The detection of spatial clusters, taking into account both spatial proximity and attribute similarity, plays a vital role in spatial data analysis. Although several dual clustering methods are currently available in the literature, most of them have detected homogeneous spatially adjacent clusters suffering from between‐cluster inhomogeneity and noise, where those spatial points have been described in the attribute domain. This article aims to accommodate both spatial proximity and attribute similarity with the presence of heterogeneity and noise. In this algorithm, Delaunay triangulation with edge‐length constraints, with consideration of arbitrary geometrical shapes, different densities, and spatial noise, is first utilized to construct spatial proximity relationships among points. Then, a clustering strategy employing information entropy is designed to identify clusters having similar attributes. The attribute clustering can adaptively and accurately detect clusters under the consideration of heterogeneity and noise. The efficacy and practicability of the proposed algorithm are illustrated by experiments employing both simulated datasets and real spatial point events.

中文翻译：

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存在异质性和噪声的双重空间聚类方法

同时考虑空间邻近性和属性相似性的空间聚类检测在空间数据分析中起着至关重要的作用。尽管目前文献中提供了几种双重聚类方法，但大多数方法都检测到了均一的空间相邻聚类，这些聚类受到群集间不均匀性和噪声的影响，这些空间点已在属性域中进行了描述。本文旨在通过存在异质性和噪声来适应空间邻近性和属性相似性。在该算法中，首先利用具有边长约束的Delaunay三角剖分，考虑了任意几何形状，不同的密度和空间噪声，以构造点之间的空间邻近关系。然后，设计采用信息熵的聚类策略以识别具有相似属性的聚类。考虑到异质性和噪声，属性聚类可以自适应且准确地检测聚类。通过使用模拟数据集和实际空间点事件的实验，说明了该算法的有效性和实用性。