## 2 Materials and Methods  
### Recognition of the Areas Prone to Strong Earthquakes with One Learning Class  
In the papers [4; 5], the EPA approach was further developed by creating a new algorithm called Barrier-3, employed in the recognition unit [13; 16; 17]. It should be especially noted that the principal difference of the Barrier-3 algorithm from the dichotomy algorithms previously used in EPA is that learning is based only on \(B_{0}\) high seismicity class set. Broadly speaking, the Barrier-3 algorithm, which learns based only on one class, is not a dichotomy algorithm. However, it can be used in the EPA. Barrier-3 also divides the territory into two non-intersecting areas that are either prone or not prone to strong earthquakes. Similarly, to the dichotomy algorithms [5], the Barrier-3 algorithm views disjunctive nodes or axis intersections of the morphobructural lineaments as recognition objects. Such selection of objects derives from their deep tectonic connection with strong earthquakes. The confinedness of the strong earthquake epicenters to the intersections of morphobructural lineaments was statistically confirmed in the paper [18]. The objective of the Barrier-3 algorithm is to study the characteristics of learning set \(B_{0}\) of the only high seismicity class and identify the objects that are \"similar\" to the learning objects based on the knowledge obtained. The latter are declared as high seismicity ones. Speaking the language of the theory of sets, Barrier-3 accomplishes the objective of constructing in the finite set of objects \(W\) and its subset \(B\), broadening the only learning class \(B_{0}\). For this reason, the disparity measure between two arbitrary objects is constructed for every characteristic. This allows finding and measuring the \"barrier,\" which divides these objects as part of the considered characteristic. This assessment acts as a proximity measure for the initial set \(W\), which enables giving exact meaning to the idea of proximity to \(B_{0}\) based on a given totality of characteristics. Let us move on to the description of the mathematical construction of the Barrier-3 algorithm [13; 16]. Let us assume that \(\Pi=\{\pi\}\) is a finite totality of numerical characteristics of recognition objects \(w\in W\), and \(\pi:W\to R\), \(B_{0}\) is own subset in \(W\) for learning of high seismicity class \(B\). Based on the totality of characteristics \(\Pi\) of a set of objects \(W\), it is necessary to construct a set \(P_{\Pi}(B_{0})\) that would adequately expand \(B_{0}\) in the sense of requirements of the formulated problem. The proximity of the objects \(w_{1}\) and \(w_{2}\) by characteristic \(\pi\) is \"hampered\" by all those objects \(w\) whose \(\pi(w)\) values lie in between the values \(\pi(w_{1})\) and \(\pi(w_{2})\). They make up a barrier:  
\[\mathrm{B}_{\pi}(w_{1},w_{2})=\{w\in W:min(\pi(w_{1}),\pi(w_{2}))\leq\pi(w) \leq max(\pi(w_{1}),\pi(w_{2}))\} \tag{1}\]  
It is natural to assume that the lower the barrier \(\mathrm{B}_{\pi}(w_{1},w_{2})\), the better it is for the proximity of \(w_{1}\) and \(w_{2}\) on \(W\) by characteristic \(\pi\). This observation explains the name of the algorithm. Let us call the ratio  
\[\rho_{\pi}(w_{1},w_{2})=|\mathrm{B}_{\pi}(w_{1},w_{2})|/|W| \tag{2}\]  
disparity measure between \(w_{1}\) and \(w_{2}\) by characteristic \(\pi\) or simply barrier measure. The Barrier-3 algorithm forms the set of \(P_{\Pi}(v)\) objects that are close to \(v\in B_{0}\) from \(W\) based on the characteristics \(\Pi\) in three phases.