论文标题
空间聚类回归
Spatially Clustered Regression
论文作者
论文摘要
空间回归或地理加权回归模型已被广泛采用，以捕获辅助信息对区域感兴趣的响应变量的影响。相反，在许多应用中，响应与辅助变量之间的关系有望表现出复杂的空间模式。本文提出了一种新的空间回归方法，称为空间簇回归，以估计关系的群集空间模式。我们将基于K-均值的聚类公式和惩罚函数结合起来，该功能是由称为Potts模型的空间过程动机，用于鼓励在相邻位置进行类似的聚类。我们提供了一种简单的迭代算法来符合所提出的方法，可扩展到大空间数据集。通过仿真研究，提出的方法证明了它与现有方法的优越性能，即使在真实结构下也不能接受空间聚类。最后，提出的方法应用于东京的犯罪事件数据，并为空间模式产生可解释的结果。 R代码可在https://github.com/sshonosuke/scr上找到。
Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region. In contrast, relationships between response and auxiliary variables are expected to exhibit complex spatial patterns in many applications. This paper proposes a new approach for spatial regression, called spatially clustered regression, to estimate possibly clustered spatial patterns of the relationships. We combine K-means-based clustering formulation and penalty function motivated from a spatial process known as Potts model for encouraging similar clustering in neighboring locations. We provide a simple iterative algorithm to fit the proposed method, scalable for large spatial datasets. Through simulation studies, the proposed method demonstrates its superior performance to existing methods even under the true structure does not admit spatial clustering. Finally, the proposed method is applied to crime event data in Tokyo and produces interpretable results for spatial patterns. The R code is available at https://github.com/sshonosuke/SCR.
