Spatial clustering is a widely used data mining method for discovery of spatial aggregation pattern. However, existing methods often neglect scale dependence, impeding the full recognition of point patterns and the detection of hierarchical spatial structures. Spatial clustering is scale dependent and linked to the size of analysis unit as well as the hierarchy of visual cognition. Therefore, this paper proposes a novel multi-scale grid clustering (MSGC) algorithm, which fuses dual scale factors, i.e., analytical scale and visual scale that sequentially integrates multi-analytical-scale clustering (MASC) and multi-visual-scale clustering (MVSC). MASC generates multi-granularity grids to transform the analytical scales, and MVSC extracts multi-level clusters to express the hierarchy of visual cognition. Comparative experiments validated the proposed algorithm against the classical Density-based Spatial Clustering of Applications with Noise (DBSCAN) and WaveCluster algorithms on both synthetic and real-world geographic datasets. The results demonstrate that MSGC can generate multi-scale clusters for increased understanding of the spatial aggregation patterns and hierarchical structures of geographic entities. Moreover, it can eliminate noise adaptively and effectively identify clusters with arbitrary shapes. Due to the nature of grid clustering, the low computational complexity enables near real-time visual analytics and efficient point pattern mining on large spatial datasets.

空间聚类是发现空间聚集模式的一种广泛使用的数据挖掘方法。但是，现有方法通常会忽略比例尺的依赖关系，从而阻碍了点模式的完全识别和分层空间结构的检测。空间聚类与规模有关，并且与分析单元的大小以及视觉认知的层次结构相关。因此，本文提出了一种新颖的多尺度网格聚类（MSGC）算法，该算法融合了双重尺度因子，即分析尺度和视觉尺度，该尺度尺度依次集成了多分析尺度聚类（MASC）和多视觉尺度聚类（ MVSC）。MASC生成多粒度网格以转换分析尺度，MVSC提取多级聚类以表达视觉认知的层次结构。对比实验在合成和真实的地理数据集上，针对经典的基于密度的带噪声应用空间聚类（DBSCAN）和WaveCluster算法，验证了该算法的有效性。结果表明，MSGC可以生成多尺度簇，以增强对地理实体的空间聚集模式和层次结构的理解。而且，它可以自适应地消除噪声，并有效地识别具有任意形状的簇。由于网格聚类的性质，低计算复杂度可在大型空间数据集上实现近实时视觉分析和有效的点模式挖掘。