Principal Component Analysis on Spatial Data

An Overview

Urška Demšar, Paul Harris, Chris Brunsdon, Stewart Fotheringham, Sean McLoone

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

This article considers critically how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data. We first provide a brief guide to how PCA works: This includes robust and compositional PCA variants, links to factor analysis, latent variable modeling, and multilevel PCA. We then present two different approaches to using PCA with spatial data. First we look at the nonspatial approach, which avoids challenges posed by spatial data by using a standard PCA on attribute space only. Within this approach we identify four main methodologies, which we define as (1) PCA applied to spatial objects, (2) PCA applied to raster data, (3) atmospheric science PCA, and (4) PCA on flows. In the second approach, we look at PCA adapted for effects in geographical space by looking at PCA methods adapted for first-order nonstationary effects (spatial heterogeneity) and second-order stationary effects (spatial autocorrelation). We also describe how PCA can be used to investigate multiple scales of spatial autocorrelation. Furthermore, we attempt to disambiguate a terminology confusion by clarifying which methods are specifically termed "spatial PCA" in the literature and how this term has different meanings in different areas. Finally, we look at a further three variations of PCA that have not been used in a spatial context but show considerable potential in this respect: simple PCA, sparse PCA, and multilinear PCA.

Original languageEnglish (US)
Pages (from-to)106-128
Number of pages23
JournalAnnals of the Association of American Geographers
Volume103
Issue number1
DOIs
StatePublished - Jan 2013
Externally publishedYes

Fingerprint

spatial data
principal component analysis
autocorrelation
raster
terminology
statistical method
factor analysis
technical language

Keywords

  • dimensionality reduction
  • multivariate statistics
  • principal components analysis
  • spatial analysis and mathematical modeling
  • spatial data

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes

Cite this

Principal Component Analysis on Spatial Data : An Overview. / Demšar, Urška; Harris, Paul; Brunsdon, Chris; Fotheringham, Stewart; McLoone, Sean.

In: Annals of the Association of American Geographers, Vol. 103, No. 1, 01.2013, p. 106-128.

Research output: Contribution to journalArticle

Demšar, Urška ; Harris, Paul ; Brunsdon, Chris ; Fotheringham, Stewart ; McLoone, Sean. / Principal Component Analysis on Spatial Data : An Overview. In: Annals of the Association of American Geographers. 2013 ; Vol. 103, No. 1. pp. 106-128.
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