A Comparison of Geographically Weighted Principal Components Analysis Methodologies

Principal components analysis (PCA) is a useful analytical tool to represent key characteristics of multivariate data, but does not account for spatial effects when applied in geographical situations. A geographically weighted PCA (GWPCA) caters to this issue, specifically in terms of capturing spatial heterogeneity. However, in certain situations, a GWPCA provides outputs that vary discontinuously spatially, which are difficult to interpret and are not associated with the output from a conventional (global) PCA any more. This study underlines a GW non-negative PCA, a geographically weighted version of non-negative PCA, to overcome this issue by constraining loading values non-negatively. Case study results with a complex multivariate spatial dataset demonstrate such benefits, where GW non-negative PCA allows improved interpretations than that found with conventional GWPCA.