## 3 Results and Discussion
Note that since the effect of frequency and the feature \(\times\) frequency band interaction were both insignificant, the distance between classes in Figure 4A is presented as an average between the 30 Hz and 3 Hz bands. Using the mean value as a feature provides the smallest distance between the seizures and normal states. Raw and PCA ensure a greater distance but it barely differs between them. For the LOF, the rm ANOVA reveals a significant main effect of the feature: F(2,78) = 53.738, \(p\) < 0.001, and an insignificant main effect of the frequency band: F(1,39) = 3.757, \(p\) = 0.06. In contrast, there was a significant feature \(\times\) frequency band interaction effect: F(2,78) = 23.109, \(p\) < 0.001. These results evidence that the distance between the classes depends on the feature and the way it changes depends on the frequency band. The direction of change is shown in Figure 4B for 30 Hz and 3 Hz. For the 3 Hz band, the distance between the classes hardly changes between the different features. For the  
Figure 4: Distance between the seizures and normal states (group mean and 95% CI) in the feature space depending on the frequency band and feature. Sub-figures correspond to the different distance-based ML algorithms: LNND (**A**); LOF (**B**); kNN (**C**). 30 Hz band, the mean value provides the highest distance, and raw data provides the lowest distance. For the kNN, the rm ANOVA reveals a significant main effect of the feature: F(2,114) = 35.854, \(p\) < 0.001, and an insignificant main effect of the frequency band: F(1,57) = 1.312, \(p\) = 0.257. There was a significant feature \(\times\) frequency band interaction effect: F(2,114) = 19.894, \(p\) < 0.001. These results evidence that the distance between the classes depends on the feature and the way it changes depends on the frequency band. The direction of change is shown in Figure 4C for 30 Hz and 3 Hz. When using the mean as a feature, the distance differs between 3 Hz and 30 Hz, for the raw and PCA this difference disappears. Combining the results of outlier detection (Figure 3) and the analysis of distances (Figure 4), we find similar tendencies in the dependence of the precision-recall curve and distance in the LNND on the frequency band and feature. First, the lowest precision-recall curve is observed for the mean value and grows when we use raw data and PCA. Second, this tendency remains similar for 3 Hz and 30 Hz. Therefore, we conclude that in the LNND, the structure of the feature space affects the distance between the classes (i.e., separability). Estimating the separability may give prior knowledge about the performance of the LNND, therefore enabling the selection of features to ensure the best performance. In terms of achievable performance rates, the obtained results are consistent with modern studies, which also propose novel methods for automated seizure identification in EEG signals using different supervised ML-based approaches. [PERSON] et al., proposed [9] a method utilizing sparse common spatial patterns (sCSPs) and adaptive short-time Fourier transform-based synchrosqueezing transforms (adaptive FSSTs) to enhance the time-frequency representation of multi-component EEG signals and reduce noise and interferences. They method achieved outstanding performance with high sensitivity, specificity, and accuracy in detecting seizures, demonstrating the potential of their proposed method for epilepsy diagnosis. [PERSON] et al., utilized [10] a computer-aided diagnosis system (CADS) for the automatic diagnosis of epileptic seizures in EEG signals, involving pre-processing, feature extraction, and classification steps. They used tunable-Q wavelet transforms (TQWTs) for EEG signal decomposition and extracted various linear and non-linear features from TQWT sub-bands. They employed different approaches based on conventional ML and DL for classification and achieved high accuracy (up to 99%) in detecting seizures using their proposed DL method based on convolutional neural network (CNN) and RNN.