Understanding Perturbation on the Simplex: A Simple Method to Better Visualize and Interpret Compositional Data in Ternary Diagrams |
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| Authors: | Hilmar von Eynatten Vera Pawlowsky-Glahn and Juan José Egozcue |
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| Institution: | (1) Institut für Geowissenschaften, FSU Jena, Burgweg 11, D-07743 Jena, Germany;(2) Departament d'Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi—P1, E-17071 Girona, Spain;(3) Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Campus Nord—C2, E-08034 Barcelona, Spain |
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| Abstract: | Perturbation is an operation defined on the simplex and can be used for centering compositional data in a ternary diagram, applying objective criteria. Because a straight line in the original diagram is still astraight line in the perturbed diagram, gridlines or compositional fields defined by straight lines can easily be included in the operation. Simultaneous perturbation of data, gridlines, and/or compositional fields is shown to improve both visualization and graphical interpretation of compositions in ternary diagrams. This is illustrated by some examples using simulated as well as real data. |
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| Keywords: | compositional fields geometric mean metric center rescaling |
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