Operator-valued Kernels for Learning from Functional Response Data

Abstract : In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.
Complete list of metadatas

Contributor : Alain Rakotomamonjy <>
Submitted on : Friday, April 26, 2019 - 11:24:18 PM
Last modification on : Thursday, June 27, 2019 - 1:36:06 PM

Links full text


  • HAL Id : hal-02112788, version 1
  • ARXIV : 1510.08231


Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Alain Rakotomamonjy, et al.. Operator-valued Kernels for Learning from Functional Response Data. Journal of Machine Learning Research, Microtome Publishing, 2016, 17 (20), pp.1-54. ⟨http://jmlr.org/papers/v17/11-315.html⟩. ⟨hal-02112788⟩



Record views