Factor analysis has been extensively used to reveal the dependence structures among multivariate variables, offering valuable insight in various fields. However, it cannot incorporate the spatial heterogeneity that is typically present in spatial data. To address this issue, we introduce an effective method specifically designed to discover the potential dependence structures in multivariate spatial data. Our approach assumes that spatial locations can be approximately divided into a finite number of clusters, with locations within the same cluster sharing similar dependence structures. By leveraging an iterative algorithm that combines spatial clustering with factor analysis, we simultaneously detect spatial clusters and estimate a unique factor model for each cluster. The proposed method is evaluated through comprehensive simulation studies, demonstrating its flexibility. In addition, we apply the proposed method to a dataset of railway station attributes in the Tokyo metropolitan area, highlighting its practical applicability and effectiveness in uncovering complex spatial dependencies.

翻译：因子分析已被广泛应用于揭示多元变量间的依赖结构，为诸多领域提供了重要洞见。然而，该方法无法处理空间数据中普遍存在的空间异质性。为解决这一问题，本文提出一种专门用于发现多元空间数据中潜在依赖结构的有效方法。我们的方法假设空间位置可近似划分为有限数量的聚类，且同一聚类内的位置具有相似的依赖结构。通过结合空间聚类与因子分析的迭代算法，我们能够同时检测空间聚类并为每个聚类估计独特的因子模型。所提方法经过全面的模拟研究验证，展现了其灵活性。此外，我们将该方法应用于东京都市圈铁路站点属性数据集，突显了其在揭示复杂空间依赖性方面的实际适用性与有效性。