Data and Code for STICC
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Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may face challenges for discovering repeated clusters with spatial contiguity maintained. In this paper, we propose a Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both attributes and spatial relationships of geographic objects for multivariate spatial clustering. Different from the traditional clustering methods that treat each geographic object independently, a subregion of each object is created serving as the basic unit when performing clustering. A Markov random field (MRF) is constructed to characterize the attribute dependencies of subregions. Using a spatial consistency strategy, nearby objects are encouraged to belong to the same cluster. To test the performance of the proposed STICC algorithm, we apply it in three use cases. The comparison results with several baseline methods show that the STICC outperforms others significantly in terms of adjusted rand index and macro-F1. Moran's I index is also calculated and shows the spatial dependency is well preserved by STICC. Such a spatial clustering method may benefit various applications in the fields of geography, remote sensing, transportation, and urban planning, etc.
空间聚类已广泛应用于空间数据挖掘与知识发现领域。理想的多变量空间聚类应同时兼顾空间连续性与非空间属性。现有空间聚类方法在维持空间连续性的前提下挖掘重复聚类时，往往面临诸多挑战。为此，本文提出一种基于空间托普利茨逆协方差的聚类（Spatial Toeplitz Inverse Covariance-Based Clustering, STICC）方法，可同时考量地理对象的属性特征与空间关系，实现多变量空间聚类。与传统将单个地理对象独立作为聚类单元的方法不同，本方法为每个地理对象创建子区域作为聚类的基本处理单元。通过构建马尔可夫随机场（Markov Random Field, MRF）刻画子区域间的属性依赖关系，并采用空间一致性策略，促使邻近对象归属于同一聚类。为验证所提STICC算法的性能，本文在三个应用场景中开展了测试实验。与多种基线方法的对比结果表明，STICC在调整兰德指数（Adjusted Rand Index）和宏F1值（Macro-F1）两项指标上均显著优于其他对比方法。同时通过计算莫兰I指数（Moran's I Index）验证，STICC能够很好地保留数据的空间依赖性。此类空间聚类方法可广泛应用于地理、遥感、交通及城市规划等多个领域。
