Geographically weighted principal components analysis

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 application 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 visualisation 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 implementation issues we investigate), we apply this technique to a study of social structure in Greater Dublin, Ireland.

Keywords:

• PCA
• GWPCA
• bandwidth selection
• visualisation
• nonstationarity
• GWR

Acknowledgements

Research presented in this article was funded by a Strategic Research Cluster grant (07/SRC/I1168) by the Science Foundation Ireland under the National Development Plan. The authors gratefully acknowledge this support. Professor Brunsdon's time was made available through the grant of study leave by the University of Leicester.