Exploring Spatial Stratified Heterogeneity Patterns in Spatial Data: Balancing Heterogeneity With Stratification Complexity

Spatial stratified heterogeneity refers to the pattern variation of the target phenomenon across different regions. Current measures mainly quantify spatially stratified heterogeneity in terms of the consistency between strata and the target variable and neglect the complexity of stratification, whereas complex stratification may lead to overfitting and an overestimated degree of heterogeneity. To address this issue, this paper enhances the relative-entropy-based spatial stratified heterogeneity measure to unit explanatory power using the entropy of the stratification. The proposed method first quantifies the stratification complexity using the minimum theoretical number of bits for encoding it, then characterizes the degree of heterogeneity per bit, i.e., unit explanatory power, by the quotient of the relative-entropy-based measure and the stratification complexity. Additionally, this paper develops two visualization tools for interpreting and comparing unit explanatory power and reveals the relation among spatial stratified heterogeneity, stratification complexity, and the log-likelihood function. Finally, we conduct experiments on both illustrative and real-life data sets to show the advantages of the unit explanatory power over traditional spatial stratified heterogeneity measures. The code for computing unit explanatory power has been released athttps://github.com/crafly/ssh_with_gran.