The nearest neighbors (k-NN) method is a simple, easy to motivate procedure for supervised classification with functional data. We first consider a recent result by Cerou and Guyader (2006) which provides a sufi- cient condition to ensure the consistency of the k-NN method. We give some concrete examples in which such condition is fulfilled. Secondly, we show the results of a comparative study, performed via simulations and some real-data examples, involving the k-NN procedure (as a “benchmark choice”) together with other some recently proposed methods for functional classification.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abraham, C., Biau, G. and Cadre, B.: On the kernel rule for function classification. Ann. Inst. Stat. Math. 58, 619-633 (2006).
Biau, G., Bunea, F. and Wegkamp, M. H.: Functional classfication in Hilbert spaces. IEEE Transactions on Information Theory. 51, 2163-2172 (2005).
Cérou, F. and Guyader, A.: Nearest neighbor classification in infinite dimension. ESAIM: Probability and Statistics. 10, 340-355 (2006).
Cuevas, A., Febrero, M. and Fraiman, R.: Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics. 22, 481-496 (2007).
Devroye, L., Györ , L. and Lugosi, G.: A Probabilistic Theory of Pattern Recogni-tion. Springer. New York. (1996).
Evgeniou , T., Poggio, T. Pontil, M. and Verri, A.: Regularization and statistical learning theory for data analysis. Computational Statistics and Data Analysis. 38, 421-432 (2002).
Ferraty, F. and Vieu, P.: Nonparametric Functional Data Analysis. Springer, New York. (2006).
Liu, Y. and Rayens, W.: PLS and dimension reduction for classification. Computa-tional Statistics. 22, 189-208 (2007).
Müller, H.-G.: Functional modelling and classification of longitudinal data. Scandi-navian Journal of Statistics. 32, 223-240 (2005).
Preda, C., Saporta, G. and Lévéder, C.: PLS classication of functional data. Com-putational Statistics. 22, 223-235 (2007).
Ramsay, J. O. and Silverman, B.: Functional Data Analysis. Second edition. Springer-Verlag. New York. (2005).
Stone, C. J.: Consistent nonparametric regression. Ann. Statist. 5, 595-645 (1977).
Wahba, G.: Soft and hard classification by reproducing kernel Hilbert space methods. Proceedings of the National Academy of Sciences. 99, 16524-16530 (2002).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Physica-Verlag Heidelberg
About this paper
Cite this paper
Baíllo, A., Cuevas, A. (2008). Supervised Classification for Functional Data: A Theoretical Remark and Some Numerical Comparisons. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2062-1_7
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2061-4
Online ISBN: 978-3-7908-2062-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)