Comparing Spatial Eigenvectors Associated with Different Spatial Autocorrelation Statistics

Authors: Sang-Il Lee*, Seoul National University
Topics: Spatial Analysis & Modeling
Keywords: spatial eigenvectors, spatial autocorrelation statistics, eigenfunctions, eigenvector spatial filtering (ESF)
Session Type: Paper
Day: 4/11/2018
Start / End Time: 1:20 PM / 3:00 PM
Room: Mid-City, Sheraton, 8th Floor
Presentation File: No File Uploaded

This study aims at providing a comparison of spatial patterns of eigenvectors associated with three different spatial autocorrelation statistics such as Moran's I, Geary's c, and Lee's S* in consideration of different specifications of spatial weights matrices. This study assumes that the variability of spatial eigenvectors arises not only from different eigenfunctions (different statistics) but from different spatial weights matrices (especially non-standardized or row-standardized). For instance, eigenvectors associated with Moran's I and Geary's c are different because they are based on different statistics associated with different eigenfunctions. However, eigenvectors for Moran's I with a binary contiguity-based spatial weights matrix may also be different from those with a row-standardized stochastic one. In order to effectively compare sets of eigenvectors, a graphical visualization technique similar to the correlation matrix is devised. On such a graph, two different sets of eigenvectors, arrayed in a rank order according to the accompanying eigenvalues, are respectively put on x- and y-axis and the direction and strength of all the correlation coefficients across the two sets of the eigenvectors are displayed in the use of a diverging color scheme. Two criteria, diagonality and (one-to-one) correspondence, are set to evaluate the degree of coincidence between two sets of eigenvectors. A preliminary result shows that different spatial autocorrelation statistics and different spatial weights matrices are jointly responsible for the variability of spatial eigenvectors. This study may have some implications for such spatial statistical techniques as eigenvector spatial filtering (ESF) approach.

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