﻿ 基于PCA的离散小波自回归情感识别
 计算机系统应用  2019, Vol. 28 Issue (5): 119-124 PDF

Discrete Wavelet and Auto-Regressive Based on Principal Component Analysis for Emotion Recognition
LIU Yi, XIE Yi
School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, China
Foundation item: Year 2018, National College Student Innovation and Entrepreneurship Training Program (201810588006)
Abstract: The research is carried out for the purpose of emotion recognition, and the signal feature method of wavelet filtering transformation combined with autoregressive model extraction is proposed on the basis of Principal Component Analysis (PCA). Besides, sentiment classification is realized on the basis of gradient promotion classification tree. The focus of feature extraction is laid on the changes of Electro Encephalo Gram (EEG) signals and the changes of wavelet components as features of EEG signals. The multimodal standard database DEAP proposed by Koelstra et al. to analyze human emotional state is adopted to extract eight positive and negative emotions to represent 14 channels of EEG data in each brain region. The results suggest that the average accuracy of the algorithm for 8 kinds of emotions in pairwise classification is 95.76%, and the highest accuracy is 98.75%, making it possible to help emotional recognition.
Key words: auto-regressive     wavelet transform     principal component analysis     emotion assessment

1 方法

1.1 离散小波变换

 $WT(\alpha , \tau ) = \dfrac{1}{\alpha }\int_{ - \infty }^\infty {f(t)} *\Psi \left(\dfrac{{t - \tau }}{\alpha }\right)dt$ (1)

 $\begin{split} S(t)&=cA_i+\sum\nolimits_{j=1}^{i}cD_j\\ &=cA_4+cD_4+cD_3+cD_2+cD_1 \end{split}$

 $\left\{ \begin{gathered} {\alpha _1} + {\alpha _2}y(1) + \cdots {{ + }}{\alpha _p}y(p - 1) = y(1) \hfill \\ {\alpha _1}y(1) + {\alpha _2}{{ + }} \cdots {{ + }}{\alpha _p}y(p - 2) = y(2) \hfill \\ \cdots \hfill \\ {\alpha _1}y(p - 1) + {\alpha _2}y(p - 2)+ \cdots +{\alpha _p} = y(p) \hfill \\ \end{gathered} \right.$ (2)

 $\left\{ \begin{gathered} {\alpha _1} + {\alpha _2}r(1) + \cdots {{ + }}{\alpha _p}r(p - 1) = r(1) \hfill \\ {\alpha _1}r(1) + {\alpha _2}{{ + }} \cdots {{ + }}{\alpha _p}r(p - 2) = r(2) \hfill \\ \cdots\hfill \\ {\alpha _1}r(p - 1) + {\alpha _2}r(p - 2)+ \cdots +{\alpha _p} = r(p) \hfill \\ \end{gathered} \right.$ (3)

 $r(k) = \frac{1}{{{s^2}(p - k)}}\sum\nolimits_{t = 1}^{p - k} {{X_t}} {X_{t + k}}, k = 1, 2, \cdots, p$

(1)设每个通道的原始脑电信号为$y(t)$, 进行一阶差分并归一化得到${{Y}}(t)$.

(2) ${{Y}}(t)$进行小波变换, 得到cA4cD4cD3cD2$c{D_1}$分量.

(3) cD4cD3$c{D_2}$进行一阶差分, 得到cD4dcD3d$c{D_{2d}}$.

(4)对$y(t)$cA4cD4dcD3d$c{D_{2d}}$分别用30, 30, 20, 25, 30阶AR模型获得总计135维AR系数, 则每个人14个脑电信号通道总计提取1890维的特征数据.

1.3 特征过滤

(1) 假设n×m的原始特征矩阵为M, 对矩阵M去中心化处理, 得到矩阵${M^*} = M - \overline M$.

(2)求${M^*}$的协方差矩阵$C$, $C = {M^*}*{({M^*})^{\rm{T}}}$.

(3)求解协方差矩阵$C$, 从而得到矩阵$C$的特征根和特征向量.

 $C = UA{U^{\rm{T}}}$ (5)

(5)式中, 协方差矩阵$C$的特征向量是$U = ({u_1}, {u_2},$$\cdots , {u_p})$, 特征根矩阵$A = diag({\lambda _1}, {\lambda _2}, \cdots, {\lambda _p})$对角矩阵, 主成分方差的大小与对应的特征根成正比.

(4)求解投影矩阵$W$, 特征根的值反映对应主成分所包含的信息量, 其主成分的贡献率CR定义为

 $CR(j) = \dfrac{{{\lambda _j}}}{{\displaystyle\sum\nolimits_{i = 1}^p {{\lambda _i}} }}, j = 1, 2, \cdots, p$ (6)

 $C{R_{\rm{total}}} = \dfrac{{\displaystyle\sum\nolimits_{j = 1}^k {{\lambda _j}} }}{{\displaystyle\sum\nolimits_{i = 1}^p {{\lambda _i}} }}$ (7)

(6) 依据矩阵M与投影矩阵$W$计算出原特征量在新特征空间中的低维特征量

 $F = M*W.$

 图 2 主成分的特征根和累积贡献率变化

2 结果与分析 2.1 数据说明

2.2 数据选取位置的影响

2.3 详细结果

3 结束语

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