3L-GBC: structure-aware granular-ball clustering for layered structure discovery

Many synthetic and real-world datasets contain clusters with heterogeneous internal densities, where dense central regions gradually transition to sparse boundaries. However, most current clustering methods rely on single-layer modeling or rigid partitioning criteria, which limits their ability to capture complex cluster shapes and heterogeneous density distributions. To address these limitations, a density-gradient-guided three-layer granular ball clustering method (3L-GBC) is proposed. The method adopts a three-layer granular-ball representation to model dense, transitional, and sparse regions within clusters. Within this framework, candidate centers are efficiently identified using a lightweight density peak–inspired strategy, followed by the construction and adaptive expansion of density-gradient-guided granular balls. A curvature-based mechanism is further introduced to reveal an explicit three-layer internal structure. Finally, granular balls are merged into complete clusters through adaptive density propagation driven by multi-regional structural consistency. Experimental results on synthetic and real datasets demonstrate that 3L-GBC achieves competitive clustering performance on complex structures.