A Unified Fisher’s Ratio Learning Method for Spatial Filter Optimization

To detect the mental task of interest, spatial filtering has been widely used to enhance the spatial resolution of electroencephalography (EEG). However, the effectiveness of spatial filtering is undermined due to the significant nonstationarity of EEG. Based on regularization, most of the conventional stationary spatial filter design methods address the nonstationarity at the cost of the interclass discrimination. Moreover, spatial filter optimization is inconsistent with feature extraction when EEG covariance matrices could not be jointly diagonalized due to the regularization. In this paper, we propose a novel framework for a spatial filter design. With Fisher's ratio in feature space directly used as the objective function, the spatial filter optimization is unified with feature extraction. Given its ratio form, the selection of the regularization parameter could be avoided. We evaluate the proposed method on a binary motor imagery data set of 16 subjects, who performed the calibration and test sessions on different days. The experimental results show that the proposed method yields improvement in classification performance for both single broadband and filter bank settings compared with conventional nonunified methods. We also provide a systematic attempt to compare different objective functions in modeling data nonstationarity with simulation studies.