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Journal Articles Journal of Machine Learning Research Year : 2016

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.
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Dates and versions

hal-01221329 , version 1 (27-10-2015)
hal-01221329 , version 2 (29-10-2015)

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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, 2016, 17 (20), pp.1-54. ⟨hal-01221329v2⟩
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