Harris, Paul and Brunsdon, Chris and Charlton, Martin
(2011)
Geographically weighted principal components analysis.
International Journal of Geographical Information Science, 25 (10).
pp. 1717-1736.
ISSN 1365-8816
Abstract
Principal components analysis (PCA) is a widely used technique in the social and
physical sciences. However in spatial applications, standard PCA is frequently applied
without any adaptation that accounts for important spatial effects. Such a naive applica-
tion can be problematic as such effects often provide a more complete understanding of
a given process. In this respect, standard PCA can be (a) replaced with a geographically
weighted PCA (GWPCA), when we want to account for a certain spatial heterogeneity;
(b) adapted to account for spatial autocorrelation in the spatial process; or (c) adapted
with a specification that represents a mixture of both (a) and (b). In this article, we focus
on implementation issues concerning the calibration, testing, interpretation and visual-
isation of the location-specific principal components from GWPCA. Here we initially
consider the basics of (global) principal components, then consider the development
of a locally weighted PCA (for the exploration of local subsets in attribute-space) and
finally GWPCA. As an illustration of the use of GWPCA (with respect to the imple-
mentation issues we investigate), we apply this technique to a study of social structure
in Greater Dublin, Ireland.
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