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It is desirable for statistical models to detect signals of interestindependently of their position. If the data is generated by some smoothprocess, this additional structure should be taken into account. We introduce anew class of neural networks that are shift invariant and preserve smoothnessof the data: functional neural networks (FNNs). For this, we use methods fromfunctional data analysis (FDA) to extend multi-layer perceptrons andconvolutional neural networks to functional data. We propose different modelarchitectures, show that the models outperform a benchmark model from FDA interms of accuracy and successfully use FNNs to classify electroencephalography(EEG) data.

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