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An Application of Principal Component Analysis on Multivariate Time-Stationary Spatio-Temporal Data

  • Stephan Stahlschmidt
  • Wolfgang Karl Härdle
  • Helmut Thome

Principal component analysis denotes a popular algorithmic technique to dimension reduction and factor extraction. Spatial variants have been proposed to account for the particularities of spatial data, namely spatial heterogeneity and spatial autocorrelation, and we present a novel approach which transfers principal component analysis into the spatio-temporal realm. Our approach, named stPCA, allows for dimension reduction in the attribute space while striving to preserve much of the data's variance and maintaining the data's original structure in the spatio-temporal domain. Additionally to spatial autocorrelation stPCA exploits any serial correlation present in the data and consequently takes advantage of all particular features of spatial-temporal data. A simulation study underlines the superior performance of stPCA if compared to the original PCA or its spatial variants and an application on indicators of economic deprivation and urbanism demonstrates its suitability for practical use.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2014-016.

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Length: 24 pages
Date of creation: Feb 2014
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2014-016
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  1. Pieter Kroonenberg & Jan Leeuw, 1980. "Principal component analysis of three-mode data by means of alternating least squares algorithms," Psychometrika, Springer, vol. 45(1), pages 69-97, March.
  2. Hogan J.W. & Tchernis R., 2004. "Bayesian Factor Analysis for Spatially Correlated Data, With Application to Summarizing Area-Level Material Deprivation From Census Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 314-324, January.
  3. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
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