Belief f-divergence for EEG complexity evaluation

Abstract

Evidence theory, as a useful uncertain reasoning method, is widely used in various fields. Nevertheless, how to quantify the divergence between the basic belief assignments in belief theory and how to apply it are still open issues. To measure the discrepancy between basic belief assignments, we first introduce belief f-divergence (BFD) in this paper. We also analyze and verify its related properties that are expected to significantly improve the performance of electroencephalogram (EEG) complexity evaluation. Then, we employ empirical mode decomposition to detrend EEG noise and reconstruct EEG signals with inherent components and develop a belief f-divergence-based complexity (BFDC) evaluation method with five different functions, including belief KL divergence, belief Hellinger divergence, belief χ2 divergence, belief triangular divergence, and belief total variation divergence, to evaluate the complexity of the EEG signals. Based on a benchmark lane-keeping EEG driving experiment, our proposed BFDC evaluation approach can identify the differences among keep–drift events more obviously and significantly reduce the root mean squared error up to the order of 102 compared to the existing complexity measurement of fuzzy entropy. We believe that our proposed BFDC evaluation method has the potential to be a new and robust approach to precisely evaluate the dynamic complexity of physiological signals.