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Enhancements to a Geographically Weighted Principal Component Analysis in the Context of an Application to an Environmental Data Set
Author(s) -
Harris Paul,
Clarke Annemarie,
Juggins Steve,
Brunsdon Chris,
Charlton Martin
Publication year - 2015
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/gean.12048
Subject(s) - principal component analysis , outlier , multivariate statistics , context (archaeology) , set (abstract data type) , data mining , data set , computer science , spatial analysis , component (thermodynamics) , adaptation (eye) , multivariate analysis , spatial contextual awareness , artificial intelligence , statistics , mathematics , geography , machine learning , physics , archaeology , optics , thermodynamics , programming language
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 GW model R package.