Extension of mathematical background for Nearest Neighbour Analysis in three-dimensional space

Abstract

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.

Keywords

• 3D GIS, spatial analysis, Nearest Neighbour Analysis