Abstract
The article addresses the issue of clustering of multidimensional data arrays with a noise using the methods of discrete mathematical analysis (DMA clustering). The theory of DMA clustering through the logical densities calculus is detailed, and the new algorithm Linear Discrete Perfect Sets (LDPS) is described. The main objective of the LDPS algorithm is to identify linearly stretched anomalies in a multidimensional array of geo-spatial data (geophysical fields, geochemistry, satellite images, local topography, maps of recent crustal movements, seismic monitoring data, etc.). These types of anomalies are associated with tectonic structures in the upper part of the Earth’s crust and pose the biggest threat for integrity of the isolation properties of the geological environment, including in regions of high-level radioactive waste disposal. The main advantage of the LDPS algorithm as compared to other cluster analysis algorithms that may be used in arrays with a noise is that it is more focused on searching for clusters that are linear. The LDPS algorithm can apply not only in the analysis of spatial natural objects and fields but also to elongated lineament structures.
Highlights
The main threat of disturbance of the isolation properties of the geological environment where high-level radioactive waste (HLRW) are disposed is associated with large-scale geodynamic processes and phenomena
This paper addresses the study of stationary data arrays representing the sets in multidimensional spaces, using the discrete mathematical analysis (DMA) methods by means of clustering
Density, which expresses a fuzzy interpretation of the “limit” property in a finite space, is a new concept that is not reducible to the concepts of classical mathematics, for which finite metric spaces are topologically arranged in the same way–zero-dimensional, separable
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In 2019, the construction of an underground research laboratory (URL) was started in granitic gneiss rocks of the Nizhne–Kansky rock mass (Russia, Krasnoyarsk Territory) to justify the safety of disposal of high-level radioactive waste (HLRW). The safety of HLRW underground insulation for a period of ten thousand years or more is guaranteed due to a geological barrier. The main threat of disturbance of the isolation properties of the geological environment where HLRW are disposed is associated with large-scale geodynamic processes and phenomena
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