## 2 Materials and Methods
In addition, the performances of the previously developed and proposed CDC-EFA methods were compared using motor image classification. The experiments were conducted using MATLAB (Ver. 2023b or later). To compare the effects of each accuracy performance improvement, we used five methods. Table 1 lists each method, with Ver. 5 indicating the results of the proposed CDC-EFA method. The 10-20 system for EEGs is a well-known technique to show the electrode locations for BCI study [33; 34]. Rather than using such symbols, we use the numbers on the electrode positions to preprocess the data in the programming. These five methods depend on the aforementioned classifications. The following methods are divided according to whether whitening or ICA and decentering are applied. Ver. 1 uses only the decentering method, Ver. 2 uses the ICA method, Ver. 3 uses the whitening method, Ver. 4 uses the ICA and decentering methods, and Ver. 5 uses both the whitening and decentering methods. Therefore, Ver. 1, Ver. 2, Ver. 3, Ver. 4, and Ver. 5 represent the decentering, ICA, whitening, ICA combined with decentering, and proposed method (CDC-EFA), respectively. For data extraction comparison, the EFA, ICA, and CDC-EFA methods used the publicly available BCI Competition III dataset IIa (C3D3a_2C) and BCI Competition IV dataset IIa (C4D2a_2C) data [35; 36; 37; 38; 39]. When selecting the time range to use for the EEG data, the time taken for the subject to begin imagining after confirming the motor imaginary instruction displayed on the screen was considered. While subjects were in relaxed conditions, the data for a total of 2 sec were used from 0.5 sec to 2.5 sec after the indication signal was generated. In the preprocessing stage, the BCI Competition III dataset IIIa data and BCI Competition IV dataset IIa data used in the experiment were filtered at about 7-30 Hz, including mu and beta waveforms related to motor imagery, using a fifth-order Butterworth filter. In addition, nine channels [F3a, F2, F4a, C3, Cz, C4, P3a, Pz, and P4a] were used to represent the left/right motion image while reducing the amount of computation. Figure 2 shows the electrode locations used in the simulation. The preprocessing of the BCI data was also filtered at approximately 7-30 Hz using a Butterworth filter, and 12 channels were used. The time was the same as in this experiment, and data for two seconds from the time point 0.5 sec after the indication point were also used. Figure 3 shows the positions of the electrodes used in the experiments. The two classes in the feature extraction were classified; therefore, two characteristics were considered for extracting data features. For an eigenface, two fundamental vectors contain the largest eigenvalues of the fundamental vectors for space reduction and noise elimination. The currently developed methods were used to estimate the motor imagery performance results. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Whitening** & **Eigenface After Decentering** \\ \hline EFA & X & X \\ Ver. 1 & X & O \\ Ver. 2 & ICA & X \\ Ver. 3 & O & X \\ Ver. 4 & ICA & O \\ Ver. 5 & O & O \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Method of classification. The LDA method was used for classification and accuracy comparison with the data. Table 2 lists the criteria for true and false answers for the left and right hands. The LDA method, the applied classification scheme that we have adapted, is not a deep learning method but a method of data regression. The LDA needs training data to obtain a fitting line or classification plan to classify the testing data. Based on the BCI competition specification [40], the BCI competition dataset is composed of two parts, training data and testing or evaluation data. Under these circumstances, we divided the BCI competition data into two parts, i.e., the training and testing datasets. \"A, True\" is the classification anticipated by the actual left hand for the actual left hand data. \"B, False\" is the classification anticipated by the incorrect left hand for the actual right hand.