Fuzzy Multivariate Variational Mode Decomposition With Applications in EEG Analysis

This article introduces a novel extension of the multivariate variational mode decomposition (MVMD) method, termed fuzzy MVMD (FMVMD), designed to enhance alignment information extraction. In contrast to MVMD, FMVMD focuses on capturing finer alignment details by leveraging fuzzy clustering techniques. The proposed FMVMD algorithm proceeds through the following steps: First, FMVMD employs a modified clustering algorithm, termed fuzzy C-means (FCM), to categorize submodes within each channel into fuzzy clusters based on their contribution to common center frequencies. Second, a variational optimization model is formulated, extending the principles of MVMD to accommodate the fuzzy clustering approach used in FMVMD. Finally, an optimization technique called the alternating direction method of multipliers is employed to derive the optimal solution for the FMVMD model. Experimental results show that FMVMD achieves a 41% and 28% improvement in center frequency alignment performance compared to MVMD when using two and three fuzzy clusters, respectively, and a 13% improvement compared to GMVMD with the same number of clusters. Under a 25 dB SNR condition, FMVMD demonstrates a noise resistance improvement of 44% and 24% compared to MVMD with two and three fuzzy clusters, respectively, and a 37% improvement compared to GMVMD. Validation using EEG data in the forms of bipolar leads and common average reference confirms the effectiveness of FMVMD, achieving consistently favorable results.