时间地理支持下的核密度估计研究进展  

Advances in kernel density estimation supported by time geography

作　　者：尹章才[1] 康自强 YIN Zhangcai;KANG Ziqiang(School of Resources and Environmental Engineering,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学资源与环境工程学院,武汉430070

出　　处：《地理科学进展》2022年第1期64-72,共9页Progress in Geography

基　　金：国家自然科学基金项目(42171415)。

摘　　要：时间地理核密度估计是经典核密度估计(KDE)基于时间地理的一种扩展,主要是将标准核函数的定义域扩展至时间地理的时空可达域,以通过增强定义域在时空方面的物理意义来避免非零密度被分配到可达域之外的问题。时空可达域包括时空碟和由时空碟复合而成的潜在路径区域(PPA)。这2类可达域用作核函数的定义域能解决上述问题,但也带来了新的问题。基于时空碟构建的核函数能叠加成PPA上的概率密度,但敏感于时空碟的时间点。而基于PPA构建的核函数相较于理想布朗桥模型缺乏双峰特性,且也不能生成时空碟上的概率密度函数。因此,时间地理与KDE相结合的研究还处于应用前的理论探索阶段,论文的目标就是对这一进程进行梳理并引出未来的发展趋势。论文围绕时空轨迹不确定性量化这一目标,首先回顾了时间地理与核密度估计的不同功用,然后对两者相融合的意义、框架和模式进行了阐述。最后,认为时间地理的可达域代替核密度估计的定义域是改进时空轨迹不确定性测度的重要手段,但距离目标的落地还有一定的距离。Time geographic kernel density estimation is an extension of classical kernel density estimation(KDE)based on time geography.It mainly extends the definition domain of the standard kernel function to the space-time reachable domain of time geography,so as to avoid the problem of non-zero density being assigned outside the reachable domain by enhancing the physical meaning of the definition domain in space-time.The space-time reachable area includes the space-time disc and the potential path area(PPA)compounded by the space-time disc.These two types of reachable domains can be used as the domain of the kernel function to solve the above problems,but they also bring new problems.The kernel function constructed based on the space-time disc can be superimposed into the probability density on the PPA,but it is sensitive to the time point of the disc.Compared with the ideal Brown Bridge model,the kernel function constructed based on PPA lacks bimodal characteristics,and cannot generate the probability density function on the space-time disc.Therefore,the research on the combination of time geography and KDE is still in the stage of theoretical exploration before application.The goal of this article is to sort out this process and elicit future development trends.Focusing on the goal of quantifying the uncertainty of space-time trajectory,this article first reviews the different functions of time geography and KDE,and then elaborates the meaning,framework and mode of the integration of the two.Finally,this article believes that the time-geographic reachable domain instead of the domain of KDE is an important means to improve the uncertainty measurement of space-time trajectory,but there is still a certain distance from the landing of the target.

关 键 词：核密度估计 时间地理学 潜在路径区域 时空轨迹 

分 类 号：P208[天文地球—地图制图学与地理信息工程]