# Preprocessing for Lessening the Influence of Eye Artifacts in EEG Analysis
## 5 Results and Discussion
### Artifact-Diminished ICA Unmixing Matrix  
In this case, we specifically altered the result of the ICA by modifying the actual input data. Thus, special attention will be paid to the influence of the proposed method on the unmixing matrix and observe the changes in it. Figure 11a shows the original unmixing matrix, \(\mathbf{W}\), and Figure 11b the artifact-diminished unmixing matrix, \(\mathbf{W}^{\prime}\), obtained as described in Section 4.4, with eye-artifacts manually detected. Figure 12a contains the difference matrix \(\mathbf{D}\) between the matrices in Figure 11, where every element has been calculated as follows:  
\[\mathbf{D}(n,m)=\mathbf{W}^{\prime}(n,m)-\mathbf{W}(n,m) \tag{6}\] \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Channel**} & \multirow{2}{*}{**Before ICA**} & \multicolumn{2}{c}{**After IC Rejection**} \\ \cline{3-4}  & & **Complete (CR)** & **Partial (PR)** \\ \hline ’Fz’ & 2.7657 & 0.3279 & 0.3354 \\ ’FCz’ & 2.4154 & 0.2192 & 0.2209 \\ ’Cz’ & 1.1386 & 0.4025 & 0.5064 \\ ’CPz’ & 0.9353 & 0.3702 & 0.4553 \\ ’Pz’ & 0.9562 & 0.2161 & 0.2582 \\ ’POz’ & 0.8500 & 0.3119 & 0.3027 \\ ’F3’ & 2.7674 & 0.3168 & 0.2911 \\ ’F4’ & 1.9507 & 0.3080 & 0.2769 \\ ’C3’ & 1.4484 & 0.3923 & 0.4330 \\ ’C4’ & 1.1308 & 0.3498 & 0.3683 \\ ’T7’ & 0.5083 & 0.2243 & 0.2378 \\ ’T8’ & 0.8184 & 0.4198 & 0.4529 \\ ’P3’ & 0.8772 & 0.2856 & 0.3490 \\ ’P4’ & 0.8021 & 0.2833 & 0.3026 \\ \hline \multicolumn{4}{c}{Reduction} & \multicolumn{1}{c}{77.13\%} & \multicolumn{1}{c}{72.68\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average cumulative cross-correlation coefficients before and after applying the considered artifact processing schemes based on complete/partial IC rejection. Note that all absolute values in this table are divided by \(10^{5}\). \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{_Experiment_} & \multirow{2}{*}{**Before ICA**} & \multicolumn{2}{c}{**After IC Rejection**} \\ \cline{3-4}  & & **Complete (CR)** & **Partial (PR)** \\ \hline The Magic Flute & 0.3328 & 0.3860 & 0.3754 \\ Emperor Waltz & 0.3361 & 0.3986 & 0.3873 \\ Universal Mind & 0.3522 & 0.4108 & 0.3846 \\ Adios Nonino & 0.3474 & 0.3983 & 0.3919 \\ Speech & 0.3423 & 0.3983 & 0.3905 \\ Global & 0.3429 & 0.3987 & 0.3853 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: SNR before and after CR/PR component removal to diminish the influence of artifacts. Global experiment makes reference to the consideration of all the experiments as a whole for the calculation of SNR. Figure 12b displays the logarithmic relative difference matrix \(\mathbf{D}_{L_{R}}\) obtained using:  
\[\mathbf{D}_{L_{R}}(n,m)=\log_{10}\left(\left|\frac{\mathbf{D}(n,m)}{\mathbf{W}( n,m)}\right|\right) \tag{7}\]  
Note that, in order to obtain a meaningful difference matrix, the vectors that perform the transformation in the unmixing matrices \(\mathbf{W}\) and \(\mathbf{W}^{\prime}\) in Figure 11 are coherently sorted in descending order of their norm. In the illustrations, component 1 refers to the vector with the largest norm, whereas component 14 corresponds to the one with the smallest norm. It can be observed that the unmixing transformation changed substantially when ICA was fed with artifact-diminished data instead of the original data. Thus, it is consequently expected that the components obtained by the devised transformation scheme will represent the underlying brain sources more accurately. Moreover, the images in Figure 12 clearly draw the changes between \(\mathbf{W}\) and \(\mathbf{W}^{\prime}\) which can be positive when a certain contribution of a certain channel in certain component rises and negative otherwise, see Figure 12a,b renders the relative magnitude of the differences. A value of 0 corresponds to no variation of the magnitude. However, it is observed that many elements suffer a change of their magnitude over the 100% of their magnitude. This observation was noticed across all the subjects and is a remarkable illustration of the importance of the preprocessing of artifacts before EEG analyzes.