New framework of Getis-Ord's indexes associating spatial autocorrelation with interaction

Spatial autocorrelation and spatial interaction are two important analytical processes for geographical analyses. However, the internal relations between the two types of models have not been brought to light. This paper is devoted to integrating spatial autocorrelation analysis and spatial interaction analysis into a logic framework by means of Getis-Ord's indexes. Based on mathematical derivation and transform, the spatial autocorrelation measurements of Getis-Ord's indexes are reconstructed in a new and simple form. A finding is that the local Getis-Ord's indexes of spatial autocorrelation are equivalent to the rescaled potential energy indexes of spatial interaction theory based on power-law distance decay. The normalized scatterplot is introduced into the spatial analysis based on Getis-Ord's indexes, and the potential energy indexes are proposed as a complementary measurement. The global Getis-Ord's index proved to be the weighted sum of the potential energy indexes and the direct sum of total potential energy. The empirical analysis of the system of Chinese cities are taken as an example to illustrate the effect of the improved methods and measurements. The mathematical framework newly derived from Getis-Ord's work is helpful for further developing the methodology of geographical spatial modeling and quantitative analysis.