Quantifying mode mixing and leakage in multivariate empirical mode decomposition and application in motor imagery-based brain-computer interface system

Improper selection of the number and the amplitude of noise channels in noise-assisted multivariate empirical mode decomposition (NA-MEMD) would induce mode mixing and leakage in the obtained intrinsic mode functions (IMF), which would degrade the performance in applications like brain-computer interface (BCI) systems based on motor imagery. A measurement (ML-index) using no prior knowledge of the underlying components of the original signals was proposed to quantify the amount of mode mixing and leakage of IMFs. Both synthetic signals and electroencephalography (EEG) recordings from motor imagery experiments were used to test the validity. The BCI classification performance using NA-MEMD with the optimal parameters selected based on the ML-index was compared with the performance under the non-optimal parameter condition and the performance using the conventional filtering method. Test on synthetic signals demonstrated the ML-index can effectively quantify the amount of mode mixing and leakage, and help to improve the accuracy of extracting the underlying components. Test on EEG recordings showed the BCI classification performance can be significantly improved under the optimal parameter condition. This study provided a method to quantify the amount of mode mixing and leakage in IMFs and realized the optimization of the parameters associated with noise channels in NA-MEMD. Graphical abstract One of the synthetic multivariate signals comprised four components oscillating at different rates (middle column). Noise-assisted multivariate empirical mode decomposition (noise-assisted MEMD) was used to extract different components. Mode mixing issue occurred under the non-optimal parameter condition (left column). The issue was alleviated under the optimal parameter condition (right column) which can be obtained with the proposed method in this study.