Abstract: Aiming at the hypothesis of strict linear model between source signals and recorded EEG signals in the Common Spatial Patterns（CSP）, an EEG feature extraction method based on Kernel Tensor Subspace Decomposition（KTSD） is proposed, which can give full play to the advantage of tensors in multidimensional and simultaneous processing. Firstly, the tensor of EEG data is generated, and the tensor decomposition problem is solved by using the least squares problem with quadratic equality constraints, subsequently the tensor is extended to the subspace to reduce the computational pressure. Finally, it is extended to the kernel space to enhance the discrimination ability by projecting data onto high-dimensional feature space. BCI competition III-3a data set is used in the experiment. The experimental results show that KTSD method can extract the corresponding features from EEG data of various motion imagery tasks, and obtain better classification results and operational efficiency.

Key words: EEG date, kernel tensor, subspace, kernel space

摘要： 针对共空间模式（Common Spatial Patterns，CSP）对源信号和记录的脑电信号之间严格的线性模式的假设关系，充分发挥张量在多维上同时处理的优势，研究了一种核张量子空间分解EEG特征提取方法。首先生成EEG数据的张量，利用带二次等式约束的最小二乘问题解决张量分解问题，并将张量扩展到子空间，减小计算的压力，最后推广到核空间，将数据投影到高维特征空间来增强辨别能力。实验数据采用2005年BCI竞赛III的数据集III_3a，实验结果表明，KTSD方法能够从多类运动想象任务的EEG数据中提取相应的特征，并得到较好分类结果和运行效率。

关键词: EEG数据, 核张量, 子空间, 核空间