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.
@InProceedings{tsutsumida_et_al:LIPIcs.COSIT.2022.21, author = {Tsutsumida, Narumasa and Murakami, Daisuke and Yoshida, Takahiro and Nakaya, Tomoki and Lu, Binbin and Harris, Paul and Comber, Alexis}, title = {{A Comparison of Geographically Weighted Principal Components Analysis Methodologies}}, booktitle = {15th International Conference on Spatial Information Theory (COSIT 2022)}, pages = {21:1--21:6}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-257-0}, ISSN = {1868-8969}, year = {2022}, volume = {240}, editor = {Ishikawa, Toru and Fabrikant, Sara Irina and Winter, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2022.21}, URN = {urn:nbn:de:0030-drops-169062}, doi = {10.4230/LIPIcs.COSIT.2022.21}, annote = {Keywords: Spatial heterogeneity, Geographically weighted, Sparsity, PCA} }
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