# Variation Trends of Fractal Dimension in Epileptic EEG Signals
## 3 Results and Discussion
The results from Figures 3-5 and Tables 2 and 3 indicated that the noise had a great influence on fractal analysis of EEG signals. After denoising, \(D_{\text{c}}\) values calculated by various algorithms could better distinguish the seizure status, the difference between the seizure and normal statuses could be more significant. After using the scaling region interception method, the RSE algorithm had a better performance in seizure detection. In addition to the above results, since the \(D_{\text{c}}\) values should reflect the complexity of the corresponding segmenting signal, i.e., theoretically the \(D_{\text{c}}\) should increase when epilepsy occurred, the following ratio was used to compare the differences among various algorithms. In this study, the following ratio meant the percentage of \(D_{\text{c}}\) increasing in the seizure status. The following ratios was 72% for raw signals of all algorithms as illustrated in Figure 6a. After denoising, all following ratios of various algorithms could reach 99%, which meant that the noise indeed had an obvious influence on the fractal analysis of EEG signals, particularly on the variation trends of \(D_{\text{c}}\) in seizure status. In practical application, the calculation speed of the algorithm also needed to be considered. The calculation times of one group of EEG signals were calculated by various algorithms of raw and denoised signals, as shown in Figure 6b. The calculated times were almost the same between raw and denoised EEG signals among various algorithms. Compared with all algorithms, the Higuchi algorithm had the shortest calculated time, while the RSE-f2 algorithm had the longest. The RSE algorithm would be shorter a little after using the scaling region interception method, however, all kinds of RSE algorithms were longer than 20 s. Higuchi algorithm, by contrast, had the shortest computing time, but its \(D_{\text{c}}\) accuracy and variation significance were not as high as RSE algorithm. In order to achieve a real-time monitoring, all the factors of high speed, \(D_{\text{c}}\) accuracy and variation significance should be considered. In our future work, RSE algorithm would be accelerated significantly by using an optimizing scheme, and the feasibility of artificial neural network [41] for fractal analysis on EEG signals would be also investigated. Besides, for the variation trends of fractal dimension in epileptic EEG signals, more data of EEG signals need to be collected, other denoising algorithms like EMD and fractal \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & \(W\) & \(p\)**-Value** \\ \hline Higuchi & 8733 & \(2.02\times 10^{-9}\) \\ RSE-f1 & 10553 & \(<\)\(2.2\times 10^{-16}\) \\ RSE-f1 sc & 10631 & \(<\)\(2.2\times 10^{-16}\) \\ RSE-f2 & 10909 & \(<\)\(2.2\times 10^{-16}\) \\ RSE-f2 sc & 10985 & \(<\)\(2.2\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Willcoxon Two-sample Rank sum test results between the different groups (raw and denoised signals). Figure 6: The results of the **(a)** following ratio and the **(b)** calculated time were illustrated by using various algorithms of raw and denoised data. The red lines represented the error bar, and red letters on each column represented the corresponding values. algorithms like Box-counting need to be used to further verify the universality and necessity of the noise reduction. The results of this study fully illustrated the influence of denoising process on EEG signal and seizure recognition, and provided a general template for studying the influence of specific signals not limited to EEG signal before and after noise reduction, and provided a reference for future signal process and device development.