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摘要: 有效的特征提取方法能提高脑机接口（Brain-computer interface，BCI）系统对脑电（Electroencephalogram，EEG）信号的识别率.因脑电信号都是多通道的，本文将分层向量自回归（Hierarchical vector autoregression，HVAR）模型用于脑电信号的特征提取，并结合传统的线性支持向量机（Support vector machine，SVM）用于脑电信号识别.该模型不仅克服了自回归（Autoregression，AR）模型只能用来提取单通道特征的局限性，而且不再采用传统VAR（Vector autoregression）模型所有通道共用一个时滞的处理方法.创新之处在于在传统的VAR模型基础上添加正则化思想，有效地压缩参数空间，实现合理的分层结构.本文首次将HVAR模型用于由Keirn等采集并整理的脑电数据中.实验结果证明HVAR模型在阶数较小的情况下（2阶）与阶数较大（6阶）的AR模型效果相当，可见低阶的HVAR能很好地刻画脑电信号的时空关联关系，这说明HVAR可能是刻画EEG信号的一种新颖的方法，这对其他多通道时间序列分析都有借鉴意义.Abstract: Feature extraction and classification of electroencephalogram (EEG) signals is a core part of brain-computer interface (BCI). For multi-channel EEG signal and high dimension of feature vector of BCI system, a novel EEG signal recognition method called hierarchical vector autoregression (HVAR) is presented, which extracts EEG feature using regression coefficient of HVAR model and linear support vector machine (SVM). It overcomes the limitations of the autoregression (AR) model that can be used to extract the single channel EEG only, and effectively avoids the vector autoregression (VAR) model sharing a same delay for all channels. Our contribution is that regularization is added on the traditional VAR model and a reasonable hierarchical structure is adopted. It effectively compresses parameter space of VAR model. In this paper, HVAR model is used for EEG data classification for the first time. Experimental results show that the recognition accuracy of extracted feature of HVAR model using a 2 lag order multi-channel is higher than that of AR model of 6 lag order. So low-level HVAR model can describe the portrayed temporal relationship of EEG well. This shows HVAR may be a novel method to portray EEG signal, which has reference significance to other multi-channel time-series.
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图 1 ${\rm{LASSO}}-{\rm{VA}}{{\rm{R}}_2}(4)$ 得到的稀疏模式示例图
Fig. 1 The sparse pattern for ${\rm{LASSO}}-{\rm{VA}}{{\rm{R}}_2}(4)$
图 2 ${\rm{HVAR}}{{\rm{C}}_{\rm{3}}}(4)$ 的分层时滞结构示例图
Fig. 2 A componentwise hierarchical lag structure: ${\rm{HVAR}}{{\rm{C}}_{\rm{3}}}(4)$
图 3 ${\rm{HVAR}}{{\rm{O}}_{\rm{3}}}(4)$ 的分层时滞结构示例图
Fig. 3 An own-other hierarchical lag structure: ${\rm{HVAR}}{{\rm{O}}_{\rm{3}}}(4)$
图 4 ${\rm{HVAR}}{{\rm{E}}_{\rm{3}}}(4)$ 的分层时滞结构示例图
Fig. 4 An elementwise hierarchical lag structure: ${\rm{HVAR}}{{\rm{E}}_{\rm{3}}}(4)$
图 7 第5 种任务组合方式对应的不同方法的正确率箱线图
Fig. 7 The boxplot of the fifth task combination fordifferent methods
图 8 第3 种任务组合方式对应的不同方法的正确率箱线图
Fig. 8 The boxplot of the third task combination fordifferent methods
图 10 阶数为 6 时不同方法的分类结果箱线图
Fig. 10 The boxplots of all methods using six order for allsubjects
表 2 任务组合方式
Table 2 Patterns of task combinations
任务编号 组合方式 任务编号 组合方式 1 基准、乘法计算 6 乘法计算、几何图旋转 2 基准、字母组合 7 乘法计算、视觉计算 3 基准、几何图旋转 8 字母组合、几何图旋转 4 基准、视觉计算 9 字母组合、视觉计算 5 乘法计算、字母组合 10 几何图旋转、视觉计算 
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表 3 VAR模型不同时滞的平均正确率
Table 3 Average accuracy rate using VAR model with differentorder
1 2 3 4 5 6 7 8 9 10 2 0.83 0.73 0.85 0.85 0.81 0.91 0.84 0.77 0.74 0.78 3 0.79 0.74 0.81 0.82 0.80 0.88 0.80 0.73 0.73 0.75 4 0.75 0.75 0.80 0.82 0.80 0.86 0.80 0.71 0.71 0.70 5 0.73 0.71 0.78 0.78 0.81 0.86 0.77 0.70 0.65 0.70 6 0.73 0.72 0.75 0.76 0.78 0.84 0.76 0.68 0.68 0.69 7 0.71 0.67 0.71 0.73 0.77 0.81 0.72 0.65 0.65 0.65
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表 4 LASSO-VAR模型不同时滞的平均正确率
Table 4 Average accuracy rate using LASSO-VAR model with different order
1 2 3 4 5 6 7 8 9 10 2 0.79 0.70 0.83 0.79 0.81 0.88 0.83 0.70 0.72 0.67 3 0.80 0.73 0.79 0.80 0.80 0.86 0.78 0.65 0.65 0.65 4 0.79 0.73 0.82 0.79 0.78 0.85 0.76 0.65 0.63 0.64 5 0.77 0.69 0.79 0.76 0.76 0.83 0.71 0.67 0.61 0.64 6 0.76 0.71 0.78 0.73 0.75 0.84 0.75 0.66 0.62 0.63 7 0.76 0.66 0.76 0.73 0.73 0.84 0.75 0.63 0.58 0.61
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表 5 HVARC模型不同时滞的平均正确率
Table 5 Average accuracy rate using HVARC model with different order
1 2 3 4 5 6 7 8 9 10 2 0.82 0.73 0.85 0.80 0.86 0.90 0.84 0.73 0.70 0.70 3 0.81 0.75 0.82 0.84 0.84 0.90 0.84 0.70 0.68 0.69 4 0.80 0.76 0.84 0.82 0.83 0.89 0.82 0.69 0.66 0.68 5 0.78 0.73 0.81 0.79 0.85 0.87 0.78 0.69 0.64 0.64 6 0.80 0.73 0.81 0.79 0.82 0.88 0.81 0.70 0.65 0.66 7 0.78 0.73 0.81 0.79 0.80 0.87 0.81 0.67 0.63 0.66
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表 6 HVARO模型不同时滞的平均正确率
Table 6 Average accuracy rate using HVARO model with different order
1 2 3 4 5 6 7 8 9 10 2 0.81 0.72 0.84 0.81 0.84 0.90 0.86 0.71 0.72 0.72 3 0.82 0.76 0.83 0.82 0.85 0.91 0.83 0.69 0.69 0.69 4 0.82 0.74 0.84 0.80 0.83 0.88 0.82 0.67 0.68 0.67 5 0.81 0.71 0.82 0.81 0.83 0.87 0.82 0.67 0.64 0.65 6 0.81 0.72 0.81 0.79 0.81 0.87 0.82 0.67 0.67 0.66 7 0.79 0.71 0.81 0.80 0.81 0.87 0.82 0.65 0.62 0.64
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表 7 HVARE模型不同时滞的平均正确率
Table 7 Average accuracy rate using HVARE model with different order
1 2 3 4 5 6 7 8 9 10 2 0.79 0.70 0.83 0.80 0.82 0.87 0.83 0.69 0.71 0.68 3 0.77 0.72 0.80 0.82 0.81 0.87 0.79 0.64 0.68 0.69 4 0.78 0.73 0.80 0.80 0.79 0.86 0.77 0.65 0.65 0.64 5 0.78 0.71 0.78 0.79 0.80 0.85 0.75 0.66 0.64 0.64 6 0.78 0.71 0.76 0.79 0.80 0.85 0.77 0.68 0.64 0.66 7 0.78 0.68 0.76 0.80 0.76 0.86 0.77 0.64 0.64 0.65
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表 8 不同特征提取方法的结果总结
Table 8 Summary of classification results for all subjects
AR-BG VAR LASSO-VAR HVARC HVARO HVARE 受 平均值 0.78 0.81 0.77 0.79 0.79 0.77 试 最大值 0.83 0.91 0.88 0.91 0.90 0.87 者 最佳任务 乘法计算、 乘法计算、 乘法计算、 乘法计算、 乘法计算、 乘法计算、 1 组合方式 几何图旋转 几何图旋转 几何图旋转 几何图旋转 几何图旋转 几何图旋转 受 平均值 0.74 0.73 0.67 0.68 0.69 0.67 试 最大值 0.89 0.82 0.76 0.74 0.77 0.76 者 最佳任务 字母组合、 字母组合、 字母组合、 字母组合、 字母组合、 字母组合、 2 组合方式 视觉计算 视觉计算 视觉计算 视觉计算 视觉计算 视觉计算 受 平均值 0.67 0.73 0.68 0.71 0.70 0.68 试 最大值 0.77 0.84 0.78 0.82 0.77 0.81 者 最佳任务 字母组合、 几何图旋转、 几何图旋转、 几何图旋转、 字母组合、 几何图旋转、 3 组合方式 几何图旋转 视觉计算 视觉计算 视觉计算 几何图旋转 视觉计算 受 平均值 0.77 0.82 0.75 0.77 0.78 0.75 试 最大值 0.93 0.91 0.86 0.89 0.91 0.86 者 最佳任务 乘法计算、 乘法计算、 乘法计算、 乘法计算、 乘法计算、 乘法计算、 4 组合方式 视觉计算 视觉计算 视觉计算 视觉计算 视觉计算 视觉计算
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