Dimensionality Reduction for Motor Imagery BCI System Using Kron Reduction, Graph Fourier Transform & Differential Evolution

The human brain is one of the most complex and heterogeneous networks, and brain signals contain a lot of information, so researchers in this field are always looking for proper solutions to select meaningful features and reduce the dimension of this information appropriately to lead to better classification. Two of the new tools for brain signal processing are Graph Signal Processing (GSP) and Meta-heuristic and Evolutionary methods. In this paper, a geometric structure and a mixed structure are considered for the brain graph and the weights of the edges in the mixed structure are calculated by a combination of two measures: geometric distance and correlation. To reduce the graph dimension, the weighted degree metric and a combination of the Kron reduction method and Graph Fourier Transform (KG) are used to properly preserve the information of all vertices of the graph into the selected vertices. Feature extraction is performed by Ledoit-Wolf shrinkage estimation and Tangent Space Mapping (TSM) method. For dimension reduction of extracted features, Principal Component Analysis (PCA) method and feature selection based on Differential Evolution (DE) are used. The selected features are given to several well-known machine learning classifiers. To evaluate the performance of the proposed method, dataset IVa from BCI Competition III has been used. The results show that the average classification accuracy of the proposed KG-PCA method with SVM-RBF and DT classifiers, in the structural graph and the functional-structural graph, is higher than the G-PCA method expressed in previous studies, and the DT classifier has achieved an average accuracy of 91.15 ± 1.17. Also, according to the obtained results, the performance of the proposed KG-DE method has been better compared to KG-PCA and in the best case, the average accuracy of the SVM-RBF classifier is equal to 95.50 ± 1.27.