## 4 Conclusions  
Brain-computer interfaces (BCIs) have come a long way since the first EEG measurements were made of the human brain. In the past, the main research purpose of BCI systems was for medical purposes to replace injured body parts, such as arms and legs. Technologies closely related to human life, such as the Internet of Things and wearable devices, are emerging with BCI technology devices. Accordingly, research on signal processing methods that distinguish various EEG signals more accurately and quickly, which is the core of BCI technology, is being actively conducted.  
Existing research is used to improve accuracy with EEG EFA methods, considering EEG signals as images. In movement imagery problems, which are studies of EEG data accuracy, the EFA considers signals as images, unlike the CSP method mainly used in existing studies; therefore, it is possible to classify more than two classes. However, we can show that different characteristics depend on the direction because EEG signal data points are three-dimensional data. When analyzing each attempt at the implementation of BCI for 2-class data points, accuracies of 52.22%, 46.67%, and 63.33% were recorded for the three subjects in the BCI Competition III dataset IIIa, showing a low and unstable pattern.  
To solve this problem, in the feature extraction process, a whitening technique was applied to the source signal, and the change in classification performance when the feature was extracted was observed. We confirmed that the accurate and stable classification of EEG data is possible using the CDC-EFA method. EEG data for the motor imagery classification problem were obtained from three subjects in the BCI Competition III dataset IIIa, which was utilized in previous studies. In addition, the performance of CDC-EFA was verified using data from nine subjects from the BCI Competition IV dataset IIa. We can confirm that  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Accuracy**} \\ \hline
**Subjects** & **EFA** & **CDC-EFA** \\ \hline
1 & 48.61 & 100 \\
2 & 54.86 & 100 \\
3 & 57.64 & 100 \\
4 & 60.42 & 100 \\
5 & 55.56 & 100 \\
6 & 56.25 & 100 \\
7 & 57.64 & 45.14 \\
8 & 57.64 & 100 \\
9 & 54.17 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Accuracy results when using the CDC-EFA methods with nine subjects.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Overall**} \\ \cline{2-4}  & **Mean** & **Median** & **Standard Deviation** \\ \hline CSP & 75.53 & 71.88 & 18.17 \\ EFA & 62.33 & 56.94 & 14.08 \\ CDC-EFA & 94.49 & 98.33 & 11.99 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical comparison results when using CSP, EFA, and CDC-EFA methods.  
the CDC-EFA method not only improves the average accuracy but also obtains a stable high accuracy with a low standard deviation. Therefore, the proposed CDC-EFA method exhibits a superior and stable performance.  
The limitation of the proposed method requires several steps (channel whitening and data image conversion) before feature extraction. Therefore, low-speed computers might be undesirable to obtain a prompt response. In the future, our proposed method will be applied to three- and four-class datasets to be generalized before actual product fabrication.  
Conceptualization, H.C., J.P., and Y.-M.Y.; methodology, H.C., J.P., and Y.-M.Y.; formal analysis, H.C., J.P., and Y.-M.Y.; writing--original draft preparation, H.C. and Y.-M.Y.; supervision, H.C. and Y.-M.Y.; All authors have read and agreed to the published version of the manuscript.  
This research was supported by Kumoh National Institute of Technology (2022-2023).  
Not applicable.  
The data presented in this study are available in article.  
The authors declare no conflicts of interests.