Representation of Functional Data in Neural Networks

TL;DR

This paper extends neural network models like RBFN and MLP to handle functional data, such as spectra and temporal series, by incorporating functional processing techniques like basis projection and PCA.

Contribution

It introduces methods to adapt neural networks for functional data analysis, integrating various functional preprocessing techniques into RBFN and MLP models.

Findings

Functional processing improves model performance on spectral data

The approach effectively handles irregularly sampled functional data

Benchmark results demonstrate the method's applicability

Abstract

Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice; usually a regular or irregular sampling is known. For this reason, some processing is needed in order to benefit from the smooth character of functional data in the analysis methods. This paper shows how to extend the Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models to functional data inputs, in particular when the latter are known through lists of input-output pairs. Various possibilities for functional processing are discussed, including the projection on smooth bases, Functional Principal Component Analysis, functional centering and reduction, and the use of differential operators. It is shown how to incorporate these functional processing into the RBFN and MLP models. The functional approach is illustrated on a benchmark of spectrometric data analysis.