Title: Quantifying Spatial Domain Explanations in BCI using Earth Mover's Distance

Abstract: Brain-computer interface (BCI) systems facilitate unique communication between humans and computers, benefiting severely disabled individuals. Despite decades of research, BCIs are not fully integrated into clinical and commercial settings. It's crucial to assess and explain BCI performance, offering clear explanations for potential users to avoid frustration when it doesn't work as expected. This work investigates the efficacy of different deep learning and Riemannian geometry-based classification models in the context of motor imagery (MI) based BCI using electroencephalography (EEG). We then propose an optimal transport theory-based approach using earth mover's distance (EMD) to quantify the comparison of the feature relevance map with the domain knowledge of neuroscience. For this, we utilized explainable AI (XAI) techniques for generating feature relevance in the spatial domain to identify important channels for model outcomes. Three state-of-the-art models are implemented - 1) Riemannian geometry-based classifier, 2) EEGNet, and 3) EEG Conformer, and the observed trend in the model's accuracy across different architectures on the dataset correlates with the proposed feature relevance metrics. The models with diverse architectures perform significantly better when trained on channels relevant to motor imagery than data-driven channel selection. This work focuses attention on the necessity for interpretability and incorporating metrics beyond accuracy, underscores the value of combining domain knowledge and quantifying model interpretations with data-driven approaches in creating reliable and robust Brain-Computer Interfaces (BCIs).