## Operator-valued Kernels for Learning from Functional Response Data

*Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Alain Rakotomamonjy, Julien Audiffren*; 17(20):1−54, 2016.

### Abstract

In this paper (This is a combined and expanded version of
previous conference papers Kadri et al., 2010, 2011c) 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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