Coherence-based correntropy spectral density: A novel coherence measure for functional connectivity of EEG signals

Abstract

Finding the interrelationship between EEG time series at both sensory and source levels during a mental task is helpful in understanding the corresponding neural functionality. Based on such connectivity measures, a functional brain connectivity network can be formed, which shows the relationship and the extent of dependency among the aforementioned time series. In order to evaluate the interdependency of EEG signals acquired from different electrodes, we proposed a new nonlinear connectivity index based on correntropy spectral density. Here, the correntropy function was defined as a sum of weighted positive definite kernels. Optimal weights were found by solving a quadratic optimization problem. In order to evaluate the proposed approach for determining the interrelationships, Henon map, two synthetically related simulated signals, and EEG signals (BCI competition IV data) were employed. The suggested coherence measure shows robustness to noise and high sensitivity to sudden changes in coupling strength. This measure is able to detect nonlinear as well as linear coupling of EEG signals. In general, the proposed method is more efficient than other methods like coherence and partial coherence method, is capable of showing the similarity between the two signals, and preserves the frequency characteristics of the system.