# Long-Term EEG Component Analysis Method Based on Lasso Regression
## 3 Experiments and Results
### Simulation and Results  
At present, the dimensional emotion model is commonly used, in which the human emotional state is formalized as a point in a two-dimensional or three-dimensional continuous space. The advantage of the dimensional model is that it can describe the fine distinction of emotional states and external physical arousal [39]. The VA dimensional model adopted in this paper was proposed by [PERSON] [40]. The model purports that emotional states are points distributed on a two-dimensional space containing Valence and Arousal. The vertical axis represents the valence, and the horizontal axis represents the activation. (1) Acoustic Feature Extraction  
The 93 sound samples in Section 3.1 were used here, and 48 dimensional features were extracted by frames. The frame shift was set to the difference between the sampling rate of the sound signal and the EEG signal. The sound signal frame shift was set to 40 ms; the frame length was 50 ms. Based on this set of acoustic features, the stimulus feature dissimilarity matrix and the dissimilarity score of each feature were calculated. Finally, 10 acoustic features with high emotional correlation were selected, including 'zero cross', 'pitch', 'centroid', 'brightness','spectral flux', 'roughness', 'tempo', 'loudness','spread', and 'roll off', as shown in Figure 7.  
Figure 5: The experimental flow of sound-induced emotion. Figure 6: Electrode location distribution. The programming language was based on Matlab. The MIRtoolbox was used in the acoustic feature extraction and the EEGLAB toolbox was used in the EEG signal processing. EEG Component Decomposition and Feature Extraction  
The preprocessing was applied on the EEG signals according to the method in Section 2.2, including re-reference, removing the artifacts, and 0.5-50 Hz band-pass filtering. For calculation convenience, the EEG signals were down-sampled from 512 Hz to 100 Hz. After that, the independent components (ICs) of EEG signals were obtained by the ICA method. After removing the artifacts of ICs, a total of 428 ICs were obtained in the five frequency bands. According to Equation (5), the power spectrum density curve was calculated, and the band powers of five EEG frequency bands \(\delta\), \(\theta\), \(\alpha\), \(\beta\), and \(\gamma\) were obtained. The envelopes were obtained by HT transform. As shown in Figure 8, (a) is the original EEG signal, (b) is the preprocessed EEG signal, and (c) is the HT envelope feature. Figure 7: Acoustic features for a specific sound. (The horizontal axis represents sampling points, and the vertical axis represents the value of features). Then, the EEG features were aligned with the auditory features according to the onset time. The silent parts were filled with 0. The features were extracted from frames and spliced together to form one-dimensional time-series features, forming a long-term sound, as shown in Figure 9.  
(3) Regression Model  
The multiple regression analysis was performed based on the EEG components and sound features of the time series. The independent variables were the acoustic features, and the dependent variable was the EEG component of each IC and band. Based on the previous feature selection, supposing the optimal feature set is \(\widetilde{F}_{i},i=1,2,\ldots,K\), then regression prediction equations for Valence and Arousal are established as Equation (14), where \(X\) is the feature set, \(Y\) is the average score of Valence or Arousal, and \(\mu\) is the random error. Figure 8: The envelope feature by Hilbert transformation. (**a**) is the original EEG signal, (**b**) is the preprocessed EEG signal, and (**c**) is the HT envelope feature. Figure 9: Acoustic and EEG features aligned. (The acoustic features are extracted from frames and spliced together to form one-dimensional time-series features. Then, they are used as independent variables to estimate each EEG component). Based on the Lasso regression model, the prediction equation is solved when the fitting coefficient \(\hat{\beta}\) is the smallest.