A Neural Network-Based Optimal Spatial Filter Design Method for Motor Imagery Classification

In this study, a novel spatial filter design method is introduced. Spatial filtering is an important processing step for feature extraction in motor imagery-based brain-computer interfaces. This paper introduces a new motor imagery signal classification method combined with spatial filter optimization. We simultaneously train the spatial filter and the classifier using a neural network approach. The proposed spatial filter network (SFN) is composed of two layers: a spatial filtering layer and a classifier layer. These two layers are linked to each other with non-linear mapping functions. The proposed method addresses two shortcomings of the common spatial patterns (CSP) algorithm. First, CSP aims to maximize the between-classes variance while ignoring the minimization of within-classes variances. Consequently, the features obtained using the CSP method may have large within-classes variances. Second, the maximizing optimization function of CSP increases the classification accuracy indirectly because an independent classifier is used after the CSP method. With SFN, we aimed to maximize the between-classes variance while minimizing within-classes variances and simultaneously optimizing the spatial filter and the classifier. To classify motor imagery EEG signals, we modified the well-known feed-forward structure and derived forward and backward equations that correspond to the proposed structure. We tested our algorithm on simple toy data. Then, we compared the SFN with conventional CSP and its multi-class version, called one-versus-rest CSP, on two data sets from BCI competition III. The evaluation results demonstrate that SFN is a good alternative for classifying motor imagery EEG signals with increased classification accuracy.

本研究提出一种新型空间滤波器设计方法。空间滤波是基于运动想象的脑机接口中特征提取的关键处理步骤。本文提出一种结合空间滤波优化的新型运动想象信号分类方法，采用神经网络方法同时对空间滤波器与分类器进行联合训练。所提出的空间滤波网络（Spatial Filter Network, SFN）包含两个层级：空间滤波层与分类器层，二者通过非线性映射函数实现互连。

本方法针对通用空间模式（Common Spatial Patterns, CSP）算法的两处核心缺陷展开改进：其一，CSP算法仅以最大化类间方差为优化目标，却未考虑类内方差的最小化，因此通过CSP方法获取的特征往往存在较大的类内方差；其二，CSP的最大化优化目标仅能间接提升分类精度，因其后续需搭配独立的分类器完成分类任务。而本研究所提SFN则同时以最大化类间方差、最小化类内方差为优化目标，并实现空间滤波器与分类器的联合优化。

针对运动想象脑电（Electroencephalogram, EEG）信号的分类任务，本研究改进了经典的前馈网络结构，并推导了适配该结构的前向传播与反向传播方程。本研究首先在简易玩具数据集上验证了所提算法的有效性，随后基于第三届脑机接口竞赛（BCI Competition III）的两个数据集，将SFN与传统CSP算法及其多分类版本“一对其余CSP（one-versus-rest CSP）”进行了对比实验。实验结果表明，SFN是一种性能更优的运动想象脑电信号分类方案，可有效提升分类精度。