Geoinformation dependencies in geographic space and beyond

The use of geospatially dependent information, which has been stipulated as a law in geography, to model geographic patterns forms the cornerstone of geostatistics, and has been inherited in many data science based techniques as well, such as statistical learning algorithms. Still, we observe hesitations in interpreting geographic dependency scientifically as a property in geography, since interpretations of such dependency are subject to model choice with different hypotheses of trends and stationarity. Rather than questioning what can be considered as trends or why it is non-stationary, in this work, we share and consolidate a view that the properties of geographic dependency, being it trending or stationary, are essentially variations can be explained further by unobserved or unknown predictors, and not intrinsic to geographic space. Particularly, geoinformation dependency properties are in fact a projection of high dimensional feature space formed by all potential predictors into the lower dimension of geographic space, where geographic coordinates are equivalent to other predictors for modelling geographic patterns. This work brings together different aspects of geographic dependency, including similarity and heterogeneity, under a coherent framework, and aligns with the understanding of modelling in high dimensional feature space with different modelling concept including the classical geostatistics, Gaussian Process Regression and popular data science based spatial modelling techniques.