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arXiv · 1510.08231

Operator-valued Kernels for Learning from Functional Response Data

Hachem Kadri·Emmanuel Duflos·Philippe Preux·Stéphane Canu·Alain Rakotomamonjy·Julien Audiffren
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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.

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Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Alain Rakotomamonjy, Julien Audiffren. 2016-11-02. Operator-valued Kernels for Learning from Functional Response Data. https://arxiv.org/abs/1510.08231

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