Faculty of Computer Science, University of Vienna, Hörlgasse 6, 1090 Vienna, Austria.
J Neural Eng. 2020 May 1;17(2):026043. doi: 10.1088/1741-2552/ab839e.
Methods based on Riemannian geometry have proven themselves to be good models for decoding in brain-computer interfacing (BCI). However, these methods suffer from the curse of dimensionality and are not possible to deploy in high-density online BCI systems. In addition, the lack of interpretability of Riemannian methods leaves open the possibility that artifacts drive classification performance, which is problematic in the areas where artifactual control is crucial, e.g. neurofeedback and BCIs in patient populations.
We rigorously proved the exact equivalence between any linear function on the tangent space and corresponding derived spatial filters. Upon which, we further proposed a set of dimension reduction solutions for Riemannian methods without intensive optimization steps. The proposed pipelines are validated against classic common spatial patterns and tangent space classification using an open-access BCI analysis framework, which contains over seven datasets and 200 subjects in total. At last, the robustness of our framework is verified via visualizing the corresponding spatial patterns.
Proposed spatial filtering methods possess competitive, sometimes even slightly better, performances comparing to classic tangent space classification while reducing the time cost up to 97% in the testing stage. Importantly, the performances of proposed spatial filtering methods converge with using only four to six filter components regardless of the number of channels which is also cross validated by the visualized spatial patterns. These results reveal the possibility of underlying neuronal sources within each recording session.
Our work promotes the theoretical understanding about Riemannian geometry based BCI classification and allows for more efficient classification as well as the removal of artifact sources from classifiers built on Riemannian methods.
基于黎曼几何的方法已被证明是脑机接口（BCI）解码的良好模型。然而，这些方法受到维度诅咒的影响，并且不可能在高密度在线 BCI 系统中部署。此外，黎曼方法缺乏可解释性，这使得分类性能可能受到伪影的驱动，这在需要进行伪影控制的领域是有问题的，例如神经反馈和患者群体中的 BCI。
我们严格证明了切空间上的任何线性函数与相应的导出空间滤波器之间的精确等价性。在此基础上，我们进一步提出了一组无需密集优化步骤的黎曼方法降维解决方案。所提出的流水线通过使用开放访问的 BCI 分析框架对经典共空间模式和切空间分类进行了验证，该框架总共包含七个数据集和 200 个主题。最后，通过可视化相应的空间模式来验证我们框架的鲁棒性。
与经典切空间分类相比，所提出的空间滤波方法具有竞争力，有时甚至略好，同时在测试阶段将时间成本降低了 97%。重要的是，无论通道数量如何，所提出的空间滤波方法的性能仅使用四到六个滤波器组件即可收敛，这也通过可视化的空间模式进行了交叉验证。这些结果揭示了每个记录会话中潜在神经元源的可能性。
我们的工作促进了基于黎曼几何的 BCI 分类的理论理解，并允许更有效的分类，以及从基于黎曼方法的分类器中去除伪影源。
