## 3 Results and Discussion  
Table 3 shows the two-class data classification results of the motor imagery of the BCI Competition III dataset IIIa using the currently developed and proposed methods. Whitening, ICA, and covariance decentering methods have been found to improve performance. As indicated by the accuracy measurement results for Ver. 1 to Ver. 3, the accuracy increased; however, they did not reach meaningful data levels when applying these algorithms for practical patient applications. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Label**} \\ \cline{2-3}  & **Class 1, Left Hand** & **Class 2, Right Hand** \\ \hline Class 1, Left Hand & A, True & B, False \\ Class 2, Right Hand & C, False & D, True \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification comparison for class 1 left and class 2 right hands. Figure 3: The electrode positions for BCI Competition IV dataset IIa. Figure 2: The electrode positions used in the simulation. Among the three methods, Ver. 1, which performed covariance decentering in the unique face construction stage, recorded accuracies of 55.56%, 81.67%, and 68.33%, with an average accuracy of 68.52% for the three subjects. Compared to the results obtained using Ver. 2 and Ver. 3, the performance was further improved. In particular, the results using only the whitening or ICA methods were 58.62%, 49.10%, and 50.00%, with mean accuracies of 52.57%, 57.78%, 55.00%, and 61.67%, respectively, with a mean accuracy of 58.15% recorded for three subjects. Therefore, these results indicate a significant performance improvement compared with the EFA method (54.07%). Ver. 4 and Ver. 5 showed a significant performance improvement. Ver. 5, in which the proposed method was used in the unique face construction stage, showed better performance with an accuracy of 100%, 98.33%, and 98.33%, and an average accuracy of 98.86% for the three subjects. This method showed significantly improved results compared to the results with the ICA method and other methods, with uniformly high accuracy for all three subjects. When feature selection was compared with whitening alone, these results did not allow the automatic selection of excellent independent components, owing to the permutation problem that occurred during ICA. As many independent components as the number of input channels could not be found after performing ICA. The whitening technique was used to improve the variance performance in the accuracy level based on Gram-Schmidt orthogonalization theory [31]. The quick-response eigenface analysis method used a three-dimensional direction so the images were converted to three-dimensional eigenface data [41]. These two techniques were also verified using the BCI competition three and four datasets together. Figure 4a shows the results of the covariance matrix when the whitening method is not used. Figure 4b presents the results of the covariance matrix when the whitening method is applied. The left and right sides in Figure 4 show the results of the covariance matrix before and after the covariance decentering process, respectively. Figure 4c is an enlarged view of the upper two Figure 4b. After applying the whitening method, we can easily observe and compare the covariance matrix variance owing to covariance decentering from the side. In Figure 4, the values or features are obtained after the CSP filtering process. The features obtained from the CSP transformation are unitless. This is because the CSP involves a linear transformation that projects the original sensor signals into the directions associated with the maximum and minimum eigenvalues of the covariance matrices. In Figure 4, the x and y axes are the number of trials in the experiments and the z axis (height) is the value of covariance matrixes. The number of trials is different from the BCI competition dataset.