# A Regionalization Approach Based on the Comparison of Different Clustering Techniques
###### Abstract  
For biodiversity conservation and the development of protected areas, it is essential to create strategic plans that ensure the preservation and sustainable use of natural resources. Biogeography plays a crucial role in supporting these efforts by identifying and categorizing geographic areas (regionalization) that represent different biotas, as well as recognizing patterns in biodiversity distribution. Another application of regionalization is in planning species sampling and inventories. Developing a species list is vital for monitoring and understanding diversity patterns. This study focuses on the Palearctic region, specifically the areas between Morocco, the Iberian Peninsula, and France. Its aim is to compare different clustering algorithms--such as K-means++, DBSCAN, PD-clustering, Infomap, and federated heuristic optimization based on fuzzy clustering--with a reference regionalization, using environmental and soil data. Various spatial contiguity approaches were applied, including the third-degree polynomial model and principal coordinates. The results demonstrated that the hybrid approach offers a robust solution in the construction of the regions and that K-means++ and PDC produced regions with strong spatial similarity to the reference regionalization, closely aligning with the expected number of regions, especially at the biome level. Our study shows that a purely statistical regionalization can approximate a global reference regionalization, making it reproducible. b  
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few groups would not be informative for such a large area [48], because k = 3 divided the territory into north (France), center (Iberian Peninsula), and south (Morocco). The silhouette scores (Figure 10) of regions of the algorithms with a higher kappa index compared to the reference regionalization (DBSCAN PCO with K = 19, Federate model with k = 7; Infomap TSA with k = 5; K-means++ TSA with k = 5; and PDC TSA with K = 3), displayed in boxplot form. In the federated model (as discussed below), all regions, except for region 3, achieved positive scores above the average value of 0.16. This suggests that the points within these regions are well assigned. For the Infomap method, regions 2 and 3 have relatively high values compared to the average of 0.14, while the other regions, particularly region 1, exhibit negative values. This indicates that there are points that are either poorly assigned or that overlap exists between the regions. In the case of K-means++, all regions except for region 3, which shows negative values, generally exhibit positive silhouette scores, with an average fixed at 0.16. The three regions estimated using PDC also show predominantly positive silhouette scores, with an average value of 0.32. Notably, regions 1 and 3 significantly exceed this average, indicating that the allocation of points to these regions is appropriate. For DBSCAN, certain regions (6, 8, 9, 12, 15, and 19) show high silhouette scores, close to 1. This suggests that the observations within these regions are well classified. However, as previously shown (Figure 4a), the majority of observations are grouped into a single region, which makes it difficult to compare this result with any reference regionalization.