A generic similarity test for spatial data

Abstract

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure. Many tests have been developed over recent years to test the similarity of certain types of spatial data, such as spatial point patterns, geostatistical data and images. This research develops a similarity test able to handle various types of spatial data, for example images (modelled spatially), point patterns, marked point patterns, geostatistical data and lattice patterns. The test consists of three steps. The first step creates a pixel image representation of each spatial data set considered. In the second step a local similarity map is created from the two pixel image representations from step one. The local similarity map is obtained by either using the well-known similarity measure for images called the Structural SIMilarity Index (SSIM) when having continuous pixel values or a direct comparison in the case of discrete pixel values. The calculation of the final similarity measure is done in the third step of the test. This calculation is based on the S-index of Andresen's spatial point pattern test. The S-index is calculated as the proportion of similar spatial units in the domain where s_i is used as a binary indicator of similarity. In the case of discrete pixel values, s_i are still used as a binary input whereas in the case of continuous pixel values the resulting SSIM values are used as a non-binary s_i input. The proposed spatial similarity test is tested with a simulation study where the simulations are designed to have comparisons that are either 80% or 90% identical. With the simulation study it is concluded that the test is not sensitive to the resolution of the pixel image. The application is done on property valuations in Johannesburg and Cape Town. The test is applied to the similarity of property prices in the same area over different years as well as testing the similarity of property prices between the different areas of properties.