Clustering of sacred objects of Ivano-Frankivsk Oblast as a modern tool of sacred geography zoning

In this paper, we present a clustering of sacred objects of Ivano-Frankivsk Oblast using mathematical-statistical methods for the purpose of sacred-geography zoning of the area. Great attention was paid to the methodology of cluster analysis and the employment of geoinformation systems (GIS) for modeling the foundational connections among the objects of sacred geography. We described the stages of clustering and provided a validation for them: collection and preparation of the data, selection of metrics of similarity, identification of optimal number of clusters, cluster analysis, evaluation of the results, and designation of sacred-geography districts. To perform the clustering, we employed the k-means method, which allows the designation of groups of objects in geospace that are compactly located. We developed a validation for choosing the metrics of similarity and criteria of evaluating the results of clustering (inertia of k-means and silhouette score). The utilized similarity metrics take into account geographic distances (Euclidean distance for geographic coordinates). The cluster analysis was conducted based on geographic coordinates of 69 natural-anthropogenic and 614 anthropogenic sacred objects. The analysis of the inertia graphs and silhouette confirmed that the optimal number of clusters is five. Based on the clustering, we carried out sacred-geography zoning of Ivano-Frankivsk Oblast, where each cluster corresponds to a certain district. Boundaries of the clusters correspond to designated districts. For each district, we determined a centroid (point that determines the mean position of objects on the plane defined by geographic coordinates). The established centroids are settlements such as the villages Bratkivtsi and Vyhivka of Ivano-Frankivsk District, the Verhnii Strutyn village of Kalush District, the Prokurava village of Kosiv District, and the Slobidka village of Kolomyia District. Within the oblast, five sacred-geography districts were designated: Opilskyi, Boikivsko-Hutsulskyi, Opilsko-Pokutskyi, Pokutskyi, and Hutsulsko-Pokutskyi. Such names of the sacred-geography districts are based on the cultural-historical, geographic, and ethnographic peculiarities of each territory. The results of the clustering are valuable for the development of tourist-recreation activity, preservation of historical-cultural heritage, and the development of communities based on the principals and objectives of sustainable development.