###### Abstract  
Electroencephalography (EEG) is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG) not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (FE), and Permutation Entropy (PE), have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE), Multiscale Permutation Entropy (MPE), and Multiscale Fuzzy Entropy (MFE) are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE) is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD)/event-related synchronization (ERS) phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM) as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields relatively high classification accuracy compared with other entropy-based and classical time-frequency-space feature extraction methods. The \(t\)-test is used to prove the correctness of the improved MFE. motor imagery electroencephalography; feature extraction; multiscale fuzzy entropy; independent optimization of parameters; complexity; \(t\)-test +
Footnote †: journal: Applied  
There are three main kinds of classical feature extraction methods, i.e., Autoregressive (AR) model, Wavelet Transform (WT), and Common Spatial Pattern (CSP). The basic idea of the AR model is making use of the AR process to approximate a real EEG signal, and then using AR model coefficients as the feature of the EEG signal. This method is simple and has good real-time performance, but it is a kind of time domain analysis method for a stationary signal. The length of data segment determines the resolution and accuracy of parameter estimation [3]. The WT method is able to take advantage of scale and shift operations to perform multiscale decomposition and time-frequency domain localization, effectively obtaining the time-frequency information of signals. Thus, the analysis of EEG signals can benefit from WT [4]. However, recent studies do not support the use of wavelet features for the discrimination of EEG signals because of redundant and irrelevant information contained in wavelet coefficients [5]. The CSP method can find two directions that maximize variance for one class and minimize variance for the opposite class by using the matrix simultaneous diagonalization theory [6]. The performance of CSP is closely related with its operational frequency band. Hence, setting a broad frequency range in CSP generally yields poor classification accuracy [7]. To overcome this problem, the Common Spatio-Spectral Pattern (CSSP) [8], Sub-band Common Spatial Pattern (SBCSP) [9], and Filter Bank Common Spatial Pattern (FBCSP) [10] have been proposed on the basis of CSP and widely applied to the feature extraction of EEG signal.