# Preprocessing for Lessening the Influence of Eye Artifacts in EEG Analysis
## 5 Results and Discussion
### Partial Rejection of ICA Components  
The method explained in Section 4.3 was applied to the available data. The base method described in Section 4.2 is considered. The cumulative cross-correlation coefficients of each channel with the EOG were computed using Equations (2)-(4) before ICA and again after the reconstruction of the data from the processed ICs. The negative cross-correlation coefficient with the EOG channel (EOG-correlation for short) is the chosen parameter to obtain a measure of the influence of the EOG signal in other channels, i.e., the effect of eye-related artifacts on them, since the EOG signal primarily contains eye movement energy [14]. Nonetheless, a zero EOG-correlation is neither desired nor actually possible considering that the EOG channel not only contains energy derived from eye movements but also brain activity. Taking into account this observation, the reduction of EOG-correlation can be used as a comparative measure on how good an artifact-cleaning method is against the others, though it never should be used as an absolute measure, since the maximum reduction value is not stated and certainly could not be 100%. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Subject** & \(S_{9}\) & \(S_{10}\) & \(S_{12}\) & \(S_{18}\) & \(S_{19}\) & **Overall** \\ \hline \# artifacts & 194 & 260 & 361 & 318 & 253 & 1386 \\ Artifact duration (\%) & 27.40 & 46.83 & 50.36 & 62.80 & 30.71 & 43.62 \\ Mean artifact duration (s) & 2.55 & 3.26 & 2.52 & 3.57 & 2.19 & 2.84 \\ Std of artifact duration (s) & 2.57 & 2.98 & 2.22 & 3.44 & 1.71 & 2.72 \\ Median artifact duration (s) & 1.68 & 1.96 & 1.75 & 2.26 & 1.55 & 1.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of artifacts manually detected and their main features. Figure 9: Simple diagram of the process to obtain the unmixing matrix \(\mathbf{W}^{\prime}\) with diminished influence of artifacts. Figure 10 contains an example of how the component removal processes considered affect channel Fz in one of the test subjects. Table 4 contains the average cumulative cross-correlation coefficients for the EEG channels before ICA and after their reconstruction using complete removal (CR) of components selected by using cross-correlation coefficients with the EOG channel, and the partial IC removal approach (PR) described in Section 4.3, with the MSF described in Section 3.3. The last row summarizes the resulting reduction of the cross-correlation coefficient. The complete component removal approach produces a large reduction of the cross-correlation coefficients, as expected, but at the same time it removes part of the brain activity as seen in Figure 10, where it is clearly visible that non-artifactual parts are significantly attenuated. This implies that ICA cannot completely separate brain signals from ocular activity or other interfering signals or noise. This is an important observation of an issue that can be due to different causes that might be related to ICA limitations derived from the signal model, measurement constraints (i.e., low-density electrode array), or computation schemes [22]. Thus, a complete removal of components is not considered an optimal choice since ICA cannot actually guarantee that certain components contain only noisy data and do not contain useful pieces of information [9]. Regarding the utilization of the proposed method of partial rejection (PR) of ICs, the reduction of the cross-correlation coefficients is also large, comparable to that of the CR method, while better preserving the shape of the signals in non-artifactual excerpts (see Figure 10) at the cost of the necessity of artifact annotation. We also investigated the effect of complete/partial removal of IC components regarding the induced changes of signal-to-noise ratio (SNR) as defined in [25]. However, note that the stimuli considered greatly differs from the commonly used ones regarding their duration and repetitiveness, implying that a single trial per user for five different experiments can be considered.