Improving two-dimensional linear discriminant analysis with L1 norm for optimizing EEG signal

Abstract

Dimensionality reduction is a critical factor in processing high-dimensional datasets. The L1 norm-based Two-Dimensional Linear Discriminant Analysis (L1-2DLDA) is widely used for this purpose, but it remains sensitive to outliers and classes with large deviations, which deteriorates its performance. To address this limitation, the present study proposed Pairwise Sample Distance Two-Dimensional Linear Discriminant Analysis (PSD2DLDA), a novel method that modeled L1-2DLDA using pair-wise sample distances. To improve computational effectiveness, this study also introduced a streamlined variant, Pairwise Class Mean Distance Two-Dimensional Linear Discriminant Analysis (PCD2DLDA), which was based on distances between class mean pairs. Different from previous studies, this study utilized the projected sub-gradient method to optimize these two improved methods. Meanwhile, this study explored the interrelationship, limitations, and applicability of these two improved methods. The comparative experimental results on three datasets validated the outstanding performance of PSD2DLDA and PCD2DLDA methods. In particular, PSD2DLDA exhibited superior robustness compared to PCD2DLDA. Furthermore, applying these two methods to optimize electroencephalogram (EEG) signals effectively enhanced the decoding accuracy of motor imagery neural patterns, which offered a promising strategy for optimizing EEG signals processing in brain-computer interface (BCI) applications.