Biplots for Compositional Data Derived from Generalised Joint Diagonalisation Methods

• U. Mueller ^[1] ; R. Tolosana Delgado ^[2] ; E.C. Grunsky ^[2] ; J.M. McKinley ^[3]
  1. [1] Center of Ecosystems Management, School of Science, Edith Cowan University Australia
  2. [2] Waterloo University, Waterloo, Canada
  3. [3] Queens University, Belfast, UK

  Mostrar afiliaciones +
• Localización: Proceedings of the 8th International Workshop on Compositional Data Analysis (CoDaWork2019): Terrassa, 3-8 June, 2019 / Juan José Egozcue Rubí (aut.), Jan Graffelman (aut.), María Isabel Ortego Martínez (aut.), 2019, ISBN 978-84-947240-2-2, págs. 105-111
• Idioma: inglés
• Enlaces
  • Texto Completo Libro (pdf)
• Resumen

  • Biplots constructed from principal components of a compositional data set are an established means to explore its features. Principal Component Analysis (PCA) is also used to transform a set of spatial variables into spatially decorrelated factors. However, because no spatial structures are accounted for in the transformation the application of PCA is limited. In Geostatistics and Blind Source Separation a variety of different matrix diagonalisation methods have been developed with the aim to provide spatially or temporally decorrelated factors. Just as PCA, many of these transformations are linear and so lend themselves to the construction of biplots. In this contribution we consider such biplots for a number of methods (MAF, UWEDGE and RJD transformations) and discuss how and if they can contribute to our understanding of relationships between the components of regionalised compositions. A comparison of the biplots with the PCA biplot commonly used in compositional data analysis for the case of data from the Northern Irish geochemical survey shows that the biplots from MAF and UWEDGE are comparable while that from RJD does not reveal any associations indicating that RJD might not be suitable for exploratory statistical analysis and that MAF might suffice to provide an adequate spatial characterisation.