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Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

Abstract : In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.
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https://hal.inria.fr/inria-00000599
Contributor : Fabrice Rossi Connect in order to contact the contributor
Submitted on : Sunday, September 23, 2007 - 3:02:49 PM
Last modification on : Friday, February 4, 2022 - 3:07:44 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:49:29 PM

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Fabrice Rossi, Brieuc Conan-Guez. Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis. Neural Networks, Elsevier, 2005, 18 (1), pp.45--60. ⟨10.1016/j.neunet.2004.07.001⟩. ⟨inria-00000599v2⟩

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