Master of Arts (MA)
Geography & Environmental Studies
Faculty of Arts
This thesis explores a new way of visualizing spatial autocorrelation in a GIS environment. It explores some relationships between spatial autocorrelation models, spatial interaction models and weighted Voronoi diagrams. Since the weighted Voronoi diagram is equivalent to a form of spatial interaction models, any GIS with the ability to generate a gravity model can be utilized to perform this new technique of exploratory spatial data analysis. This thesis demonstrates how the cross product form of‘ spatial autocorrelation models like the Geary and the Moran statistics is equivalent to the form of a multiplicatively weighted distance utilized in the deﬁnition of weighted Voronoi diagrams. A transformation of the multiplicatively weighted distance into a representation of the Geary or the Moran statistic can be used to generate different weighted Voronoi diagrams. Since such a representation incorporates the spatial variation of data points and the spatial variation of the attribute values assigned to the data points, it provides a more appropriate visual representation than do existing representations that only operate on the spatial distribution of the data points. Data sets with a known degree of spatial autocorrelation are created with a simultaneous autoregressive model. The behaviour of the visual representations of the Geary and the Moran statistics for spatial autocorrelation varying from a high positive to a high negative degree is examined.
Cassel, Martin A., "Voronoi diagrams as a visualization technique for spatial autocorrelation in point data sets" (1993). Theses and Dissertations (Comprehensive). 378.