An Application of Principal Component Analysis on Multivariate Time-stationary Spatio-temporal Data

Abstract

Principal component analysis (PCA) 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 PCA into the spatio-temporal realm. Our approach, named spatio-temporal principal component analysis (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.