Density-based cluster detection at multiple spatial scales via kullback-leibler divergence of reachability profiles

Density-based clustering methods are frequently used to define spatial clusters and outliers (noise) for location-only data. Different algorithms for solving this problem emerged over the past few decades, with their main difference being the numerical representation of the spatial density. A problem not addressed by conventional density-based clustering methods is defining alternate spatial cluster maps at statistically significant spatial scales. This problem differs from conventional clustering, as the goal of finding alternate clusters is to define different spatial cluster maps for all statistically significant spatial scales. Knowledge of distinct spatial scales pertinent to clustering is important for understanding various scales underlying the data. In addition, alternate clusters with different spatial scales can inform decisions that require to be made at different spatial granularity. In this paper, we introduce a statistical test that uses Kullback-Leibler (KL) divergence loss between different spatial density profiles to identify all statistically significant spatial scales at which clustering occurs. The proposed method defines different clustering maps that reflect different scales at which spatial clusters occur. We define the divergence on a 1-D representation of cluster density, the reachability profile, to cluster spatial units with varying spatial scales. We illustrate the use of multiple spatial clustering at different scales by comparing the proposed method to the state-of-the-art for defining a single map of multiscale clusters, HDBScan. We conclude the paper by applying the proposed method to physical and human geography problems, area of interest delineation, and wildfire cluster modeling, respectively.