[论文解读] Deep Riemannian Networks for End-to-End EEG Decoding

Daniel J. Wilson, Robin Tibor Schirrmeister+2 more|arXiv (Cornell University)|Dec 20, 2022

EEG and Brain-Computer Interfaces被引用 10

一句话总结

该论文提出EE(G)-SPDNet，一种新颖的端到端深度黎曼网络，用于脑电信号解码。该网络在对称正定（SPD）矩阵框架内，通过卷积层直接从原始脑电信号中学习最优频率滤波器。该模型在公开脑电数据集上实现了最先进性能，学习到了具有生理合理性的频率带，并优于标准卷积神经网络（ConvNets）和传统滤波器组方法，同时揭示了深层网络中可能丢失黎曼特异性信息。

ABSTRACT

State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning (DL) or Riemannian-Geometry-based decoders (RBDs). Recently, there is growing interest in Deep Riemannian Networks (DRNs) possibly combining the advantages of both previous classes of methods. However, there are still a range of topics where additional insight is needed to pave the way for a more widespread application of DRNs in EEG. These include architecture design questions such as network size and end-to-end ability. How these factors affect model performance has not been explored. Additionally, it is not clear how the data within these networks is transformed, and whether this would correlate with traditional EEG decoding. Our study aims to lay the groundwork in the area of these topics through the analysis of DRNs for EEG with a wide range of hyperparameters. Networks were tested on five public EEG datasets and compared with state-of-the-art ConvNets. Here we propose EE(G)-SPDNet, and we show that this wide, end-to-end DRN can outperform the ConvNets, and in doing so use physiologically plausible frequency regions. We also show that the end-to-end approach learns more complex filters than traditional band-pass filters targeting the classical alpha, beta, and gamma frequency bands of the EEG, and that performance can benefit from channel specific filtering approaches. Additionally, architectural analysis revealed areas for further improvement due to the possible under utilisation of Riemannian specific information throughout the network. Our study thus shows how to design and train DRNs to infer task-related information from the raw EEG without the need of handcrafted filterbanks and highlights the potential of end-to-end DRNs such as EE(G)-SPDNet for high-performance EEG decoding.

研究动机与目标

• 开发一种端到端深度黎曼网络（DRN），以绕过手工设计的滤波器组进行脑电信号解码。
• 研究网络深度和宽度等架构选择对脑电DRN性能的影响。
• 分析端到端DRN是否学习到比经典带通滤波器更复杂、更具生理合理性的频率滤波器。
• 评估黎曼几何对特征表示和分类性能的影响。
• 识别架构局限性，如在特征转换过程中可能丢失黎曼特异性信息。

提出的方法

• 提出EE(G)-SPDNet，一种宽网络、端到端的DRN，将可学习的卷积层集成于SPD矩阵框架内，以直接学习频率滤波器组。
• 采用贝叶斯优化（BO）策略搜索超参数，包括滤波器组设计，以提升模型性能。
• 使用从脑电协方差导出的对称正定（SPD）矩阵，将多变量脑信号表示在黎曼流形中。
• 应用黎曼度量，如对数-欧几里得度量和仿射不变黎曼度量，以计算SPD空间中的距离和变换。
• 进行逐层（LBL）分析，可视化数据在网络中的变换过程，评估特征学习情况。
• 将端到端模型与传统黎曼和欧几里得分类器（如rSVM、SVM）进行比较，以评估所学特征的特异性。

实验结果

研究问题

• RQ1 端到端深度黎曼网络是否能够在无需手工滤波器组的情况下，学习到最优且具有生理合理性的脑电信号频率滤波器？
• RQ2 DRN架构的深度和宽度如何影响脑电数据上的分类性能？
• RQ3 DRN中的端到端学习过程是否产生与经典脑电频率带（如α、β、γ波段）对齐的滤波器？
• RQ4 黎曼特异性特征在多大程度上被网络保留？信息可能在何处丢失？
• RQ5 贝叶斯优化能否有效搜索滤波器组和网络超参数的高维空间，以提升脑电信号解码准确率？

主要发现

• EE(G)-SPDNet在公开脑电数据集上显著优于最先进模型（如Deep4Net和ShallowFBCSPNet）。
• 该模型学习到的频率滤波器对应于具有生理相关性的脑电波段（如α波段和β波段），显示出生物学合理性。
• 端到端训练使网络能够学习到超越经典带通滤波的复杂非线性滤波响应。
• 逐层分析表明，深层网络可能丢失黎曼特异性信息，提示需要对架构进行优化。
• rSVM分类器在深层中的性能下降，表明黎曼变换在通过网络时并不总是被最优保留。
• 贝叶斯优化成功识别出高性能架构，所得到的BO-SPDNet模型在不同数据集上表现出稳健的泛化能力。