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Principal Component Analysis for Spatial Point Processes — Assessing the Appropriateness of the Approach in an Ecological Context

  • Janine Illian
  • Erica Benson
  • John Crawford
  • Harry Staines
Part of the Lecture Notes in Statistics book series (LNS, volume 185)

Summary

There is a need to characterise spatial point patterns of ecological plant communities in which a very large number of points exist for many different plant species. We further investigate principal component analysis for spatial point patterns using functional data analysis tools on second-order summary statistics as introduced in [10, 11]. The approach is used to detect different types of point patterns in a multi-type pattern to classify the species by their spatial arrangement. The developed method is evaluated in a detailed feasibility study, giving rise to a number of recommendations including the choice of the appropriate summary statistic. In addition, we investigate the performance of the method under noisy conditions simulating a number of settings typically occurring in an ecological context. Overall, the method produces stable results, the best results being achieved when the pair-correlation function is used. In all settings the level of noise needs to be very high to invalidate the results.

Key words

Ecological plant communities Functional data analysis Functional principal component analysis Multi-type spatial point patterns 

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Copyright information

© Springer Science+Business Media Inc. 2006

Authors and Affiliations

  • Janine Illian
    • 1
  • Erica Benson
    • 1
  • John Crawford
    • 1
  • Harry Staines
    • 1
  1. 1.SIMBIOSUniversity of Abertay DundeeScotlandUK

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