The common spatial pattern analysis (CSP) is a widely used signal processing technique in brain-computer interface (BCI) systems to increase the signal-to-noise ratio in electroencephalogram (EEG) recordings. Despite its popularity, the CSP's performance is often hindered by the nonstationarity and artifacts in EEG signals. The minmax CSP improves the robustness of the CSP by using data-driven covariance matrices to accommodate the uncertainties. We show that by utilizing the optimality conditions, the minmax CSP can be recast as an eigenvector-dependent nonlinear eigenvalue problem (NEPv). We introduce a self-consistent field (SCF) iteration with line search that solves the NEPv of the minmax CSP. Local quadratic convergence of the SCF for solving the NEPv is illustrated using synthetic datasets. More importantly, experiments with real-world EEG datasets show the improved motor imagery classification rates and shorter running time of the proposed SCF-based solver compared to the existing algorithm for the minmax CSP.

翻译：公共空间模式分析（CSP）是一种广泛应用于脑机接口（BCI）系统的信号处理技术，旨在提高脑电图（EEG）记录中的信噪比。尽管该方法应用广泛，但EEG信号的非平稳性和伪迹常常影响其性能。极小极大CSP通过采用数据驱动的协方差矩阵来适应不确定性，从而增强了CSP的鲁棒性。我们证明，通过利用最优性条件，极小极大CSP可重新转化为依赖于特征向量的非线性特征值问题（NEPv）。我们提出了一种带线性搜索的自洽场（SCF）迭代方法，用于求解极小极大CSP的NEPv。通过合成数据集验证了该SCF方法求解NEPv的局部二次收敛性。更重要的是，基于真实EEG数据集的实验表明，相较于现有极小极大CSP算法，本文提出的基于SCF的求解器不仅提高了运动想象分类准确率，还缩短了运行时间。