## 5 Discussion  
This paper addresses the study of stationary data arrays, which are finite sets in multidimensional spaces, using the DMA methods by means of clustering. A complex local condition is a conjunction of the conditions of local linearity and local representativeness. Local linearity: each point L has a linear corridor containing it that is dense against the background of \(Q\), i.e., each point \(q\in L\) on the plane has a rectangle \(K(q)\) centered at \(q\), which is a local corridor for \(L\), and the intersection \(K(q)\cap Q\) is dense against the background \(Q\). Local representativeness: the intersection \(K(q)\cap L\) is dense in \(K(q)\cap Q\). The global condition for \(L\) consists of the requirement that \(L\) has no isolated points, i.e., in its discrete perfection. The detection of local linearity in the implementation of LDPS consists of a direct check for all points of the original space \(Q\) of this property. Analytical procedures are available to reduce routine calculations. In addition, in the future, we propose to modify the algorithm so that the dimensions of the corridors generally change from point to point. The points in \(Q\) that pass the local linearity test form a subset of \(Y\)--the first approximation in \(Q\) to linear structures. We checked the linear representativity on \(Y\) in the LDPS algorithm as an implementation of the DPS scheme with respect to the special density \(G\) (clause 4.5.3). In the future, we plan to implement other variants of the LDPS algorithm based on a change in the interpretation of linear representativeness. Studies have shown that, among the subset of points \(Z\subset Q\) that have passed the local test for representativeness, there may be isolated points. The global condition in LDPS eliminates this drawback: its check for \(Z\) is also organized as an implementation of the DPS scheme with respect to the density \"monolithicity\" (MDPS algorithm). The points that pass the global test will be the result of applying the LDPS--that is, the union of all linear structures in \(Q\). In the general case, the set of linear structures \(L\) is divided into connected components. For example, in the examples given in Figures 13(b) and 13(b), two connectivity components are obtained. In the first example, the components of connectivity should be considered independent linear structures, and in the second example, as part of a single whole. In the future, we plan to introduce an additional procedure for joining the results of applying the LDPS algorithm in order to obtain global linear structures in the original space \(Q\). Comparison of the LDPS algorithm with the well-known new generation cluster analysis algorithms DBSCAN and OPTICS, as well as with the previously created DMA clustering algorithms, shows that the LDPS algorithm is not inferior to them in detecting clumps; however, at the same time, it is more focused on recognizing clumps with a linear structure. The implementation of the formal approach as shown in the article can be very effective in various fields of Earth sciences where linear structures play a special role in the investigation of spatial patterns of geographical location and geometric configuration of natural objects. This is vital when solving the issue of predicting the isolation properties of the geological environment for the preparation of a rationale for the geodynamic stability over long periods of time (ten to one hundred thousand years), arising in the selection of HLRW disposal sites. Further to this task, the algorithm can apply to the analysis of elongated artificial structures, such as road networks, etc. All authors contributed to the study conception and design. Conceptualization, original draft preparation: S.A., S.B. and V.T. ; conceptualization, methodology, review and editing and validation: D.K. and V.K. ; material preparation, formal analysis, data curation, algorithm development: S.B. and M.O. All authors have read and agreed to the published version of the manuscript.