Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification

TL;DR

This paper introduces functional neural networks (FNNs), a new class of shift-invariant models designed for smooth functional data, demonstrating improved accuracy in EEG classification tasks.

Contribution

The paper develops FNN architectures that incorporate shift invariance and smoothness preservation, extending neural networks with methods from functional data analysis.

Findings

FNNs outperform FDA benchmark models in accuracy

FNNs successfully classify EEG data

Models maintain shift invariance and smoothness

Abstract

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.