## 2 Materials and Methods
### Recognition of the Areas Prone to Strong Earthquakes with One Learning Class
Here, 16 intersections of the axes of morphonstructal lineaments with known epicenters of crustal earthquakes with \(M\geq 6.0\), starting from 1900, in their vicinities (with a radius of 50 km in the Altai-Sayan-Baikal region and 25 km in the Caucasus) were used as the learning sets \(B_{0}\) of high seismicity class in both regions. The list of the geological-geophysical and geomorphological characteristics of considered vicinities of lineament intersections used for recognition by Barrier-3 algorithm is given in Table 1. Highlighted in bold type are 7 characteristics that were selected to be used for recognition in the Altai-Sayan-Baikal region based on the findings from the assessment of informativeness for the instance of one learning class; in italics, 11 characteristics selected for recognition in the Caucasus are given. It is noteworthy that 4 characteristics (Hmin, Top, R2, and dB) were selected for recognition using the Barrier-3 algorithm in both regions. Based on the threshold magnitude of the recognized earthquake-prone areas (\(M\geq 6.0\)), the circles with a radius of 25 km were selected as vicinities within which the values of characteristics were computed. For reproducibility of the result and its greater reliability, the values of characteristics of objects were computed automatically using the smart GIS developed by the Geophysical Center of the Russian Academy of Sciences ([[http://seismgis.gcras.ru/](http://seismgis.gcras.ru/)]([http://seismgis.gcras.ru/](http://seismgis.gcras.ru/)) access date: 30 July 2021) [19,20]. \begin{table}
\begin{tabular}{c c} \hline _Maximum height_ & _Hmax_ \\ \hline _Minimum height_ & _Hmin_ \\ \hline _The range of heights_ & _dH_ = _Hmax-Hmin_ \\ \hline Distance between points where Hmax and Hmin are measured & 1 \\ \hline Height gradient & dH/1 \\ \hline _The combination of relief types_ & _Top_ \\ \hline _The area of Quaternary sediments_ & \(Q\) \\ \hline _The highest rank of lineament_ & _HR_ \\ \hline The number of lineaments at the intersection & NL \\ \hline _The distance to the nearest intersection_ & _Rint_ \\ \hline _Number of lineaments in the neighborhood of the intersection_ & _NLC_ \\ \hline _The distance to the nearest lineament of rank 1_ & _R1_ \\ \hline _The distance to the nearest lineament of rank II_ & **R2** \\ \hline **The maximum value of the Bouguer anomaly** & **Bmax** \\ \hline **The minimum value of the Bouguer anomaly** & **Bmin** \\ \hline _The range of the Bouguer anomaly values_ & _dB_ = _Bmax-Bmin_ \\ \hline **The maximum value of magnetic anomaly** & **MOmax** \\ \hline The minimum value of magnetic anomaly & MOmin \\ \hline The range of the magnetic anomaly values & Modif = MOmax-MOmin \\ \hline \end{tabular}
\end{table} 
Table 1: The list of characteristics of the recognition objects (intersections of lineaments). Bold type—characteristics used by the Barrier-3 algorithm for recognition in the Altai–Sayan–Baikal region; italics—the Caucasus; bold italics—both regions. Recognition of Strong Earthquake-Prone Areas Based on Identifying Dense Condensations of Point Objects  
In this part of the article, let us depart from the recognition objects described above (disjunctive nodes and intersections of the axes of morphobstructural lineaments) and their geological-geophysical and geomorphologic characteristics. The task considered here will be closer to reality. Namely, in addition to the reliable classification of a finite set of point objects, a formalized and reproducible transition from a recognized high seismicity set \(B\) to a real two-dimensional region in the plane with the cardinality of the continuum will be required. Strong earthquakes can occur within and cannot occur outside of this sought region.