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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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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Multivariate statistics
Keywords
  • Spatial heterogeneity
  • Geographically weighted
  • Sparsity
  • PCA

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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.

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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

Author Details

Narumasa Tsutsumida
  • Saitama University, Japan
Daisuke Murakami
  • Institute of Statistical Mathematics, Tokyo, Japan
Takahiro Yoshida
  • The University of Tokyo, Japan
Tomoki Nakaya
  • Tohoku University, Sendai, Japan
Binbin Lu
  • Wuhan University, China
Paul Harris
  • Rothamsted Research, Harpenden, UK
Alexis Comber
  • University of Leeds, UK

Funding

This research was funded by the Joint Support Center for Data Science Research at Research Organization of Information and Systems (ROIS-DS-JOINT) under Grant 006RP2018, 004RP2019, 003RP2020, and 005RP2021.

References

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