On the Interpretation of Orthonormal Coordinates for Compositional Data

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Systematic comparison of five machine-learning models in classification and interpolation of soil particle size fractions using different transformed data (2020, background): “The balance of each step remains the same as before and the total number of steps is D-1 (the dimension of SD) (Fiserova and Hron, 2011), finally.”
Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal (2022, methodology): “” (first sentence of abstract of [66]) • “Compositional vectors need to be expressed in orthonormal coordinates, thereby allowing further processing using standard statistical tools” [26]; • “Compositional data should be expressed with respect to orthonormal coordinates2 that “guarantee isometry bet”