发表机构
Universitat de València（瓦伦西亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文受拓扑数据分析启发，提出面状数据空间连通性的全局与局部指标，通过Betti-0曲线及局部分解衡量区域参与度，并应用于意大利COVID-19数据，发现高、低发病率区域均存在显著连通性。
AI 中文摘要
面状数据的方法通常通过全局自相关度量或基于邻近值的局部指标来描述空间结构。然而，在许多应用中，了解高值或低值区域是否形成连通的空间结构也同样重要。受拓扑数据分析的启发，我们为定义在面状邻接图上的观测值开发了空间连通性的全局和局部指标。我们构建阈值化空间图，并使用Betti-0曲线记录其连通分量的数量。我们进一步推导出一种局部分解，其中每个区域对Betti-0曲线的贡献被表示为一个激活项减去一个合并项。每个分量融合通过进入区域与发生融合的邻近区域之间的对称分配来贡献于合并项。对合并贡献进行积分，可得到区域级指标，用于衡量区域在高值或低值区域的连通性中的参与程度。全局和局部推断基于随机重新标记，其中全局检验用于检验偏离空间可交换性的情况，条件检验用于局部指标。我们使用意大利各省在两次疫情波次中的COVID-19发病率来展示该框架。对于高发病率和低发病率区域，均发现了显著偏离且趋向更大连通性的情况，其中最大差异对应于第一波中的高发病率。所提出的指标补充了传统的空间关联度量，并且适用于任何关注阈值超出或不足的空间一致性的情况。
英文摘要
Methods for areal data commonly describe spatial structure through global autocorrelation measures or local indicators based on neighboring values. In many applications, however, it is also relevant to know whether high- or low-valued areas form connected spatial structures. Motivated by topological data analysis, we develop global and local indicators of spatial connectivity for observations defined on an areal adjacency graph. We construct thresholded spatial graphs and use the Betti-0 curve to record their number of connected components. We further derive a local decomposition in which each area's contribution to the Betti-0 curve is expressed as an activation term minus a merging term. Each component fusion contributes to the merging term through a symmetric allocation between the entering area and the neighboring areas through which the fusion occurs. Integrating the merging contributions yields area-level indicators of participation in the connectivity of high- or low-valued regions. Global and local inference is based on random relabeling, with a global test for departures from spatial exchangeability and a conditional test for the local indicators. We illustrate the framework using COVID-19 incidence in Italian provinces during two epidemic waves. Significant departures toward greater connectivity were found for both high- and low-incidence areas, with the largest discrepancy corresponding to high incidence during the first wave. The proposed indicators complement conventional measures of spatial association and are applicable whenever the spatial coherence of threshold exceedances or deficits is of interest.
