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

Author

Listed:
  • Stephan Stahlschmidt
  • Wolfgang Karl Härdle
  • Helmut Thome

Abstract

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.

Suggested Citation

  • Stephan Stahlschmidt & Wolfgang Karl Härdle & Helmut Thome, 2014. "An Application of Principal Component Analysis on Multivariate Time-Stationary Spatio-Temporal Data," SFB 649 Discussion Papers SFB649DP2014-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2014-016
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    References listed on IDEAS

    as
    1. Pieter Kroonenberg & Jan Leeuw, 1980. "Principal component analysis of three-mode data by means of alternating least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 69-97, March.
    2. 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.
    3. 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.
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    More about this item

    Keywords

    PCA; spatio-temporal analysis; dimension reduction; factor extraction; economic deprivation; urbanism;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

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