Algorithms for Topological Analysis of Spatial Data

The analysis of spatial relations and the search for abstract structures are some of the main tasks of geoinformatics. Huge arrays of spatial information contain hidden abstract structures. Existing methods of clustering do not take into account topological features of spatial objects. It is necessary to create new algorithms for finding regularities in the set of objects on the map. Algorithms for selecting abstract spatial structures based on topological data analysis are developed in the article. The developed algorithms allow us to find common structures in a set of unrelated spatial data. The algorithms for collecting spatial information from point and polygonal objects are also developed in the article. These algorithms allow us to present the initial information for processing by methods of persistent homology. An algorithm for constructing a barcode using simplicial complexes is shown. The study includes topological analysis of point and contour objects. An original approach for searching for repeating structures in a set of randomly distributed spatial objects is shown. Information about the repeating structures is calculated from the barcode. Computer modeling to analyze the structure of a sequence of objects with deformation is demonstrated. Examples for determining the similarity of natural spatial objects based on information from the barcode are given.