Harris, Paul and Clarke, Annemarie and Juggins, Steve and Brunsdon, Chris and Charlton, Martin
(2015)
Enhancements to a Geographically Weighted
Principal Component Analysis in the Context of
an Application to an Environmental Data Set.
Geographical Analysis, 47 (2).
pp. 146-172.
ISSN 1538-4632
Abstract
In many physical geography settings, principal component analysis (PCA) is applied
without consideration for important spatial effects, and in doing so, tends to provide an
incomplete understanding of a given process. In such circumstances, a spatial adaptation
of PCA can be adopted, and to this end, this study focuses on the use of geographically
weighted principal component analysis (GWPCA). GWPCA is a localized version of PCA
that is an appropriate exploratory tool when a need exists to investigate for a certain spatial
heterogeneity in the structure of a multivariate data set. This study provides enhancements
to GWPCA with respect to: (i) finding the scale at which each localized PCA should
operate; and (ii) visualizing the copious amounts of output that result from its application.
An extension of GWPCA is also proposed, where it is used to detect multivariate spatial
outliers. These advancements in GWPCA are demonstrated using an environmental freshwater
chemistry data set, where a commentary on the use of preprocessed (transformed and
standardized) data is also presented. The study is structured as follows: (1) the GWPCA
methodology; (2) a description of the case study data; (3) the GWPCA application,
demonstrating the value of the proposed advancements; and (4) conclusions. Most GWPCA
functions have been incorporated within the GWmodel R package.
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