Regularized RKHS-Based Subspace Learning for Motor Imagery Classification

Brain–computer interface (BCI) technology allows people with disabilities to communicate with the physical environment. One of the most promising signals is the non-invasive electroencephalogram (EEG) signal. However, due to the non-stationary nature of EEGs, a subject’s signal may change over time, which poses a challenge for models that work across time. Recently, domain adaptive learning (DAL) has shown its superior performance in various classification tasks. In this paper, we propose a regularized reproducing kernel Hilbert space (RKHS) subspace learning algorithm with K-nearest neighbors (KNNs) as a classifier for the task of motion imagery signal classification. First, we reformulate the framework of RKHS subspace learning with a rigorous mathematical inference. Secondly, since the commonly used maximum mean difference (MMD) criterion measures the distribution variance based on the mean value only and ignores the local information of the distribution, a regularization term of source domain linear discriminant analysis (SLDA) is proposed for the first time, which reduces the variance of similar data and increases the variance of dissimilar data to optimize the distribution of source domain data. Finally, the RKHS subspace framework was constructed sparsely considering the sensitivity of the BCI data. We test the proposed algorithm in this paper, first on four standard datasets, and the experimental results show that the other baseline algorithms improve the average accuracy by 2–9% after adding SLDA. In the motion imagery classification experiments, the average accuracy of our algorithm is 3% higher than the other algorithms, demonstrating the adaptability and effectiveness of the proposed algorithm.