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

Conan-Guez, Brieuc; Rossi, Fabrice

Conan-Guez, Brieuc; Rossi, Fabrice (2005), Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis, Neural Networks, 18, 1, p. 45--60. http://dx.doi.org/10.1016/j.neunet.2004.07.001

Type

Article accepté pour publication ou publié

External document link

http://hal.inria.fr/inria-00000599/en/

Date

2005

Journal name

Neural Networks

Volume

Number

Publisher

Elsevier

Pages

45--60

Abstract (EN)

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.

Subjects / Keywords

Functional data analysis; Multi-Layer Perceptron; Universal Approximation; Supervised learning; Curves discrimination; Learning consistancy; Nonlinear functional model; Spectrometric data