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A Comparison of Geographically Weighted Principal Components Analysis Methodologies (Short Paper)
Authors
Narumasa Tsutsumida 
,
Daisuke Murakami ,
Takahiro Yoshida ,
Tomoki Nakaya ,
Binbin Lu ,
Paul Harris ,
Alexis Comber
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Volume:
15th International Conference on Spatial Information Theory (COSIT 2022)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Spatial Information Theory (COSIT) - License:
Creative Commons Attribution 4.0 International license
- Publication date: 2022-08-22
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Narumasa Tsutsumida, Daisuke Murakami, Takahiro Yoshida, Tomoki Nakaya, Binbin Lu, Paul Harris, and Alexis Comber. A Comparison of Geographically Weighted Principal Components Analysis Methodologies (Short Paper). In 15th International Conference on Spatial Information Theory (COSIT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 240, pp. 21:1-21:6, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.COSIT.2022.21
https://doi.org/10.4230/LIPIcs.COSIT.2022.21
Abstract
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.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Multivariate statistics
Keywords
- Spatial heterogeneity
- Geographically weighted
- Sparsity
- PCA
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References
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