H. and Herbert, R. A. (2003). Shape classification using smooth principal components. Pattn Recogn. Lett., 24, 2021-2030.
14. Hall, P. and Hosseini-Nasab, M. (2006) On properties of functional principal components analysis. J. R. Statist. Soc. B, 68, 109-126.
15. Hall, P. and Marron, J. S. (1991) Local minima in cross-validation functions. J. R. Statist. Soc. B, 53, 245-252; correction, 54 (1992), 907.
16. Hall, P., Poskitt, D. and Presnell, B. (2001) A functional data-analytic approach to signal discrimination. Technometrics, 43, 1-9.
17. Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. New York: Springer.
18. Huang, D.-S. and Zheng, C.-H. (2006) Independent component analysis-based penalized discriminant method for tumor classification using gene expression data. Bioinformatics, 22, 1855-1862.
19. James, G. and Hastie, T. J. (2001) Functional linear discriminant analysis for irregularly sampled curves. J. R. Statist. Soc. B, 63, 533-550.
20. James, G. and Sugar, C. (2003) Clustering for sparsely sampled functional data. J. Am. Statist. Ass., 98, 397-408.
21. Kalivas, J. H. (1997) Two data sets of near infrared spectra. Chemetr. Intell. Lab. Syst., 37, 255-259.
22. Leng, X. Y. and Müller, H.-G. (2006) Classification using functional data analysis for temporal gene expression data. Bioinformatics, 22, 68-76.
23. López-Pintado, S. and Romo, J. (2006) Depth-based classification for functional data. In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol., pp. 103-120. Providence: American Mathematical Society.
24. Müller, H.-G. and Stadmüller, U. (2005) Generalized functional linear models. Ann. Statist., 33, 774-805.
25. Preda, C. and Saporta, G. (2005) PLS regression on a stochastic process. Comput. Statist. Data Anal., 48, 149-158.
26. Preda, C., Saporta, G. and Leveder, C. (2007) PLS classification of functional data. Comput. Statist., 22, 223-235.
27. Ramsay, J. O. and Silverman, B. W. (2005) Functional Data Analysis, 2nd edn. New York: Springer.
28. Rossi, F. and Villa, N. (2006) Support vector machine for functional data classification. Neurocomputing, 69, 730-742.
29. Shin, H. (2008) An extension of Fisher's discriminant analysis for stochastic processes. J. Multiv. Anal., 99, 1191-1216.
30. Song, J. J., Deng, W., Lee, H.-J. and Kwon, D. (2008) Optimal classification for time-course gene expression data using functional data analysis. Computnl Biol. Chem., 32, 426-432.
31. Tian, S. T. and James, G. (2010) Interpretable dimensionality reduction for classification with functional data. Manuscript.
32. Vilar, J. A. and Pertega, S. (2004) Discriminant and cluster analysis for Gaussian stationary processes: local linear fitting approach. J. Nonparam. Statist., 16, 443-462.
33. Wang, X. H., Ray, S. and Mallick, B. K. (2007) Bayesian curve classification using wavelets. J. Am. Statist. Ass., 102, 962-973.