Mark distance correlation functions: from moment-based to distributional mark summary characteristics in spatial point processes

2026-09-22

AI Summary

本文针对空间点模式数据中事件位置与标记之间的结构关系分析问题，通过调整距离协方差和距离相关性方法，引入了一种新的适用于不同类型标记特征的分析技术。

Abstract

With the rapid advancement in data collection devices and storage capacities, we have access to increasing amount of spatial point pattern data where each event location is augmented by multiple, potentially non-scalar marks. Therefore, there is need for efficient analysis techniques to investigate the structural relationships between the marks. In this paper, we recall the distance covariance and distance correlation and adjust them to the marked point process setting. As a result, we introduce a novel class of mark characteristics for single real-valued marks as well as multivariate combinations of marks, including mixtures of integer- and real-valued quantities, and non-scalar marks.

Problem

• spatial point pattern
• marks
• structural relationships

Innovation

• distance covariance
• distance correlation
• marked point process
• multivariate marks