The Journal of Machine Learning Research
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Functional Data Analysis with R and MATLAB
Functional Data Analysis with R and MATLAB
The Representation of Chemical Spectral Data for Classification
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
A functional density-based nonparametric approach for statistical calibration
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
No effect tests in regression on functional variable and some applications to spectrometric studies
Computational Statistics
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Many regression tasks in practice dispose in low gear instance of digitized functions as predictor variables. This has motivated the development of regression methods for functional data. In particular, Naradaya-Watson Kernel (NWK) and Radial Basis Function (RBF) estimators have been recently extended to functional nonparametric regression models. However, these methods do not allow for dimensionality reduction. For this purpose, we introduce Support Vector Regression (SVR) methods for functional data. These are formulated in the framework of approximation in reproducing kernel Hilbert spaces. On this general basis, some of its properties are investigated, emphasizing the construction of nonnegative definite kernels on functional spaces. Furthermore, the performance of SVR for functional variables is shown on a real world benchmark spectrometric data set, as well as comparisons with NWK and RBF methods. Good predictions were obtained by these three approaches, but SVR achieved in addition about 20% reduction of dimensionality.