Operator-valued Kernels for Learning from Functional Response Data

Hachem Kadri 1 Emmanuel Duflos 2 Philippe Preux 2, 3 Stéphane Canu 4 Alain Rakotomamonjy 4 Julien Audiffren 5
1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]
LIF - Laboratoire d'informatique Fondamentale de Marseille
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
5 CMLA - Centre de Mathématiques et de Leurs Applications
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.
Keywords : audio signal processing operator-valued kernels nonlinear functional data analysis function-valued reproducing kernel Hilbert spaces
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01221329
Contributor : Hachem Kadri <>
Submitted on : Thursday, October 29, 2015 - 4:33:01 PM
Last modification on : Monday, November 4, 2019 - 12:58:03 PM
Long-term archiving on: Friday, May 5, 2017 - 1:16:29 PM

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  • HAL Id : hal-01221329, version 2
  • ARXIV : 1510.08231

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CNRS | INRIA | EC-MARSEILLE | LITIS | UNIV-AMU | COMUE-NORMANDIE | CRISTAL-SEQUEL | CRISTAL-SIGMA | ENS-CACHAN | UNIV-PARIS-SACLAY | LIF | INSA-ROUEN | LIS-LAB | UNIROUEN | UNILEHAVRE | CRISTAL | UNIV-LILLE | INSA-GROUPE

Citation

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. ⟨hal-01221329v2⟩

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