Triangulation-Based Spatial Clustering for Adjacent Data With Heterogeneous Density

In diverse fields such as geography, meteorology, and economics, data often exhibit complex, nonlinear relationships, irregular structures, and are frequently collected over intricate domains. While effectively identifying regularly shaped clusters (e.g., ellipsoidal or spherical) within regular domains, traditional clustering algorithms often struggle with irregular cluster shapes, heterogeneous densities, noisy inter-cluster boundaries, and datasets spread across complex spatial domains. To address these challenges, we introduce a novel Density and Triangulation-based Clustering (DTC) framework, designed to excel in these complex scenarios through three key innovations: (1) density-based separation using an advanced density estimation method tailored for complex domains, (2) Delaunay triangulation-based spatial clustering, effectively managing nonlinear geometries and resolving adjacency issues, and (3) noise mitigation through proximity analysis leveraging nearest neighbors. The DTC framework uniquely integrates graph-based methods with robust density estimation methods, enabling it to handle cases where traditional algorithms fail. Extensive experiments on both synthetic and real-world datasets demonstrate its superior capability to identify nested and contiguous clusters with heterogeneous densities, even in the presence of noise and over complex domains. These findings underscore the practical applicability and versatility of DTC in extracting meaningful insights from challenging datasets.