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

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

2007-09-23

arxiv.org/abs/0709.3642v1

Neural Networks 18, 1 (2005) 45--60

Computer Science

Neural and Evolutionary Computing

http://www.sciencedirect.com/science/journal/08936080

Scientific paper

10.1016/j.neunet.2004.07.001

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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