三维空间中最近邻分析数学背景的扩展

Eva Stopková
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引用次数: 2

摘要

接着论述了基于最近邻分析的GRASS GIS[1]模块的开发与测试。该方法可用于评估感兴趣区域内的点是随机分布、聚类分布还是单独分布。该方法的主要原理是将观测到的最近邻居之间的平均距离r A与随机分布情况下期望的最近邻居之间的平均距离r E进行比较。这个结果应该经过统计检验。二维或三维空间的方法在计算r E的方式上有所不同。文中还介绍了推导分析结果统计检验所需的r E标准差的数学背景的扩展。正如现象的配置(如鸟巢或植物物种的分布)和测试结果所表明的那样,各向异性函数比本工作中使用的各向同性函数更能表示三维空间中点之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Extension of mathematical background for Nearest Neighbour Analysis in three-dimensional space
Proceeding deals with development and testing of the module for GRASS GIS [1], based on Nearest Neighbour Analysis. This method can be useful for assessing whether points located in area of interest are distributed randomly, in clusters or separately. The main principle of the method consists of comparing observed average distance between the nearest neighbours r A to average distance between the nearest neighbours r E that is expected in case of randomly distributed points. The result should be statistically tested. The method for two- or three-dimensional space differs in way how to compute r E . Proceeding also describes extension of mathematical background deriving standard deviation of r E , needed in statistical test of analysis result. As disposition of phenomena (e.g. distribution of birds’ nests or plant species) and test results suggest, anisotropic function would repre- sent relationships between points in three-dimensional space better than isotropic function that was used in this work.
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