Weighted Hermite Variable Projection Networks for Classifying Visually Evoked Potentials

The occipital cortex responds to visual stimuli regardless of a patient's level of consciousness or attention, offering a noninvasive diagnostic tool for both ophthalmologists and neurologists. This response signal manifests as a unique waveform referred to as the visually evoked potential (VEP), which can be extracted from the electroencephalogram (EEG) activity of a human being. We propose a trainable VEP representation to disentangle the underlying explanatory factors of the data. To enhance the learning process with domain knowledge, we present an innovative parameterization of classical Hermite functions that effectively captures VEP pattern variations arising from patient-specific factors, disorders, and measurement setup influences. Then, we introduce a differentiable variable projection (VP) layer to fuse Hermite basis function expansions (BFEs) of VEP signals with machine learning (ML) approaches. We prove the existence of an optimal set of parameters in the least-squares sense, assess the representation power of such layers, and calculate their analytical derivatives, which allows us to utilize backpropagation for training. Finally, we evaluate the effectiveness of the proposed learning framework in VEP-based color classification. To achieve this, we have designed a novel measurement system dedicated to intraoperative clinical use cases, which presents new ways for patient monitoring during neurosurgical procedures.