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Discriminability of single-trial EEG during decision-making of cooperation or aggression: a study based on machine learning

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Abstract

Decision-making is a very important cognitive process in our daily life. There has been increasing interest in the discriminability of single-trial electroencephalogram (EEG) during decision-making. In this study, we designed a machine learning based framework to explore the discriminability of single-trial EEG corresponding to different decisions. For each subject, the framework split the decision-making trials into two parts, trained a feature model and a classifier on the first part, and evaluated the discriminability on the second part using the feature model and classifier. A proposed algorithm and five existing algorithms were applied to fulfill the feature models, and the algorithm Linear Discriminative Analysis (LDA) was used to implement the classifiers. We recruited 21 subjects to participate in Chicken Game (CG) experiments. The results show that there exists the discriminability of single-trial EEG between the cooperation and aggression decisions during the CG experiments, with the classification accuray of 75% (±6%), and the discriminability is mainly from the EEG information below 40 Hz. The further analysis indicates that the contributions of different brain regions to the discriminability are consistent with the existing knowledge on the cognitive mechanism of decision-making, confirming the reliability of the conclusions. This study exhibits that it is feasible to apply machine learning methods to EEG analysis of decision-making cognitive process.

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Acknowledgements

Faqiang Peng participated in this work when he studied at Fuzhou University. We thank him for his contribution.

Funding

This work was supported by the Transformation Project of Scientific and technological achievements of Fuzhou, China (2020-GX-12) and Natural Science Foundation of Fujian Province, China (2019J01242).

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Correspondence to Zhihua Huang.

Appendices

Appendix A. Chicken game

The CG experimental task aims to study the mechanisms underlying cooperative and aggressive behaviors. In this game, two players independently decide to cooperate or aggress. Every time, the payoff for each player depends on the combination of two players’ decisions. The payoffs of mutual cooperation and mutual aggression are represented with “R” and “P”, respectively. If one player cooperates while his/her opponent aggresses, the payoffs of the player and his/her opponent are represented with “S” and “T”, respectively. The payoffs are arranged such that T>R>S>P and 2R\(\ge\)T+S. The players make their decisions in a social dilemma when they are conducting the CG experimental task.

Appendix B. The period of inputting decision

During the period of inputting decision, the subjects expressed their decisions by a c-VEP BCI. The procedure is shown in Fig. 7. The “Rest” screen guides subjects to rest for 1000–1200 ms. The “Cue” screen prompts subjects to get ready to input their decisions. The “Gaze” screen represents the brain-computer interaction lasting 3000 ms. On the screen, the “A” and “C” rectangles means “aggress” and “co-operate”, respectively. The subjects are instructed to gaze at one of the two rectangles according to their own decisions. The two rectangles flash in a pseudo-random pattern specified respectively by 15-bit m-sequence “000010100110111” and its shift “110111000010100”. Each bit of m-sequence corresponds to 40 ms, meaning on by 1 or off by 0 and the flashes of 15-bit m-sequence are repeated 5 times. For each trial, the EEG signals recorded from the electrodes of O1, Oz, O2, PO7, POz, and PO8 during the 3000 ms are transformed to a feature vector, which is further recognized as the subject’s decision by a linear discriminant analysis classifier.

Fig. 7
figure 7

Inputting decision by brain-computer interaction

Appendix C. The description of AFRCSP

AFRCSP establishes a feature model \({\varPhi }\) based on the K frequency bands for a subject (target subject) using not only his own training set but also the training sets of other subjects (source subjects). Firstly, AFRCSP filters all EEG segments of each training set with the K bandpass filters. Secondly, AFRCSP processes each frequency band in same way to obtain a transformation model for each frequency band. Thirdly, AFRCSP selects the most informative frequency bands for a subject. Finally, AFRCSP integrates the transformation models of the selected frequency bands into a feature model of the subject.

For the simplicity, we still use \(X_i\) to represent the EEG segment of a trial in a frequency band. The procedure of AFRCSP processing a frequency band for a targrt subject can be depicted as follows.

Step-1 calculates the regularized covariance matrices. The covariance matrix of a trial is obtained according to Eq. 1,

$$\begin{aligned} C_i=\frac{X_i X_i^T}{tr(X_i X_i^T)},\quad i\in [1,N] \end{aligned}$$
(1)

where \(tr(\cdot )\) represents solving the trace of a matix. The covariance matrices of cooperation and aggression are calculated according to Eqs. 2 and 3,

$$\begin{aligned} C_c=\frac{1}{M_c}\sum \limits _{i\in \mathbb {T}_c}C_i\end{aligned}$$
(2)
$$\begin{aligned} C_a=\frac{1}{M_a}\sum \limits _{i\in \mathbb {T}_a}C_i \end{aligned}$$
(3)

where \(\mathbb {T}_c\) and \(\mathbb {T}_a\) respectively represents all trials of the cooperation decision and all trials of the aggression decision and \(M_c=|\mathbb {T}_c|,\, M_a=|\mathbb {T}_a|\). For each source subject, the covariance matrices of cooperation and aggression can be calculated in the same way. We notate the mean covariance matrices of cooperation and aggression for all source subjects as \(\bar{C}_c\) and \(\bar{C}_a\). Then, we define the regularized covariance matrices of the target subject as \(\breve{C}_c\), \(\breve{C}_a\) and \(\breve{C}\) by Eqs. 4-8

$$\begin{aligned} \hat{C}_c= & {} (1-\beta )C_c+\beta \bar{C}_c \end{aligned}$$
(4)
$$\begin{aligned} \hat{C}_a= & {} (1-\beta )C_a+\beta \bar{C}_a \end{aligned}$$
(5)
$$\begin{aligned} \breve{C}_c= & {} (1-\gamma )\hat{C}_c+\frac{\gamma }{N_c}tr(\hat{C}_c) I \end{aligned}$$
(6)
$$\begin{aligned} \breve{C}_a= & {} (1-\gamma )\hat{C}_a+\frac{\gamma }{N_c}tr(\hat{C}_a) I \end{aligned}$$
(7)
$$\begin{aligned} \breve{C}= & {} \breve{C}_c+\breve{C}_a \end{aligned}$$
(8)

where the parameters \(\beta ,\gamma \in [0,1]\) are determined by cross-validation during the implementation, I is a \(N_c\times N_c\) identity matrix, \(tr(\cdot )\) represents the operation of the trace of a matrix.

Step-2 conducts the Eigendecomposition of \(\breve{C}\) (Eq. 9),

$$\begin{aligned} \breve{C}=B\lambda B^T \end{aligned}$$
(9)

where \(\lambda\) is the diagonal matrix of eigenvalues of \(\breve{C}\) and B is a matrix composed of normalized eigenvectors of \(\breve{C}\). We then get a matrix W by \(W=\lambda ^{-1/2}B^T\), and transform \(\breve{C}_c\) and \(\breve{C}_a\) to \(S_c\) and \(S_a\) by \(S_c=W \breve{C}_c W^T\) and \(S_a=W \breve{C}_a W^T\). In accordance with [17, 18], we know that \(S_c\) and \(S_a\) have the same eigenvectors. This can be described as Eqs. 10 and 11,

$$\begin{aligned} S_c=U\psi _c U^T \end{aligned}$$
(10)
$$\begin{aligned} S_a=U\psi _a U^T \end{aligned}$$
(11)

where U is the common eigenvector matrix of \(S_c\) and \(S_a\), \(\psi _c\) and \(\psi _a\) are diagonal matrices of eigenvalues of \(S_c\) and \(S_a\) respectively, and the sum of \(\psi _c\) and \(\psi _a\) is an identity matrix.

Step-3 computes the transformation matrix P by Eq. 12,

$$\begin{aligned} P=(\hbar (U))^T W \end{aligned}$$
(12)

where \(\hbar (\cdot )\) represents selecting the first and last columns of U after sorting the eigenvectors in descending order of the eigenvalues.

We use \(k\in \{1,\cdots ,K\}\) to represent a frequency band and then can represent the transformation matrices and EEG segments of the K frequency bands with \(P_k\in \mathbb {R}^{2\times N_c}\) and \(X_i^k\in \mathbb {R}^{N_c\times N_t}\). Furthermore, for all \(i\in \{1,\cdots ,N\},\, k\in \{1,\cdots ,K\}\), \(Y_i^k\in \mathbb {R}^{2\times N_t}\) and \(h_i^k\in \mathbb {R}^2\) are obtained respectively by Eqs. 13 and by 14.

$$\begin{aligned} Y_i^k= & {} P_k X_i^k \end{aligned}$$
(13)
$$\begin{aligned} h_i^k= & {} \ln \frac{diag\left( Y_i^k (Y_i^k)^T\right) }{tr\left( Y_i^k (Y_i^k)^T\right) } \end{aligned}$$
(14)

As the counterpart of \(X_i\), \(h_i\) is obtained by concatenating all \(h_i^k\) for \(k\in \{1,\cdots ,K\}\). But, \(h_i\in \mathbb {R}^{2K}\) are not yet the appropriate feature vectors of \(X_i\), since the information from the frequency bands in which no significant discriminability exists is included in \(h_i\).

The NCA [24,25,26,27] is used for further feature selections. We define a weight vector \(w\in \mathbb {R}^{2K}\), and denote the weighted distance between \(h_i\) and \(h_j\) by Eq. 15.

$$\begin{aligned} D_w(h_i,h_j)=\sum \limits _{k=1}^{2K}w_k^2|h_{ik}-h_{jk}| \end{aligned}$$
(15)

The probability of \(h_i\) selecting \(h_j\) as its reference point is defined as Eq. 16,

$$\begin{aligned} p_{ij}=\left\{ \begin{array}{ll} \frac{\kappa (D_w(h_i,h_j))}{\sum _{k\ne i}\kappa (D_w(h_i,h_k))}, &{} if\quad i\ne j\\ 0, &{} if\quad i=j \end{array}\right. \end{aligned}$$
(16)

where \(\kappa (z)=exp(-z/\sigma )\) is a kernel function with a parameter \(\sigma\). Then, the objective function is obtained by Eq. 17,

$$\begin{aligned} \xi (w)=\sum \limits _{i=1}^N\sum \limits _{j=1}^N l_{ij}p_{ij}-\alpha \sum \limits _{k=1}^{2K}w_k^2 \end{aligned}$$
(17)

where \(l_{ij}=1\) if and only if \(l_i=l_j\), or \(l_{ij}=0\) otherwise; \(\alpha >0\) is a regularization parameter which is set to 1/N here. Our goal is to maximize \(\xi (w)\) with respect to w. In the process of solving this problem, the regularization term drives many of the weights in w to 0. After obtaining the solution w, we notate the subscript set of the weights in w that are much greater than 0 as \(\mathbb {L}=\{k\,|\,w_k\gg 0\}\) and construct \(x_i\), the feature vector of \(X_i\), by selecting the features \(\{h_{ik}|k\in \mathbb {L}\}\) and concatenating them.

The above descriptions are the implementation of AFRCSP to \({\varPhi }\). As a combination of CSP, regularization idea and NCA, AFRCSP meets our need to probe the discriminability of EEG segments in a broad frequency range and in small-sample setting.

Appendix D. The results of SVM and KNN

A reviewer thinks that the results of Support Vector Machine (SVM) and K-Nearest Neighbors (KNN) should be reported in the paper. We show them in Table 4.

Table 4 The results of the combinations of SVM and KNN with AFRCSP, DSNP, WM, ICA, PCA and CSP (mean±std)

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Huang, Z., Jiang, K., Li, J. et al. Discriminability of single-trial EEG during decision-making of cooperation or aggression: a study based on machine learning. Med Biol Eng Comput 60, 2217–2227 (2022). https://doi.org/10.1007/s11517-022-02557-5

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