Feature Extraction of Motor Imagery EEG via Discrete Wavelet Transform and Generalized Maximum Fuzzy Membership Difference Entropy: A Comparative Study

Abstract

Identifying motor imagery (MI) electroencephalogram (EEG) is an important way to achieve brain–computer interface (BCI), but its applicability is heavily dependent on the performance of feature extraction procedure. In this paper, a feature extraction method based on generalized maximum fuzzy membership difference entropy (GMFMDE) and discrete wavelet transform (DWT) was proposed for the feature extraction of EEG signals. The influence of different distance calculation methods, embedding dimensions and tolerances were studied to find the best configuration of GMFMDE for the feature extraction of MI–EEG. The gradient boosting decision tree (GBDT) classifier was used to classify the features extracted from GMFMDE and DWT. The average classification accuracy of 93.71% and the maximum classification accuracy of 96.96% were obtained, which proved the effectiveness of the proposed feature extraction method for EEG signal feature extraction.

1. Introduction

Brain–computer interface (BCI) is a device that enables the human brain to communicate with the outside world, enabling people with normal thinking but limited physical movement to communicate with the outside environment [1]. Through the feature extraction of electroencephalogram (EEG) signals and using machine learning classifier to obtain accurate classification results of motor imagery (MI), the successful application of BCI technology can be achieved [2]. At present, MI-based BCI signals have played a role in intelligent assisted driving [3], brain-controlled robots [4], and life support for the disabled [5].

At present, many feature extraction and pattern recognition methods have been successfully applied to the process of feature extraction and classification of MI–EEG signals. For pattern recognition methods, Lu et al. used support vector machine (SVM) to accurately classify MI–EEG signals from four kinds of different motions [6]. Li et al. classified EEG signals of left- and right-hand motion imagination using a K-nearest neighbor (KNN) classifier [7]. Chen et al. introduced the convolutional block attention module in convolutional neural network (CNN) and proposed an IS-CBAM-CNN method to improve the classification accuracy of MI–EEG using CNN [8]. For feature extraction methods, there are several common spatial pattern algorithms (CSP) with different characteristics: Park et al. and Lu et al. used the regularization CSP (R-CSP) method to process EEG signals [9,10]. Mishuhina et al. proposed a feature weighting and regularization method based on a CSP method to extract EEG features [11]. Power spectral density algorithm (PSD) is also being used to extract EEG signals’ features. Liu et al. proposed a time-varying modeling framework combining multiwavelet basis functions and regularized orthogonal forward regression (ROFR) algorithm to obtain high resolution power spectral density (PSD) features [12]. Meanwhile, methods based on multiple entropy have also been applied to feature extraction in MI–EEG task.

Entropy measures the degree of chaos in a system and can evaluate the randomness, complexity, information content, or other indicators of a signal. Researchers have developed a series of methods to extract features from EEG signals using sample entropy (SE), approximate entropy (AE), and fuzzy entropy (FE). Li et al. proposed a personalized weighted composite multiscale fuzzy entropy method based on a multiscale fuzzy entropy method to process EEG signals [13]. Sharma et al. used average Shannon entropy, average Renyi’s entropy, average approximate entropy, average sample entropy, and average phase entropy to extract EEG features [14]. Cao et al. used approximate entropy, sample entropy, fuzzy entropy, and inherent fuzzy entropy to evaluate the EEG complexity, respectively [15]. However, because these entropy methods can only measure one aspect of the nonlinear characteristics of signals, the accuracy of the final classification of MI still needs to be improved.

The maximum fuzzy membership difference entropy (MFMDE) was proposed by Zhang et al. [16]. MFMDE is a two-index algorithm that can quantify the randomness and complexity of signals, and has been verified to be effective in MI–EEG and rolling bearing fault diagnosis tasks. Its performance is better than fuzzy entropy (FE), and the calculation time is almost half of FE. However, traditional MFMDE measurement criteria are relatively simple. Although it can quantify the randomness and complexity of signals, there may be situations where the ability to measure the nonlinearity of EEG signals is weak. Therefore, this paper proposes a generalized MFMDE (GMFMDE) based on traditional MFMDE, which achieves better feature extraction results by introducing different distance metric criteria.

Wavelet transform (WT) is an ideal tool for the time–frequency analysis of signals. Various forms of WT have been used for processing EEG signals, such as Tan et al., who used dual-tree complex wavelet transform (DTCWT) to reconstruct BCI signals in each level to overcome frequency aliasing in wavelet transform [17]. Lee et al. proposed a motor imagery classification scheme based on the continuous wavelet transform with three mother wavelets and the convolutional neural network to capture a highly informative EEG image by combining time–frequency and electrode location, to classify motor imagery tasks, and reduce computation complexity [18]. Wang et al. proposed a new MI–EEG classification method to improve classification accuracy by combining Shannon complex wavelets and convolutional neural networks [19]. Discrete wavelet transform (DWT) is a traditional discrete version of WT, and many works have proven that combining DWT with machine learning pattern recognition methods can classify MI–EEG signals [20,21,22]. This article adopts a combination of classic DWT and GMFMDE methods to verify the performance of GMFMDE in MI–EEG problems.

Gradient boosting decision tree (GBDT) uses the decision tree as a weak classifier, achieving the effect of a strong classifier after gradient boosting. GBDT can process various types of data, and is widely used to solve different classification problems [23,24,25,26].

In this paper, the feature extraction method combining generalized maximum fuzzy membership difference entropy (GMFMDE) and DWT is adopted. The features extracted by the two methods were combined as the input of GBDT in the pattern recognition part, and then the accurate classification results of MI–EEG signals were obtained. At the same time, this paper also discusses the influence of MFMDE calculated under different distance calculation method, embedded dimension, and tolerance conditions on the classification performance of MI–EEG signals. The novelty of the method is as follows:

(1) Generalized maximum fuzzy membership difference entropy (GMFMDE) was proposed;

(2) The effects of different distance calculation methods, embedded dimensions, and tolerances on GMFMDE were explored;

(3) DWT-based GMFMDE was proposed for the feature extraction of MI–EEG, and 93.71% accuracy was achieved.

Section 2 includes datasets, feature extraction methods, and the pattern recognition method. The results of the classification of MI–EEG as the input of GBDT after the combination of MFMDE and DWT features, as well as the impact of different distance calculation methods, embedded dimensions and tolerances on MFMDE are given in Section 3. The final conclusion is given in Section 4.

2. Methods

2.1. Dataset

We used the I-b dataset from “BCI competition-III” [27] to train and test our proposed method. This dataset is from an ALS patient undergoing artificial respiration. Subjects were asked to move their cursor up and down on a computer screen and measure their cortical potential. During the signal acquisition process, the subjects received auditory and visual feedback from their slow cortical potentials (Cz Masters). Cortical positivity can cause the cursor to move downward on the screen. Cortical negativity can cause the cursor to move up on the screen. Each experiment lasted for 8 s, and in each experiment, from 0.5 s to 7.5 s, tasks were presented visually and audibly with a high-brightness target at the top (negative) or bottom (positive) of the screen. In addition, the task (“up” or “down”) emits a sound at 0.5 s. Visual feedback is presented from the 2–6.5 s, and only those presented at 4.5 s are collected for training and testing in each experiment. A sampling rate of 256 Hz and a signal acquisition time of 4.5 s obtained 1152 data points per channel. The cortical positivity and cortical negativity EEG signals are shown in Figure 1.

2.2. Feature Extraction Method

The feature extraction part of this paper adopted the method of combining the features extracted from GMFMDE and DWT. The feature extraction process of GMFMDE and DWT are introduced below.

2.2.1. Generalized Maximum Fuzzy Membership Difference Entropy (GMFMDE)

Entropy refers to the degree of chaos of a system and is a basic tool to evaluate the randomness, complexity, information content or other indicators of signals. Many entropy-based methods have been used for feature extraction of EEG signals [28,29,30]. The traditional maximum fuzzy membership difference entropy (MFMDE) method proposed by Zhang. et al. in 2021 can quantify the randomness and complexity of the signal, and successfully extract the features of the dataset of Sets A–E from Bonn EEG, describing the characteristics of EEG in normal, interictal, and paroxysmal periods. The algorithm flow of maximum fuzzy membership difference entropy is shown in Figure 2. More details of the algorithm are as follows.

Suppose the analyzed sequence is $U=\{u\left(1\right),u\left(2\right),\dots ,u(n\left)\right\}$ and it has been normalized with mean 0 and variance 1. The steps to calculate GMFMDE are given below:

(i) Phase-space reconstruction. Under the condition of embedding dimension m, the m-dimensional vectors ${X\left(i\right)}^m$ are reconstructed by Formula (1):

$$\begin{gathered} {X\left(i\right)}^m=\left\{u\left(i\right),u\left(i+1\right),\dots ,u\left(i+m-1\right)\right\} \\ i=1,2,\dots ,N-m+1 \end{gathered}$$

(1)

(ii) Distance matrix construction. For a pair of reconstructed vectors ${X\left(i\right)}^m$ and ${X\left(j\right)}^m$, their Chebyshev distance ${CD}_{i,j}^m({X\left(i\right)}^m,{X\left(j\right)}^m)$ is computed by Formula (2):

$${CD}_{i,j}^m=\underset{k=\mathrm{0,1},2,\dots ,\mathit{m}-1}{\max }\left\{\left|u\left(i+k\right)-u\left(j+k\right)\right|\right\},i,j\in N+,1\le i,j\le N-m+1,i<j$$

(2)

(iii) The calculation of maximum fuzzy membership. For MFMDE, the exponential function is employed to determine the fuzzy membership ${FM}_{i,j}^m$ of distance ${CD}_{i,j}^m$:

$${FM}_{i,j}^m=exp[-{{(CD}_{i,j}^m/r)}^2]$$

(3)

where r is the tolerance and it is often set to a percentage of the standard deviation (SD) of the raw signal. In this paper, the value range of embedded dimension was 2, 3, 4, 5. After calculating all fuzzy memberships, the maximum fuzzy membership with regard to each reconstructed vector ${X\left(i\right)}^m$ is defined as:

$$\begin{gathered} {MFM}_i^m=\max \left\{{FM}_{i,i+1}^m,{FM}_{i,i+2}^m,\dots ,{FM}_{i,N-m+1}^m\right\} \\ i=\mathrm{1,2},\dots ,N-m+1 \end{gathered}$$

(4)

(iv) The calculation of normalized maximum fuzzy memberships. After computing all the maximum fuzzy memberships ${MFM}^m=\{{MFM}_1^m,{MFM}_2^m,\dots ,{MFM}_{N-m+1}^m\}$, they are normalized with variance 1, i.e.:

$${NMFM}^m={MFM}^m/SD\left({MFM}^m\right)$$

(5)

(v) The calculation of statistical distance via different distance calculation method. The embedded dimension is increased to $m+1$ and steps (1)–(4) are repeated. Under the circumstances, the normalized maximum fuzzy memberships (NMFMs) ${NMFM}^{m+1}$ for adjacent higher embedded dimension $m+1$ are obtained. Finally, difference between ${NMFM}^m$ and ${NMFM}^{m+1}$ is measured by six distance calculation methods (DCM). The six distance calculation methods are: Anderson–Darling distance (ADD); Cramer–Von Mises distance (CVMD); Kuiper distance (KD); Kolmogorov–Smirnov distance (KSD); maximum mean discrepancy (MMD); and Wasserstein–Anderson–Darling distance (WADD). Their calculation formulas are shown in

Table 1. The formulas of the six distance calculation methods.

Distance Calculation Methods	Formulas
Anderson–Darling distance (ADD)	$A=\int \frac{{\left[F_n\left(x\right)-F\left(x\right)\right]}^2}{F\left(x\right)\left[1-F\left(x\right)\right]}dF\left(x\right)$	(7)
Cramer–Von Mises distance (CVMD)	$C=\int {\left|F_n\left(x\right)-F\left(x\right)\right|}^{2}dF\left(x\right)$	(8)
Kuiper distance (KD)	$\mathrm{K}={sup}_{d\left(x\right)>0}\left[\widehat{F}\left(x\right)-F\left(x\right)\right]-{inf}_{d\left(x\right)<0}\left[\widehat{F}\left(x\right)-F\left(x\right)\right]$	(9)
Kolmogorov–Smirnov distance (KSD)	$D_n=\sqrt{n}\underset{x}{\sup }\left|F_n\left(x\right)-F\left(x\right)\right|$	(10)
maximum mean discrepancy (MMD)	$M=\underset{f\in F}{\sup }\{E_p\left[F\left(x\right)\right]-E_q\left[F\left(y\right)\right]\}$	(11)
Wasserstein–Anderson–Darling distance (WADD)	$W=\int \frac{{\left[F_n\left(x\right)-F\left(x\right)\right]}^2}{F\left(x\right)\left[1-F\left(x\right)\right]}dF\left(x\right)(Power=1)$	(12)

. MFMDE is thus defined as:

$$GMFMDE\left(m,r,N\right)=DCM({NMFM}^{m+1},{NMFM}^m)/N$$

(6)

In [16], Zhang. et al. only used the Cramer–Von Mises distance (CVMD) as the distance calculation method to calculate the maximum fuzzy membership difference entropy.

However, the impact of different parameter combinations under different distance calculation methods on the final result was not considered. The measurement criteria for different distance calculation methods are different. CVMD is to square the differences of each data point and then add them together to obtain the total distribution deviation. ADD results in a higher weight when calculating the square distance of the data distribution located at the tail of the data; when calculating the square distance of the data distribution located in the middle of the data, a smaller weight is given to it. KSD is the upper bound that identifies the difference between the cumulative probability of experience and the cumulative probability of target distribution at each data point. MMD is mainly used to measure the distance between the distributions of two different but related random variables. Therefore, using different distance calculation methods can have different effects on the calculation of GMFMDE. In step (v) of GMFMDE, this paper used six distance calculation methods to calculate the generalized maximum fuzzy membership difference entropy.

2.2.2. Discrete Wavelet Transform (DWT)

Wavelet transform (WT) has the ability of dual time–frequency analysis and multi-resolution analysis, and has been widely used in noise filtering, feature extraction, image processing, and other fields [31,32,33]. DWT is a kind of WT and has been used for the feature extraction of EEG signals. In this paper, the db4 wavelet, which is widely used, was used to carry out a four-layer wavelet decomposition, and the coefficients of high-frequency details are extracted as one of the features. The calculation formula for discrete wavelet transform is:

$$DWT\left(x\right)=\sum x\left(n\right)\times \phi \left(n\right)$$

(13)

where $x\left(n\right)$ represents an input signal, $\phi \left(n\right)$ represents the db4 wavelet function, and $n$ represents the sampling point of the signal.

2.3. Gradient Boosting Decision Tree (GBDT)

After MFMDE and DWT extracted the features, we combined the features as the input of GBDT. Decision tree (DT) is a tree-like structure and a commonly used supervised machine learning method [34,35,36]. GBDT is a boosting algorithm which uses DT as the basic classifier and uses a gradient boosting method to solve the problem. It has excellent performance and has been used in many fields to solve classification problems. In this paper, the logistic loss function was used, the learning rate was set to 0.1, the five-fold cross validation was adopted, and the recognition accuracy after 30 iterations was taken as the final classification accuracy. A total of 240 features extracted from GMFMDE combined with DWT under the conditions of different distance calculation methods and embedded dimension and tolerance parameter combinations were verified for recognition accuracy. The final strong learner model obtained by GBDT can be expressed as:

$$f_M\left(x\right)={\sum }_{m=1}^M{\gamma }_{m}T(x;{\theta }_m)$$

(14)

The overall workflow of feature extraction and pattern recognition is shown in Figure 2b. We have conducted multiple GMFMDE feature extractions for different distance calculation methods, embedded dimension and tolerance parameter combinations, and discussed the impact of different distance calculation methods, embedded dimensions and tolerances on the final classification accuracy in Section 3. The calculation method of accuracy is as follows:

$$Accuracy\left(\%\right)=\frac{number of samples correctly judged in the test set}{total number of samples in the test set}\times 100\%$$

(15)

In this article, we used MATLAB R2020a software and wavelet Analyzer app for programming, with computer conditions of CPU: Intel 12400f, GPU: AMD 6600XT, RAM: DDR4 3200 MHz.

3. Results and Discussion

For the binary I-b dataset of “BCI competition-III”, we recorded the classification accuracies of the GMFMDE extracted under 240 different distance calculation methods, embedded dimension and tolerance parameter combinations, combined with the features extracted by DWT, after 30 iterations using the GBDT in Section 2.3 (as shown in

Table 2. The classification accuracy (%) obtained under 240 different parameter combinations.

ADD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	95	94.64	96.07	95.36	94.11	94.46	93.75	95.89	96.25	95.89
	3	95.36	94.11	94.29	94.11	95	95	94.82	93.57	94.11	92.68
	4	94.82	94.46	95	93.57	93.75	93.93	93.21	94.82	93.39	94.64
	5	93.57	94.82	93.04	95	93.39	94.11	94.64	95.36	94.46	94.82
CVMD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	92.5	95.18	95.54	95.18	94.92	93.93	94.46	95	95.18	94.82
	3	94.46	94.29	95	94.11	93.57	94.46	93.57	94.29	93.93	94.29
	4	93.21	94.29	94.46	93.75	92.68	93.21	94.46	93.04	93.57	94.29
	5	94.64	95.36	95.36	95	93.39	93.93	93.21	94.46	94.11	94.29
KD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	93.93	96.25	95	96.79	94.11	94.29	94.82	94.11	95.18	94.11
	3	92.86	93.57	92.14	91.77	92.14	94.29	93.93	91.61	92.32	93.04
	4	92.5	94.11	93.04	94.64	94.46	91.96	92.86	93.57	92.68	91.77
	5	91.61	90.89	94.82	93.39	93.93	93.39	93.04	93.57	93.57	94.29
KSD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	92.14	93.57	94.46	95.18	95.54	95	93.58	94.29	93.75	92.86
	3	93.93	91.25	91.79	93.39	92.14	91.96	93.21	93.39	93.57	94.29
	4	93.57	94.11	92.5	94.29	93.75	91.61	89.29	91.79	90.89	90.54
	5	93.04	93.39	94.46	94.64	93.21	92.32	93.39	95.36	91.61	91.61
MMD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	91.61	92.68	93.93	91.61	92.68	92.68	92.68	91.07	93.57	91.43
	3	91.96	92.86	92.5	92.5	93.21	92.5	93.39	91.07	90.36	92.32
	4	92.32	90.89	90.36	92.14	91.79	91.43	91.43	91.79	91.25	93.39
	5	92.68	93.04	94.29	92.14	91.96	92.5	91.96	90.71	92.5	91.43
WADD	Embedded Dimension \Tolerance	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	2	93.93	93.93	93.04	92.5	94.46	92.68	93.21	93.39	92.86	92.68
	3	95.18	94.29	94.11	93.57	93.75	93.57	93.39	94.46	94.27	94.46
	4	95.71	94.64	95.71	93.57	94.11	93.57	93.93	93.93	94.82	94.11
	5	94.46	95.36	95	93.93	94.64	93.29	95.18	94.82	95	94.64

).

In order to find the most stable parameter combination method, we first determined one of the three variable parameters to make the other two parameters change within the value ranges (the distance calculation method includes six methods; the value range of embedded dimension was 2, 3, 4, 5; the value range of tolerance was 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1) and calculated the average classification accuracies corresponding to the determined parameters, as shown in Figure 3.

According to the results shown in Figure 3, we can see that different parameter combination conditions have an impact on the final classification results. For different distance calculation methods, the average classification accuracy of ADD is 94.48%, which is 2.31% higher than the average classification accuracy of 92.17% of the lowest MMD. For different embedded dimensions, the average classification accuracy is 94.01% when the embedded dimension was 2, but only 0.63% higher than the average classification accuracy of 93.38% when the lowest embedded dimension was 3. Similarly, for different tolerances, the average classification accuracy at the tolerance of 0.3 is 94.06%, which is 0.56% higher than 93.50% of the average classification accuracy at the lowest tolerance of 1. Evidently, using different distance calculation methods had the greatest impact on the final classification accuracy. Relatively speaking, the impact of embedding dimension and tolerance on classification accuracy was relatively small, but it cannot be ignored. The above results showed that it is necessary to select the appropriate distance calculation method, embedded dimension, and tolerance to extract features from datasets.

Table 3. The corresponding classification accuracy under different embedded dimensions and tolerance conditions (%) when ADD is used as the distance calculation method.

Embedded Dimension\Tolerance	2	3	4	5
0.1	95	95.36	94.82	93.57
0.2	94.64	94.11	94.46	94.82
0.3	96.07	94.29	95	93.04
0.4	95.36	94.11	93.57	95
0.5	94.11	95	93.75	93.39
0.6	94.46	95	93.93	94.11
0.7	93.75	94.82	93.21	94.64
0.8	95.89	93.57	94.82	95.36
0.9	96.25	94.11	93.39	94.46
1	95.89	92.68	94.64	94.82

shows the classification accuracy corresponding to different embedded dimension and tolerance combinations under the ADD distance calculation method. According to the results in Figure 3b,c, the condition with the embedded dimension is 2, and the tolerance condition is 0.3, thus showing the highest average classification accuracy.

When using ADD as the distance calculation method, the final classification accuracy is 96.07% under the condition that the embedded dimension is 2 and the tolerance is 0.3.

Next to the 96.25% classification accuracy, which, under the condition of the embedded dimension is 2, the tolerance is 0.9. It can be seen from Table 2 that 96.07% of the classification accuracy rate ranks second among all 240 classification accuracies and is 0.18% lower than the highest 96.25%. Considering stability and universality, we believe that the most stable parameter combination was to set the parameter as the ADD distance calculation method, with the embedded dimension of 2 and the tolerance of 0.3. If the highest recognition accuracy is considered, the parameter can be set as the ADD distance calculation method, with the embedded dimension of 2 and the tolerance of 0.9.

However, this paper adopted the feature extraction method of GMFMDE combined with DWT, and used GBDT as a classifier to obtain a high classification accuracy for the MI–EEG classification task of the binary I-b dataset of “BCI competition-III”, with an average classification accuracy of 93.60% for 240 times’ recognition. We also used the traditional combination of FE and DWT for feature extraction, and the classification accuracy results after GBDT are shown in

Table 4. Performance comparison with FE method on the same dataset.

Feature Extraction Methods	Machine Learning Classification Methods	Average Classification Accuracy (%)
MFMDE+DWT	GBDT	93.60
FE+DWT	GBDT	88.39

. Under all parameter combinations, GMFMDE using GBDT as a classifier has a higher recognition accuracy than when using FE for feature extraction. We think that this was due to the fact that MFMDE can quantify the randomness and complexity of the signal, and combined the high-frequency signal extracted by DWT to extract the MI information contained in the original EEG signal more comprehensively.

4. Conclusions

This paper proposed the feature fusion method of GMFMDE and DWT to extract the features of EEG signals and used GBDT as a classifier. The experimental results showed the effectiveness of our proposed method. The average classification accuracy of all 240 times’ five-fold cross-validation reached 93.60%, and the highest classification accuracy reached 96.25%. At the same time, it is discussed that using ADD as the distance calculation method, the embedding dimension is set to 2, and the tolerance is set to 0.3, which is the most stable parameter combination required by MFMDE for classification results. However, for different BCI datasets and experimenters, finding the most stable parameter combination means that it has the highest average recognition accuracy, but it may not necessarily achieve the highest recognition accuracy. For the I-b dataset from “BCI Competition-III” used in this article, the parameter combination for GMFMDE to achieve the best performance in extracting information is to use ADD as the distance calculation method, set the embedding dimension to 2, and set the tolerance to 0.9. However, it is still necessary to find the most stable parameter combination that uses ADD as the distance calculation method, and sets the embedded dimension to 2 and the tolerance to 0.3. The significance to find the most stable parameter combination is that the average accuracy rate of the most stable parameter combination is higher. Additionally, when the GMFMDE is combined with transfer learning technology for subsequent research, it can provide a stable performance of extracting effective information from EEG signals when facing different target domains and source domains. Compared with other methods, GMFMDE quantifies the randomness and complexity of the signal, DWT has a dual analysis of time–frequency, and the combination of the extracted features provides better classification performance. This method can effectively improve the recognition accuracy of MI–EEG tasks and can be widely applied.

In future work, we will attempt to use GMFMDE combined with different forms of wavelet transform methods, such as CWT, SCWT, DTCWT, etc., to verify the performance of GMFMDE combined with other time–frequency transform methods for MI–EEG tasks. At the same time, we will also try to combine GMFMDE with transfer learning technology to verify the performance of GMFMDE when facing different target domains and source domains.