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.

Special Issue: Data-Driven Discovery in Geosciences: Opportunities and Challenges

“…The paper entitled "Geographically Optimal Similarity" by Song (2022) develops a mathematical model of geographically optimal similarity (GOS) for accurate and reliable spatial prediction of geological variables (e.g., trace elements) based on the Third Law of Geography-namely, the geographical similarity principle, which describes the comprehensive degree of approximation of a geographical structure instead of alternative explicit relationships between variables. GOS employs a small number of samples and then derives better spatial predictions compared to the traditional methods.…”

Elucidation of spatial disparities of factors that affect air pollutant concentrations in industrial regions at a continental level

“…Currently, the spatial disparities of the factors that affect air pollutant concentrations, which indicate the internal characteristics of industrial regions, remain undiscovered. Spatial association modelling is an effective approach to examine relationships between spatial variables and it has been widely implemented in geographical factor exploration and spatial prediction (Luo et al, 2022;Song et al, 2021;Song, 2022aSong, , 2022b. To explore such spatial relationships, geographically weighted regression (GWR) is a suitable method (Fotheringham, 2002).…”

sandwichr: Spatial prediction in R based on spatial stratified heterogeneity

“…MPS can account for complex spatial structures and nonstationary behaviors, but it can also be computationally intensive and require large amounts of data to capture complex spatial structures (Tahmasebi, 2018). Newer methods, such as the second dimension of spatial associations (SDA) (Song, 2022b) and the geographically optimal similarity model (Song, 2022a), have also emerged that leverage auxiliary data associated with the inferred variables to make predictions, but these methods require the availability of auxiliary variables that may not always be available. Spatial stratified heterogeneity (SSH) (Wang et al, 2016) is a key feature of many geographical variables that can be used to overcome challenges in spatial prediction based on SAC and other methods that account for spatial heterogeneity.…”