Geographically Optimal Similarity

Abstract Understanding geographical characteristics of distribution patterns and spatial association is essential for spatial statistical inference such as factor exploration and spatial prediction. The geographical similarity principle was recently developed to explain the association between geographical variables. It describes the comprehensive degree of approximation of a geographical structure instead of explicit relationships between variables. However, there are still challenges for geographical similarity-based methods. For instance, all samples are used for prediction, leading to increased calculation burden and reduced prediction accuracy due to the noise and unrelated data in large spatial data sets. This study develops a geographically optimal similarity (GOS) model for accurate and reliable spatial prediction based on the geographical similarity principle. In GOS, the geographical configurations are first characterized, and similarities between unknown and known observation locations are assessed. Next, an optimal threshold is determined to select a small number of observations with optimal similarities for the prediction at each unknown location. Finally, a reliable uncertainty assessment approach is developed to assess and map uncertainties of GOS predictions. A new R package “geosimilarity” is developed to conduct GOS models. In this study, GOS is implemented in predicting spatial distributions of trace elements in a mining region in Australia. Results show that GOS can use a small number of observations to derive more accurate and reliable spatial predictions than linear regression and basic configuration similarity models. In addition, pattern characteristics of predictions can be improved by GOS by eliminating the phenomenon wherein predictions are clustered near mean values and contain striped textures. Therefore, GOS demonstrates greater potential for implementing the geographical similarity principle in spatial predictions by bringing information from samples with relatively high similarities at any location across space for more accurate and effective predictions in broader fields and practice.