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Description of Clustering Tools

Within the framework of the Discrete Mathematical Analysis (DMA), which is maintained at the Geophysical Center RAS, a set of clustering algorithms has been developed. These algorithms are designed to identify subtle distribution patterns of objects in the original spatial domain. Among these are methods aimed at detecting zones with a high concentration of points. The clustering algorithms Discrete Perfect Sets (DPS), Modified DPS, Monolith, and Roden-2 are aimed at identifying dense regions within a set of point objects.

Algorithm – DPS (Discrete Perfect Sets)

Configurable Parameters:

  • ω – a parameter influencing the determination of the proximity radius;
  • β – a parameter specifying the density threshold required for a point to be included in a cluster.

Features: DPS defines the density of a point as the number of neighbors within a specified proximity radius. It identifies groups of points where density exceeds the given threshold. It performs well in detecting local, clearly defined clusters.

Algorithm – Modified DPS

Configurable Parameters:

  • ω – parameter influencing the proximity radius;
  • β – parameter specifying the density threshold for cluster inclusion.

Features: The Modified DPS differs from the standard DPS in the method of density calculation. Instead of a simple count of neighbors, it uses a weighted average distance from a point to all others. This approach is less sensitive to outliers and noise, resulting in smoother clusters that are more robust to random variations in the data.

Algorithm – Roden-2

Configurable Parameters:

  • P – parameter influencing how the distance between points is taken into account (proximity calculation parameter);
  • α – parameter specifying the density threshold for cluster inclusion.

Features: Roden-2 uses the Kolmogorov mean and a fuzzy comparison method to assess point "proximity." It considers not only the number of neighbors but also their relative arrangement. This algorithm is particularly effective for detecting complex cluster shapes, such as elongated lines or ring-like structures.

Algorithm – Monolith

Configurable Parameters:

  • α – density level at which points are considered part of a dense area.

Features: Density is calculated based on distances to neighbors across multiple zones (rings) with different weights. Monolith is effective for identifying local regions of maximum density, allowing users to detect the "core" of dense areas without including sparsely populated peripheral points.

All algorithms are applicable only to point data. The results are automatically added to the map, and users have the option to view and save the output.

Key References

Lisenkov I.A., Soloviev A.A., Kuznetsov V.A., Nikolova Yu I. Generalized dataset of geological and geophysical information on the eastern sector of the Russian Arctic for machine learning–based analysis // Russian Geology and Geophysics. 2025. Vol. 66. No. 2. P. 232–246. DOI: 10.2113/rgg20244747

Agayan S.M., Bogoutdinov Sh.R., Dzeboev B.A., Dzeranov B.V., Kamaev D.A., Osipov M.O. DPS clustering: new results // Applied Sciences. 2022. Vol. 12. No. 18. P. 1–16. DOI: 10.3390/app12189335

Gvishiani A. D., Dzeboev B. A., Agayan S. M., Belov I.O., Nikolova J.I. Fuzzy Sets of High Seismicity Intersections of Morphostructural Lineaments in the Caucasus and in the Altai–Sayan–Baikal Region // Journal of Volcanology and Seismology. 2021. Vol. 15. No. 2. P. 73–79. DOI: 10.1134/S0742046321020032

Gorshkov A.I., Soloviev A.A., Zharkikh J.I. Recognition of Strong Earthquake Prone Areas in the Altai–Sayan–Baikal Region // Doklady Earth Sciences. 2018. Vol. 479. No. 1. P. 412–414. DOI: 10.1134/S1028334X1803025X

Soloviev A.A., Krasnoperov R.I., Nikolov B.P., Zharkikh J.I., Agayan S.M. Web-Oriented Software System for Analysis of Spatial Geophysical Data Using Geoinformatics Methods // Izvestiya, Atmospheric and Oceanic Physics. 2018. Vol. 54. P. 1312–1319. DOI: 10.1134/s0001433818090360

Soloviev A.A., Gvishiani A.D., Nikolov B.P., Nikolova Y.I. GIS-Oriented Database on Seismic Hazard Assessment for Caucasian and Crimean Regions // Izvestiya, Atmospheric and Oceanic Physics. 2018. Vol. 54. No. 9. P. 1363–1373. DOI: 10.1134/S0001433818090505

Agayan S.M., Bogoutdinov Sh.R., Krasnoperov R.I. Short introduction into DMA // Russian Journal of Earth Sciences. 2018. Vol. 18. No. 2. P. 1–10. DOI: 10.2205/2018ES000618

Soloviev A.A., Zharkikh J.I., Krasnoperov R.I., Nikolov B.P., Agayan S.M. GIS-oriented solutions for advanced clustering analysis of geoscience data using ArcGIS platform // Russian Journal of Earth Sciences. 2016. Vol. 16. No. 6. P. 1–6. DOI: 10.2205/2016ES000587

Nikolov B.P. Zharkikh J.I., Soloviev A.A., Krasnoperov R.I., Agayan S.M. Integration of data mining methods for Earth science data analysis in GIS environment // Russian Journal of Earth Sciences. 2015. Vol. 15. No. 4. P. 1–14. DOI: 10.2205/2015ES000559