## 4 Discussion  
Currently, the methods of spontaneous EEG analysis, including both linear classifiers [38] and artificial neural networks (ANN), have become quite widespread for solving  
Figure 8: Scatter diagram for the sample comprising all 16 subjects in the space of LDA components after finding discriminative frequencies and time intervals using interchannel cross-correlation coefficients for three motor imagery classes. Figure 7: Scatter diagram for the sample comprising all 16 subjects in the space of LDA components after finding discriminative frequencies and time intervals using Hjorth parameters for three motor imagery classes. neural communication problems [23; 39]. The results of the comparative analysis, on the one hand, show the superiority of nonlinear neural network algorithms over linear ones, primarily in terms of the efficiency of their functioning and adaptive settings [40; 41; 42]. This is achieved, in particular, through the development of new neural network methods [43] that integrate extensive customization capabilities and advantages of various approaches that can effectively detect specific and invariant MI patterns of bioelectric brain activity. On the other hand, linear classifiers are still a clear and easy-to-interpret method; in addition, they form a low computational load. However, since quasi-stationary EEG can lead to nonlinear discriminant functions, this type of classification does not always show high accuracy of detecting control commands in the BCI circuit. In this regard, improving the accuracy of linear methods requires an additional method of preprocessing and highlighting significant features for invariant EEG patterns [44]. The results of EEG-based multiclass MI pattern classification in the methodology and approach developed by us showed that the method is capable of increasing the accuracy (up to 71.6 \(\pm\) 3.9%) of detecting randomly generated control commands in the BCI circuit. The results obtained are consistent with the already available data, indicating that neural interfaces exploiting mental equivalents of real movement execution (MI) and various approaches for solving neurofeedback problems are able to provide a reliable and effective nonmuscular communication channel. However, it requires the development of new user training techniques and scenarios, as well as thorough training and adaptation of methods themselves [45; 46] to ensure a reliable and fast integration of technical units into the somatosensory map of the human body. Finally, our results are in good agreement with the well-researched characteristics of event-related desynchronization (ERD) and synchronization (ERS) phenomena in the mu- and beta-rhythms of the EEG. They are primarily considered events that reflect the performance of MI or mental movements [5; 47]. The ERD phenomenon develops not only when performing a movement execution, but also when the subject only mentally imagines movement or sensation in a certain part of the body [48; 49]. At the same time, the authors note a characteristic somatotopic localization of the effects: the ERD effect is more pronounced in the contralateral hemisphere of the working hand [50]. These EEG phenomena are usually obtained statistically by averaging EEG signals recorded in different mental tasks identical in content and other characteristics by a group of subjects in the field of classical EEG frequencies corresponding to lower (delta, theta, alpha (mu)), or higher (beta and gamma) rhythms. The analysis of single events in the EEG, in turn, is relatively rarely used, especially at short time intervals [25; 51]. Comparative analysis has shown [52; 53; 54] that by single implementations of short (up to 500 ms) EEG segments, it is possible to identify the type of visual stimulus that indicates, for example, the direction of movement and the areas of the brain involved in its processing. In addition, even shorter EEG epochs (up to 200 ms) may be sufficient in identifying the readiness potential, indicating the lateralization of the upcoming motor act.