Functional multi-layer perceptron: a non-linear tool for functional data analysis

Authors:
Fabrice Rossi;Brieuc Conan-Guez
Affiliations:
CEREMADE, UMR CNRS 7534, Université Paris-IX Dauphine, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France and Projet AxIS, INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt ...;Projet AxIS, INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France
Venue:
Neural Networks
Year:
2005

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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.