# A Study of EEG Feature Complexity in Epileptic Seizure Prediction
## 3 Results and Discussion
### Cross-Patient Variability Assessment  
To get a deeper insight into the epilepsy prediction problem formulated as a classification of inter-ictal and pre-ictal intervals using extracted features from EEG raws, it is necessary to check the variability of the information characterizing the pre-ictal state across patients. Therefore, similar to the suggested strategy to evaluate the complexity of the pre-ictal and inter-ictal classification, we analyze the data complexity measures for the extracted features from the pre-ictal state of all patients, where the classification task is to  
\begin{table}
\begin{tabular}{l l l} \hline \hline \multirow{2}{*}{**Data-Sets**} & **Maximum Fisher** & \multirow{2}{*}{**Maximum Feature Efficiency**} \\  & **Discriminant Ratio** & \\ \hline Iris: Setosa-Versicolor & 31.19 & 1.0 \\ Iris: Setosa-Virginica & 49.94 & 1.0 \\ Iris: Versicolor-Virginica & 4.27 & 0.63 \\ HAR & 2.66 & 0.61 \\ Letter & 0.9 & 0.25 \\ Epilepsy & 0.024 & 0.003 \\ Random data 1 & \(5.3\times 10^{-5}\) & 0.007 \\ Random data 2 & \(1.7\times 10^{-5}\) & \(1.6\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the maximum Fisher discriminant ratio and the maximum feature efficiency for various classification problems: (1) Iris: Versicolor-Virginica, (2) Iris: Setosa-Virginica, (3) Iris: Setosa-Versicolor, (4) Letter recognition, (5) epilepsy prediction, (6) human activity recognition (HAR) and couple random noise sets, (7) random data 1 and, (8) random data 2.  
Figure 4 presents the evaluation with different complexity metrics. Figure 3a reveals that two bivariate spectral power attributes, \(b_{37}\) and \(b_{40}\), the mean phase coherence, \(R\), and the indexes based on conditional probability, \(\lambda_{cp}^{W}\), and Shanon entropy, \(\rho_{se}^{W}\), evaluated both using the wavelet transform, the largest Lyapunov exponent, \(L_{max}\), and the surrogate-corrected version of the largest Lyapunov exponent, \(L_{max}^{*}\), exceed the Fisher discriminant ratio threshold value of 0.48. For the volume of the overlap region interval, only four bivariate spectral power attributes, \(b_{13}\), \(b_{26}\), \(b_{31}\), and \(b_{39}\), and the correlation density, \(D_{e}\), exceed the threshold value, as shown in Figure 3b. Finally, Figure 3c displays the results of the assessment of the feature efficiency, showing that the variance, \(\sigma^{2}\), signal energy, \(E\), accumulated energy, \(AE\), correlation density, \(D_{e}\), largest Lyapunov exponent, \(L_{max}\), and the surrogate-corrected version of the largest Lyapunov exponent, \(L_{max}^{*}\), have higher values than the threshold 0.087. In conclusion, a total of 14 out of 88 features are shown to distinguish well the pre-ictal observations by patient. Therefore, performing the one-way ANOVA test for each of the fourteen recalled features exhibits significant differences between patients as null p-values are obtained for all the features, which validates that each individual characteristic has large between-class distances. As a result, it is safe to conclude that the extracted features from the pre-ictal state vary significantly between patients, which raises a concern when using cross-patient models in real-world applications. Moreover, the high variability of the extracted features motivates research on searching new invariant features between patients.  
Figure 5: Empirical and fitted distribution for the complexity measures (**a**) Fisher discriminant ratio F1, (**b**) the volume of the overlap interval F2, and (**c**) the individual feature efficiency F3.