A Spatial Co-Location Pattern Mining Method Based on Hausdorff Distance Alignment

Spatial co-location patterns are used to describe the spatial associations between features, finding wide applications in geographic information systems, urban planning, and other fields. Traditional frameworks for mining spatial features typically consist of two stages: constructing spatial proximity relationships and discovering frequent patterns. However, existing methods have limitations: the construction of proximity relationships relies on fixed distance thresholds or clustering centers, making it difficult to adapt to spatial density heterogeneity; meanwhile, frequency metrics overly depend on participation indices, lacking quantitative analysis of the strength of geometric associations between features. To address these issues, a spatial co-location pattern mining method based on Hausdorff distance is proposed. Drawing on the concept of Hausdorff distance, this method employs Voronoi tessellation to achieve data-adaptive partitioning of the spatial domain. Combined with a K-dimensional tree, it adopts an iterative strategy of direct allocation, proportional allocation, and residual allocation to align instances, generating a spatial proximity relationship graph. Additionally, a new frequency metric based on instance distribution—alignment rate—is introduced, leveraging the decreasing trend of alignment rate in conjunction with a pruning optimization algorithm. Experimental results demonstrate that this method excels in handling noise points, effectively addressing the challenges of uneven data density distribution while enhancing the identification of weakly associated yet potentially valuable patterns.