  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.
