Feature Extraction and Classification of Motor Imagery EEG Signals in Motor Imagery for Sustainable Brain–Computer Interfaces

Abstract

Motor imagery brain–computer interface (MI-BCI) systems hold the potential to restore motor function and offer the opportunity for sustainable autonomous living for individuals with a range of motor and sensory impairments. The feature extraction and classification of motor imagery EEG signals related to motor imagery brain–computer interface systems has become a research hotspot. To address the challenges of difficulty in feature extraction and low recognition rates of motor imagery EEG signals caused by individual variations in EEG signals, a classification algorithm for EEG signals based on multi-feature fusion and the SVM-AdaBoost algorithm was proposed to improve the recognition accuracy of motor imagery EEG signals. Initially, the electroencephalography (EEG) signals are preprocessed using Finite Impulse Response (FIR) filters, and a multi-wavelet framework is constructed based on the Morlet wavelet and the Haar wavelet. Subsequently, the preprocessed signals undergo multi-wavelet decomposition to extract energy features, Common Spatial Patterns (CSP) features, Autoregressive (AR) features, and Power Spectral Density (PSD) features. The extracted features are then fused, and the fused feature vector is normalized. Following that, classification is implemented within the SVM-AdaBoost algorithm. To enhance the adaptability of SVM-AdaBoost, the Grid Search method is employed to optimize the penalty parameter and kernel function parameter of the SVM. Concurrently, the Whale Optimization Algorithm is utilized to optimize the learning rate and number of weak learners within the AdaBoost ensemble, thereby refining the overall performance. In addition, the classification performance of the algorithm is validated using a brain-computer interface (BCI) dataset. In this study, it was found that the classification accuracy reached 95.37%. Via the analysis of motor imagery electroencephalography (EEG) signals, the activation patterns in different regions of the brain can be detected and identified, enabling the inference of user intentions and facilitating communication and control between the human brain and external devices.

1. Introduction

The BCI is an innovative technology designed to enable seamless interaction between the human brain and computers and to provide a new way for people to communicate and control [1]. MI-BCI systems not only represent the forefront of technological advancement but also serve as a potent driving force for promoting sustainable societal development. In the realm of sustainable living, the precise capture of electroencephalography (EEG) signals has paved a path towards sustainable and autonomous living and working for individuals with disabilities, thereby enhancing their social participation and life independence [2]. In the field of medical rehabilitation, by analyzing patients’ EEG signals during motor imagery, physicians are able to precisely assess the recovery status of their nervous systems and subsequently tailor personalized rehabilitation programs. This breakthrough not only accelerates the patients’ recovery process but also reduces excessive consumption of medical resources in the long run, laying a foundation for the construction of a sustainable healthcare system [3]. In the realm of industrial production, the revolutionary transformation of enabling workers to directly control machinery and equipment via thought has been achieved. This innovation not only reduces production costs for enterprises but also propels the transformation of the manufacturing industry towards intelligence, injecting new vitality into the sustainable development of industry [4]. However, it is noteworthy that current BCI technology still faces numerous challenges, with the most critical being the enhancement of recognition accuracy for motor imagery EEG signals. Consequently, optimizing feature extraction algorithms for motor imagery EEG signals and improving classifier performance have emerged as significant research foci.

In recent years, because EEG signals exhibit low amplitude, high randomness, non-stationarity, and nonlinearity, researchers have proposed numerous feature extraction methods. For example, Alickovic et al. (2018) used discrete wavelet transform (DWT) to extract EEG wavelet coefficients [5] and establish the correspondence between time domain signals and frequency domain signals. Additionally, Dutta et al. (2018) [6] used an Autoregressive (AR) model to analyze single-factor time series and predict an epilepsy EEG time series model, and Feng et al. (2019) [7] used spatial enhancement to increase differences between different classes using a Common Spatial Patterns (CSP) model. However, each individual feature extraction method has its own set of limitations. For instance, the time or frequency domain feature extraction methods potentially lead to information loss [8]. In the case of fewer channels, less information is obtained by spatial feature extraction [9], and therefore, in order to achieve a more effective feature extraction method, multiple feature extraction methods can be combined.

Accurate classification of EEG signals into different categories relies on the judicious design of the classifier, with the classifier’s performance determining the quality of the classification outcome. At present, there are many common methods of EEG classification and recognition, such as linear discriminant analysis [10], decision tree [11], and Random Forest [12]. However, the results of EEG classification in motor imaging are not ideal due to single weak classification algorithms in most of the traditional processing methods. In machine learning, ensemble learning is a common approach that takes the predictions of multiple learners and combines them via some strategy to improve the final prediction performance [13]. Therefore, the combination of a single-algorithm classifier and an ensemble learning algorithm is the focus of this research.

To address the current limitations in EEG signal classification, particularly the scarcity of research on fusion feature frameworks and the utilization of ensemble learning algorithms to enhance individual weak algorithms, this paper proposes a multi-feature fusion based on multi-wavelet decomposition combined with an SVM-AdaBoost algorithm for motor imagery EEG signal classification, aiming to improve EEG analysis through feature extraction and classification recognition. The primary innovations of this paper are as follows:

(1)

The introduction of multi-wavelet transform decomposition into the feature extraction process of EEG signals, resulting in the construction of a multi-wavelet decomposition framework based on the Morlet wavelet and the Haar wavelet.

Although wavelet decomposition methods have been well applied in EEG signal feature extraction, single-wavelet methods struggle to overcome the inherent limitations of wavelet basis functions. In contrast, multi-wavelets, which have evolved from wavelet theory, possess multiple scaling functions and wavelet functions, thereby overcoming the limitations of single wavelets that cannot simultaneously satisfy desirable properties such as compact support, symmetry, orthogonality, and high-order vanishing moments [14]. Multi-wavelets can match different characteristic information in signals from various angles, which confers them with significant advantages over single wavelets in terms of feature extraction [15]. Based on a comprehensive consideration of the characteristics of the Morlet and Haar wavelets, this paper constructs a multi-wavelet decomposition framework that integrates the Morlet and Haar wavelets. This constructed multi-wavelet framework is then utilized to decompose EEG signals.

(2)

Based on the multi-wavelet decomposition, a multi-feature fusion process is applied to EEG signals, resulting in the construction of multi-wavelet decomposition fusion features for EEG signals. A Finite Impulse Response (FIR) filter is employed to extract EEG signals in the vicinity of the β rhythm frequency band ranging from 16 to 32 Hz. Subsequently, a three-level wavelet packet decomposition is performed on the extracted signals using multi-wavelets. The resulting wavelet coefficient matrices are then combined to enhance feature diversity. From the combined multi-wavelet coefficients, energy features, Common Spatial Patterns (CSP) features, Autoregressive (AR) features, and Power Spectral Density (PSD) features are individually extracted. These extracted features are then subjected to adaptive fusion to obtain multi-wavelet decomposition-based fused features.

(3)

To perform EEG classification and recognition, SVM-AdaBoost ensemble learning is introduced. The Whale Optimization Algorithm (WOA) is employed to optimize the learning rate and number of weak learners within AdaBoost, resulting in the construction of an SVM-WOA-AdaBoost prediction model for EEG signal recognition. The energy features, CSP features, AR features, and PSD features, obtained after multi-wavelet decomposition, undergo fusion and normalization. Following this, the SVM-AdaBoost algorithm is utilized for EEG classification and recognition. Considering the impact of the penalty parameter and the kernel function parameter on SVM, a Grid Search method with Cross-Validation (CV) is applied to optimize the penalty parameter and the kernel function parameter. Furthermore, taking into account the significant influence of the number of weak learners and their learning rate on the AdaBoost algorithm, the WOA (Whale Optimization Algorithm) is utilized to optimize both the number of weak learners and their learning rate within AdaBoost.

Experimental results demonstrate that the comprehensive use of the four feature extraction algorithms based on multi-wavelet decomposition can effectively analyze EEG features from multiple perspectives, addressing the limitation of insufficient information coverage in the time–frequency domain by a single feature and effectively avoiding the constraints imposed by individual features. The ensemble learning algorithm SVM-AdaBoost mitigates the deficiencies of the weak classifier SVM, effectively enhancing the classification and recognition capabilities of SVM. As evidenced by the classification accuracy and kappa value of the classification results, the proposed method is able to improve accuracy to a certain extent, achieving a classification accuracy of 95.37% and a kappa value of 0.907. This indicates that it is a relatively effective algorithm for EEG signal recognition.

2. Feature Extraction Method

2.1. Multi-Wavelet Framework Combining Morlet Wavelet and Haar Wavelet

The basic idea of multi-wavelet theory is to generate multi-resolution analysis space from a multi-scale function [16]. In orthogonal multi-resolution analysis space, the r-layer multi-scale function Φ(t) and r-layer multi-wavelet function φ(t) satisfy the following two scale relations:

$$\Phi \left(t\right)=\sqrt{2}\sum _{k=0}^l{H}_k\Phi \left(2t-k\right),k\in Z$$

(1)

$$\phi \left(t\right)=\sqrt{2}\sum _{k=0}^l{G}_k\Phi \left(2t-k\right),k\in Z$$

(2)

where H_k and G_k are the r × r low-pass filter coefficient matrix and high-pass filter coefficient matrix, respectively.

In a multi-wavelet system, the one-dimensional signal needs to be properly vectorized before multi-wavelet decomposition to convert the signal into an r dimension signal. Conversely, post-processing is required during reconstruction to convert the conversion results into one-dimensional signals. If the initial input signals s₀ = {s_0,1, s_0,2, ……, s_0,N}∈V₀, Q and P are preprocessing matrices and post-processing matrices, respectively. The decomposition and reconstruction process of multi-wavelet transform is shown in Figure 1 and Figure 2.

Since the Morlet wavelet is closely related to human auditory and visual perception, the Haar wavelet has fast response speed and good anti-interference performance [17]. In this study, a two-dimensional coefficient matrix generated by the Morlet wavelet and the Haar wavelet is combined to construct a new multi-wavelet coefficient fusion matrix.

The Morlet wavelet is defined as:

$$M(t)={\mathrm{e}}^{j{\omega }_{0}t}{\mathrm{e}}^{-t^2/2}\hspace{1em}$$

(3)

where ω₀ is the center frequency of the wavelet, and its Fourier transform is:

$$\Phi (\omega )=\sqrt{2\pi }{\mathrm{e}}^{-1/2{(\omega -{\omega }_0)}^2}.$$

(4)

It can be seen from Equations (3) and (4) that the Morlet wavelet waveforms in the time domain and frequency domain are Gaussian window function forms, which naturally have the ability to separate various modes.

The Haar wavelet is defined as:

$$h(t)=\left\{\begin{array}{c}1\\ -1\\ 0\end{array}\begin{array}{c},\\ ,\\ ,\end{array}\begin{array}{c}0\le t\le 0.5\\ 0.5\le t\le 1\\ \mathrm{otherwise}\end{array}\right.$$

(5)

where t represents the sampling time and e represents the natural constant.

2.2. Energy Feature Extraction

The decomposition level of the wavelet packet determines the decomposition effect. For signals with different frequencies, different levels of decomposition should be adopted. The frequencies of each layer corresponding to the decomposition sampling frequency of 128 HZ are shown in

Table 1. The frequencies of each layer corresponding to the sampling frequency of 128 HZ decomposed.

Decomposed Signal	Frequency Range (HZ)
A1	32~64
D1	16~32
D2	8~16
D3	0~8

.

It can be seen from Table 1 that D1 (16–32 HZ) is near the β-rhythm frequency band of EEG signals, and the mean energy of the wavelet coefficients corresponding to the D1 frequency band can be extracted as the characteristic quantity. Therefore, different wavelet basis functions are used to perform three-layer wavelet packet decomposition of the original signal. Then, the wavelet coefficient matrix obtained after the decomposition of each wavelet packet is combined to enhance the feature diversity, and the dimension size of the multi-wavelet coefficient fusion matrix is set as:

$$M=⌈\sqrt{N\times (J+K\cdots \hspace{0.17em})}⌉$$

(6)

where M is the size of the multi-wavelet coefficient matrix after fusion, ⌈·⌉ is the symbol representing rounding up, N is the length of the single-wavelet coefficient matrix, and J and K are the widths of different single-wavelet coefficient matrices, respectively. The formula for calculating the mean energy feature of wavelet coefficients in the D1 frequency band is:

$$E_{mean}={\displaystyle \frac{1}{{{\displaystyle N}}_{D1}}}\sum _{i=1}^{{{\displaystyle N}}_{D1}}|D1\_coeffs[i]{|}^2$$

(7)

where N_D1 represents the total number of wavelet coefficients in the D1 frequency band and D1_coeffs[i] denotes the i-th wavelet coefficient.

2.3. CSP Feature Extraction

Common Spatial Pattern is a widely utilized technique for extracting features from and classifying EEG signals [18]. The basic principle is to construct a spatial filter to project the two types of EEG signals in the optimal direction to obtain an optimal space and then maximize the variance difference of the signals according to the diagonalization knowledge of the mathematical matrix, so as to obtain the two EEG features with the greatest difference, achieving the purpose of classification. A flow chart of the CSP method is shown in Figure 3.

After spatial filtering, the EEG feature vectors of left- and right-hand motor imagination are obtained. 2T feature vectors need to be selected from them to form the final feature vector. Generally, the first T rows and the last T rows are selected as the features of the signal matrix. In this study, a 2-dimensional feature vector is constituted, so the T value chosen is 1.

2.4. AR Feature Extraction

The AR model method is widely used in EEG classification because it can summarize signal information and easily transform it into feature vectors. The AR algorithm is as follows:

$$x\left(n\right)=-\sum _{i=1}^q{a}_q\left(i\right)x\left(n-\mathrm{i}\right)+\epsilon \left(n\right)$$

(8)

where ε(n) is a sequence with a variance of 2 and a mean of zero white noise and q is the order of the AR algorithm. Therefore, the EEG sequence x(n) can be regarded as the output of the white noise sequence (n) through the AR model H(z).

When the Levinson–Durbin recursion method is used, each set of parameters from low order to high order can be given [19]. When the minimum prediction error power of the model does not change, the correct order required has been achieved. In this study, 6 orders are selected. The coefficient solving methods of the AR model include the autocorrelation method, the Brug algorithm and the improved covariance method. Since the Brug algorithm minimizes the sum of the power of forward and backward prediction error, the recursion process of the algorithm is based on a time series and does not directly estimate the parameter a_i but estimates the reflection coefficient k_i, avoiding the estimation of sequence autocorrelation function, so that the obtained result is closer to the actual value. The Brug algorithm formula is as follows:

$$I_i(\omega )={\displaystyle \frac{1}{U}}{\left|\sum _{n=0}^{M-1}{x}_i(n)w(n)e^{-j\omega n}\right|}^2,i=1,2\dots ,M-1$$

(9)

In this context, the symbol U may represent a normalization factor, used to ensure that I_i(ω) is, in some sense, a normalized version of x_i(n), which typically denotes a discrete-time signal, where i is the index of the signal, n is the time index, w(n) is a weighting function or window function that modifies each sample of x_i(n) during the summation process, and e^−jωn represents the complex exponential function. Here, j is the imaginary unit (satisfying j² = −1), and ω is the angular frequency (measured in radians per sample).

Since the intermediate observations are filtered out, the qth reflection coefficient k_i is a measure of the correlation between x(n) and x(n − q). In the first step of the algorithm, the autocorrelation function is obtained by biased estimation, and the reflection coefficient can be converted into an AR coefficient by using the Levinson–Durbin recursion formula, which can ensure the stability of the AR model.

2.5. PSD Feature Extraction

An EEG signal is inherently non-stationary and random due to its infinite duration and total energy. However, within a short time frame, it exhibits stability [20]. Therefore, PSD is used to analyze the frequency domain characteristics of motor imaging EEG signals, and the Pwelch function [21], a non-parametric method, is utilized to calculate the Power Spectral Density, offering a more refined approach compared to traditional periodic graph methods. The calculation steps for a PSD feature vector are as follows:

(1)

The N-length signal is divided into several overlapping segments, the length of each segment A = N/B, and the specified window is applied to each segment of EEG x_p(n). There are a total of L segments. Then the period diagram J_P(w) of a signal is:

$$\left\{\begin{array}{c}{J}_p\left(w\right)={\displaystyle \frac{1}{AU}}\mid {\displaystyle \sum _{n=0}^{A-1}{x}_p}\left(\begin{array}{c}n\end{array}\right)w(\begin{array}{c}n\end{array}){\mathrm{e}}^{-\mathrm{j}wn}{\mid }^{2}p=1,2,\cdots ,A-1\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} U={\displaystyle \frac{1}{A}}{\displaystyle \sum _{n=0}^{A-1}{w}^2}(n)\hfill \end{array}\right.$$

(10)

where U is the normalization factor and w(n) is a Hamming window, which is a type of window function.

(2)

Fourier transform is applied to window data to calculate the period graph of each window segment, which is called the modified period graph.

(3)

The spectrum estimation is obtained by averaging the modified period graph, so the PSD estimation of the signal is as follows:

$$B_x(w)={\displaystyle \frac{1}{L}}\sum _{l=0}^L{J}_p(w)$$

(11)

However, the performance of the motor imagination task is affected by the current state of the subjects, and the subjects cannot maintain a consistent amplitude. Therefore, the PSD estimation of the signal with the number W needs to be normalized as follows:

$$\overline{B_x\left(w\right)}={\displaystyle \frac{B_x\left(w\right)-\frac{1}{W}{\displaystyle \sum _{w=1}^W}{B}_x\left(w\right)}{\max [\begin{array}{c}{B}_x\left(w\right)\end{array}]-\min \left[\begin{array}{c}{B}_x\left(w\right)\end{array}\right]}}$$

(12)

3. EEG Classification Using the GS-SVM-WOA-AdaBoost Algorithm

3.1. GS-SVM Methodology

Support Vector Machines (SVMs) [22] are a type of machine learning approach rooted in statistical learning theory. They involve mapping training samples through a nonlinear transformation into a higher dimensional space, where an optimal decision boundary is sought within this transformed space. Assuming a sample set (N) with a total of (n) samples:

$$N=\left\{(x_i,y_i),i=1,2,\dots ,n\right\}$$

(13)

where y ∈ {−1, +1} represents the class label of each sample, the objective function for the expression of the classification hyperplane can be formulated as follows:

$$f(x)=w^{\mathrm{T}}{x}_i+b=0$$

(14)

The objective function is given by:

$$\{\begin{array}{c}\min {\displaystyle \frac{1}{2}}\parallel w{\parallel }^2+c{\displaystyle \sum _{i=1}^n}{\xi }_i\\ st.y_i[(w·x_i)+b]+{\xi }_i⩾1,{\xi }_i⩾0,i=1,\cdots ,n\end{array}$$

(15)

where w represents the normal vector to the hyperplane; b is the intercept term; ξ_i is the non-negative slack variables, introduced to enhance the generalization ability of the model; and c is the penalty parameter, which balances the trade-off between the classification loss and the maximization of the margin.

The choice of kernel function in SVM is crucial, with the Radial Basis Function (RBF) kernel exhibiting favorable local performance [23]. It is capable of approximating any nonlinear function with a relatively small number of parameters, effectively reducing the complexity of the model. The expression for the RBF kernel is given as:

$$K(x_i·x_j)=\exp (-g\parallel x_i-x_j{\parallel }^2)$$

(16)

Previous studies have shown that the classification performance of SVM is primarily influenced by the penalty parameter c and the kernel function parameter g. In this paper, Grid Search (GS) is employed to optimize these parameters, aiming to identify the optimal combination of hyperparameters that enhances the SVM model [24]. Grid Search, as a widely applied parameter optimization technique, demonstrates its significance particularly in the tuning process of Support Vector Machine (SVM) models.

The specific process involves first defining a reasonable search range for the penalty parameter c and the kernel function parameter g. In this paper, the search range for c is set as [0.1, 1, 10, 100], while the search range for g is [0.01, 0.1, 1, 10]. Subsequently, the defined search ranges for c and g are combined to generate all possible parameter combinations, forming a parameter grid. Finally, each (c, g) combination within the parameter grid is trained, and the accuracy achieved under different (c, g) combinations is used as data points to generate a contour plot. The contour plot of the multi-class parameter selection results obtained using the Grid Search (GS) optimization method for GS-SVM is depicted in Figure 4.

As illustrated in Figure 4, it can be observed that different combinations of the penalty factor c and the kernel parameter g yield varying levels of accuracy. Specifically, a favorable performance is achieved when the penalty factor c is set to 2 and the kernel parameter g is set to 0.35. Therefore, the optimal parameters are set as a penalty factor c of 2 and a kernel parameter g of 0.35.

3.2. GS-SVM-AdaBoost Methodology

The merits of Support Vector Machines (SVMs) lie in their ability to address classification problems with small sample sizes. However, for the classification of new samples, more sophisticated algorithms are often required to enhance their accuracy [25]. The AdaBoost training approach is built upon the boosting methodology, having the criterion of minimizing the classification error rate. It iteratively augments the weights of misclassified instances, undergoing multiple iterations, to progressively strengthen the classification capabilities of the classifier. As a result, AdaBoost demonstrates remarkable efficacy in boosting the performance of weak classifiers [26].

In this paper, the AdaBoost training method is employed to enhance the classification capability of the SVM classifier [27], utilizing the Radial Basis Function (RBF) kernel. The optimal values of the penalty parameter c and the kernel parameter g are identified through a Grid Search optimization approach. The algorithm process of the SVM-AdaBoost method to classify EEG signals is as follows:

(1)

The training sample set is S, where the number of samples is n, the number of categories is Z, and the number of iterations is R. The labeled training sample set is:

$$R=\left\{\left(s_1,y_1\right),\dots ,\left(s_n,y_n\right)\right\},\hspace{1em}{s}_i\in S\hspace{1em}{y}_i\in \left\{1,2,\cdots ,Z\right\}$$

(17)

(2)

Initialize the weights corresponding to the samples. In the loop, sample the training set according to the weights of the samples to obtain the training set of the component SVM classifier.

(3)

Calculate the standard deviation of the training set as the parameter of the classifier.

(4)

Calculate the training error of the classifier, which is the sum of the weights of the misclassified samples.

(5)

Calculate the weight of the classifier as follows:

$${\alpha }_i={\displaystyle \frac{1}{2}}\ln \left({\displaystyle \frac{1-{\epsilon }_t}{{\epsilon }_t}}\right)$$

(18)

where ε_t represents the error rate of the t-th weak classifier on the weighted training set.

(6)

Update the weight:

$${\omega }_{i+1}\left(i\right)={\displaystyle \frac{{\omega }_i\left(i\right)\exp \left\{-{\alpha }_t{\mathrm{y}}_i{h}_t\left(x_i\right)\right\}}{Z_i}}={\displaystyle \frac{{\omega }_i\left(i\right)}{Z_i}}\times \left\{\begin{array}{l}{e}^{-{\alpha }_t},\hspace{1em}{y}_i=h_t\left(x_i\right)\\ e^{{\alpha }_t}, \hspace{1em}{y}_i\ne h_t\left(x_i\right)\end{array}\right.$$

(19)

The notation ω_i+1(i) represents the weight of the i-th sample for the (t + 1)-th weak learner, while ω_i(i) denotes the weight of the i-th sample for the t-th weak learner. The symbol α_t stands for the weight of the t-th weak learner, which is typically related to its error rate. The lower the error rate, the larger α_t is, indicating a greater contribution of this weak learner to the final strong learner. y_i represents the true label of the i-th sample. h_t(x_i) indicates the predicted label of the i-th sample by the t-th weak learner. The expression exp{−α_ty_ih_t(x_i)} is an exponential function that adjusts the sample weight based on the prediction outcome of the weak learner and the true label. If the weak learner correctly predicts the sample (i.e., y_i = h_t(x_i)), the weight is multiplied by e^−αt (decreasing the weight); if the prediction is incorrect (i.e., yi ≠ h_t(xi))), the weight is multiplied by e^αt (increasing the weight). Z_i is a normalization factor that ensures the sum of all sample weights remains 1 after the update. Specifically, Z_i (though usually denoted as Z_t to emphasize its relationship to the t-th iteration) is the sum of the updated weights for all samples, ensuring the overall weights are properly scaled.

(7)

At the end of T iterations, the decision function value of the final classifier is obtained:

$$H\left(x\right)=\mathrm{sgn}\left[\sum _{i=1}^{n}v{\alpha }_i{h}_i\left(x\right)\right]$$

(20)

where n represents the number of weak learners and v represents the learning rate.

3.3. GS-SVM-WOA-AdaBoost Methodology

3.3.1. Whale Optimization Algorithm (WOA)

The Whale Optimization Algorithm (WOA) primarily consists of two phases: contraction encircling and position updating [28]. The mathematical expression for the hunting behavior during the contraction encircling phase is described as follows:

$$X(t+1)=X^{\ast }(t)-A·D_1$$

(21)

$$K_1=\left|C·X^{\ast }(t)-X(t)\right|$$

(22)

In the equation, t represents the current iteration number; X(t) denotes the position of the humpback whale at the current time; X(t + 1) represents the position of the humpback whale at the next time step; k₁ is the absolute value of the difference between the prey’s position scaled by C and the whale’s position; X*(t) is the position vector of the current optimal solution; A is the convergence coefficient; and C is the fluctuation factor.

$$A=2a{r}_1-a$$

(23)

$$C=2r_2$$

(24)

$$a=2-2t/T_{\max }$$

(25)

where r₁ and r₂ are random numbers within the interval [0, 1], and Tmax denotes the maximum number of iterations, which is set to 50 in this study. Consequently, the value of a varies within the range [0, 2], adapting dynamically as t increases.

Position updating involves both spiral position updating and random search position updating. In this paper, spiral position updating is selected, and its expression is given as:

$$X\left(t+1\right)=k_2·e^{bl}·\cos \left(2\pi l\right)+X^{\ast }(t)$$

(26)

In the equation, k₂ = /x ∗ (t) − x(t)∣ represents the distance between the prey and the whale; b is a parameter controlling the shape of the spiral; and l has a value range of [−2, 1].

The formula chosen for random search position updating is:

$$X(t+1)={\mathit{X}}_{rand}(t)-A·D_{rand}$$

(27)

where X_rand(t) represents the position vector of a randomly selected whale and K_rand is the absolute value of the difference between C times X_rand(t) and X(t).

3.3.2. Parameter Optimization of AdaBoost Based on WOA

In the AdaBoost algorithm, the number of weak learners n and the learning rate v are of paramount importance. An excessively large value for the parameter n, representing the number of weak learners, can lead to overfitting, whereas an overly small value can result in underfitting. The learning rate v serves to adjust the weights during each iteration of the model aggregation process. The number of weak learners n and the learning rate v must be carefully balanced in the AdaBoost algorithm, as a reasonable adjustment of these two parameters can enhance the predictive accuracy of the algorithm. However, the process of balancing the number of weak learners n and the learning rate v often relies on default values or predictions, which can be cumbersome and may not always achieve optimal results.

To address this issue, this paper utilizes the WOA (Whale Optimization Algorithm) to optimize the number of weak learners n and the learning rate v in the AdaBoost algorithm [29]. We set the range for the number of weak learners n in the AdaBoost algorithm to [2, 200] and the range for the learning rate v to [0.05, 1.00], within which the optimal value of the objective function is sought. The best fitness value obtained by the WOA (Whale Optimization Algorithm) represents the optimal value of the objective function. To ensure that the fitness value converges to a stable value upon completion of the WOA (Whale Optimization Algorithm) optimization iterations, we set the number of whales to 60 and the number of WOA optimization iterations to 50. The final positions of the whales represent the optimal values for the two parameters. The optimization process of the WOA at different iteration numbers is illustrated in Figure 5.

As depicted in Figure 5, the correlation coefficient stabilizes when the number of WOA iterations exceeds 5, indicating the effectiveness of the WOA optimization process. To conserve computational time, we set the number of WOA iterations to 5. Ultimately, under the optimal conditions of 165 weak learners n and a learning rate v of 0.396, the correlation coefficient converges to a stable value.

4. Experimental Verification

4.1. Introduction of Experimental Data

To verify the experiment, the data of different data sets are selected for simulation.

(1)

Data 1

Experimental data 1 are from dataset III of the 2003 BCI Competition II provided by the BCI Laboratory, Graz University of Technology [30]. The data sampling frequency is 128 Hz, and there are three channels, C3, CZ, and C4, using AgCl as the electrode, as shown in Figure 6.

(2)

Data 2 and data 3

The experimental data came from data set 2b of BCI Competition IV. Nine subjects collected data at three electrodes [31], C3, CZ, and C4, with a sampling frequency of 250 Hz. 01T and 02T of data set 2b in BCI Competition IV are analyzed in this study. Each experiment included the following processes, as shown in Figure 7.

4.2. Data Preprocessing

To prevent the interference of high-frequency signals (e.g., myoelectric or other noise signals) and ensure that the fast waves in EEG signals are not affected, a Finite Impulse Response (FIR) filter is used to preprocess EEG data [32]. Compared with an Infinite Impulse Response (IIR) filter [33], the FIR filter has strict linear phase characteristics, so that the signal does not produce phase distortion in the transmission process, meaning that the FIR filter is stable. The FIR filter system function in this work can be expressed as:

$$H(z)=\sum _{n=0}^{E-1}h(\mathrm{n})z^{-n}$$

(28)

In addition, the response frequency is:

$$H({\mathrm{e}}^{\mathrm{j}\omega })=\sum _{n=0}^{E-1}h(n){\mathrm{e}}^{-\mathrm{j}\omega n}=\mid H({\mathrm{e}}^{\mathrm{j}\omega })\mid {\mathrm{e}}^{\mathrm{j}\theta (\omega )}$$

(29)

where θ(ω) is the phase characteristic function, ω is the digital frequency, and E is the length of the unit impulse response h(n).

In EEG signals, the low-pass frequency is usually set at 30 Hz to extract the frequency band of EEG signals [34]. In FIR filter design, the window function can adjust the spectrum characteristics of the signal and improve the time domain characteristics of the filter. Therefore, this paper uses the rectangular window function and sets the low-pass frequency at 30 Hz to design the FIR filter. The model diagram is shown in Figure 8.

The preprocessing of right-handed three-channel data via the FIR filter is shown in Figure 9, Figure 10 and Figure 11.

The preprocessing of right-handed three-channel data via the FIR filter is shown in Figure 12, Figure 13 and Figure 14.

It can be seen from the figures that after the FIR filter is used to pretreat the EEG signal, the interference of the noise signal is effectively dealt with, which is convenient for the subsequent study of the EEG signal.

As blinking induces high-amplitude, rapid variations in EEG signals captured by electrodes positioned over the frontal lobe region, with these artifacts being particularly pronounced in electrodes situated closer to the eyes, it necessitates the implementation of artifact removal processes during the preprocessing phase. Independent Component Analysis (ICA) emerges as a valuable preprocessing technique for EEG signals, effectively eliminating artifacts and noise, segregating independent components, and thereby enhancing the overall signal quality. In this paper, Independent Component Analysis (ICA) is utilized for artifact removal [35]. The topoplot resulting from the ICA is shown in Figure 15.

Taking the removal of the second component (i.e., ICA001) as an illustrative example, the topoplot of ICA Component 001 is shown in Figure 16.

As evident from Figure 16, the energy of component ICA001 is predominantly high over the forehead, particularly in lower frequencies, and exhibits significant enhancement in some trials, indicating it to be an ocular movement artifact that requires removal. The difference between the signal after removing the component and the original signal is illustrated in Figure 17.

As evident from Figure 17, the signal after artifact removal exhibits a clearer presentation, significantly facilitating subsequent processing.

4.3. Feature Fusion Extraction

Studies have shown that the C3 and C4 electrodes reside in the motor function area of the primary sensorimotor cortex of the brain, providing the most accurate reflection of changes in the brain state when subjects imagine movement [36]. Consequently, signals recorded by the C3 and C4 electrodes were chosen for feature extraction and classification in this study, with Cz serving as the reference electrode.

Visualize the data in two dimensions to show the differences between different categories. The horizontal and vertical coordinates represent the two dimensions in the feature space, respectively. The original EEG test signal is transformed into a two-dimensional feature problem after feature extraction. The feature extraction diagrams are shown in Figure 18, Figure 19, Figure 20 and Figure 21.

4.4. Evaluation of Feature Importance

The assessment of feature importance in motor imagery EEG signals aims to quantify the contribution of different features in distinguishing between left-hand and right-hand motor imagery EEG signals, thereby facilitating the selection of optimal features for classification. Random Forest (RF), as an ensemble learning algorithm, exhibits significant advantages in EEG feature importance assessment due to its strong tolerance to outliers and noise, as well as its ability to handle high-dimensional data [37]. Therefore, this study utilizes the Random Forest algorithm to evaluate the importance of extracted features. The feature relevance diagram obtained from the Random Forest model is shown in Figure 22.

The feature relevance diagram in Figure 2 visually illustrates the interconnectivity among the 12 sets of feature vectors extracted via four different methods. This visualization analysis not only reveals the complex network of relationships between the feature vectors but also distinctly highlights the significant importance of specific feature vectors. Feature vectors 1–4 are obtained through multi-wavelet decomposition, feature vectors 5–8 are obtained using the Common Spatial Patterns (CSP) method, feature vectors 9–10 are derived from the Autoregressive (AR) model, and feature vectors 11–12 are extracted via Power Spectral Density (PSD) analysis. Notably, feature vector 1, derived from multi-wavelet decomposition; feature vector 8, extracted through Common Spatial Patterns (CSP); feature vector 10, obtained from the Autoregressive (AR) model; and feature vector 12, extracted via Power Spectral Density (PSD) analysis all exhibit prominent importance markers on the feature relevance diagram. Consequently, based on the evaluation results from this diagram, we have selected these identified feature vectors for normalization processing.

4.5. Feature Vector Construction

In multi-feature fusion extraction of the obtained feature vectors, the obtained feature vector is integrated to obtain the input feature vector F’ = {F1, F2, F3, F4}, which is constructed by integrating the obtained vectors. Since different features have different meanings, it is necessary to normalize the input feature vector by:

$$F_k^{\prime }=(F_k-{\mathit{\mu }}_k)/{\sigma }_k;k=1,2,3,4$$

(30)

where μ_k is the vector consisting of the mean of the Kth feature, and σ_k is the standard deviation of the Kth feature.

The entire experimental flow chart is shown in Figure 23.

4.6. Comparative Analysis of Classification Results

In order to compare the classification performance of the EEG multi-wavelet decomposition and multi-feature fusion with the SVM-AdaBoost algorithm, three single-wavelet transform algorithms (i.e., Haar wavelet, Morlet wavelet, and Daubechies Wavelet 4 (Db4) [38]) and the multi-wavelet transform algorithm composed of the Haar wavelet and the Morlet wavelet are used for classification experiments on the same sample data set, and the classification accuracy is shown in

Table 2. Comparison of classification accuracy of multi-wavelet SVM.

Method	Haar & Morlet	Haar	Morlet	Db4
Data 1	54.18%	50.82%	50.83%	49%
Data 2	49.17%	47.33%	48.67%	46.67%
Data 3	50%	48.17%	47.17%	43.33%

.

As demonstrated in Table 2, the application of a combination of two wavelet functions, as opposed to a single-wavelet function, exhibits higher accuracy in the motor imagery EEG classification task. Recognizing this, the current study innovatively introduces the multi-wavelet transform technique, aiming to delve deeper into enhancing and optimizing the classification of motor imagery EEG signals. To further explore the potential of a multi-feature fusion strategy within the SVM-AdaBoost framework for EEG signal classification, the study integrates the features extracted via the various methods mentioned earlier and conducts a comprehensive validation of the SVM-AdaBoost classification algorithm on a unified sample dataset. This strategy seeks to significantly improve classification performance via the complementary enhancement of features. The classification accuracies under different combinations of mixed features are presented in

Table 3. Classification accuracy of mixed-feature extraction.

	Data 1	Data 2	Data 3
Haar & Morlet	75%	69.13%	74%
CSP	70%	69%	70%
AR	72.70%	70%	71.67%
PSD	76%	67%	72%
Haar & Morlet + CSP	73.60%	71.30%	76%
Haar & Morlet + AR	74.92%	72.50%	75%
Haar & Morlet + PSD	77%	70%	74.12%
CSP + AR	73%	69.30%	72.83%
CSP + PSD	70.12%	67.20%	71.64%
PSD + AR	66.90%	66.70%	70.16%
Haar & Morlet + CSP + AR	87.13%	77.80%	85.20%
Haar & Morlet + CSP + PSD	85.00%	76%	83.10%
CSP + PSD + AR	83%	70.30%	79.25%
Feature Fusion	95.37%	83.33%	92.85%

as follows:

Based on the classification accuracy data presented in Table 3 for mixed-feature extraction, it becomes evident that the implementation of a feature fusion strategy on the same sample data, compared to single-feature extraction methods, significantly boosts classification accuracy. To further validate the superiority of the SVM-AdaBoost algorithm in EEG signal classification, particularly when combined with multi-feature fusion, this study conducted detailed comparative classification experiments by applying the mixed features as input to commonly used EEG signal processing algorithms, such as 1D-CNN and RNN, as well as standalone SVM and AdaBoost algorithms. The comparison graph of classification algorithm model accuracy is shown in Figure 24.

As shown in Figure 24, the proposed SVM-AdaBoost-based mixed-feature extraction and classification algorithm demonstrates a remarkable performance advantage, achieving a peak classification accuracy of 95.37%. This result significantly outperforms the other compared classification models. This finding not only validates the efficiency and accuracy of the proposed algorithm in EEG signal classification tasks but also underscores the crucial role of the multi-feature fusion strategy in enhancing classification performance. Compared to traditional 1D-CNN [39] and RNN models [40], and standalone SVM and AdaBoost algorithms, the proposed algorithm is more effective in capturing complex features within EEG signals, enabling more precise classification research.

Then, the kappa coefficient is introduced to further verify the experimental results. The kappa coefficient is an index utilized for consistency testing and can measure the effectiveness of classification [41]. The expression of the kappa coefficient is as follows:

$$Kappa={\displaystyle \frac{Acc-p_e}{1-p_e}}$$

(31)

where Acc is the accuracy.

$$p_e={\displaystyle \frac{{\displaystyle \sum _i}\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{elements} \mathrm{in} \mathrm{row} \mathrm{i}\ast \mathrm{Sum} \mathrm{of} \mathrm{column} \mathrm{i} \mathrm{elements}}{{\left(\sum \mathrm{All} \mathrm{elements} \mathrm{of} \mathrm{matrix}\right)}^2}}$$

(32)

since the research in this paper focuses on a binary classification problem, the random classification accuracy, represented as p_e = 0.5.

Based on the same sample data set, a single SVM algorithm and single-feature extraction are used to conduct the classification experiment again, and the kappa values are shown in Figure 25.

Figure 25 shows the kappa value using the SVM-AdaBoost classification algorithm. Compared with the SVM single classification algorithm, the SVM-AdaBoost classification algorithm has a higher kappa value, indicating that using an AdaBoost training method to strengthen SVM classification can obtain a better classification situation, with a kappa value of 0.907.

In order to further verify the effectiveness of the proposed method for EEG feature extraction and classification recognition, the proposed method is compared with the classification accuracy of references [42,43,44], and the results are shown in

Table 4. Comparison of classification accuracy with related literature.

Methods	Proposed Method	Reference [42]	Reference [43]	Reference [44]
Data 1	95.37%	89.82%	80.83%	91.17%
Data 2	83.33%	81.08%	75.67%	83.67%
Data 3	92.85%	87.86%	78.44%	87.65%

.

As can be seen from Table 4, compared with the HHT + SVM method found in the literature [42], the CapsNet method found in the literature [43], and the PS0-CSP + SVM method found in the literature [44], the classification accuracy of the proposed algorithm has improved to a certain extent, reaching 95.37%. On the one hand, this paper adopts multiple methods for multi-feature extraction to overcome the problem of single EEG features; on the other hand, it uses the AdaBoost algorithm to enhance the SVM classification algorithm, which is more conducive to improving classification accuracy.

5. Conclusions

To tackle the challenges posed by single-feature EEG signals, insufficient information description, and low recognition accuracy in motor imagery EEG signal classification, this paper constructed a multi-wavelet decomposition framework based on the Morlet and Haar wavelets. On this basis, energy features, CSP features, AR features, and PSD features of EEG signals were extracted, and a multi-feature fusion was performed. Subsequently, the WOA-optimized AdaBoost training method was employed to enhance the SVM classifier for the classification of the fused multi-feature vectors. The experimental results demonstrate that the method proposed in this paper improves the classification accuracy of motor imagery EEG signals, outperforming single EEG signal classification algorithms. It provides an effective new approach for the recognition of multi-class motor imagery EEG signals.

While the experimental results and analysis have demonstrated the effectiveness of the proposed method in this paper and have addressed the issue of EEG signal classification, further research is needed to explore whether the method can be applied to other biomedical signals and whether there exist better combinations of hybrid feature extraction methods. Therefore, expanding applications and enhancing hybrid feature extraction methods should be the foci of future research.