an:05116154
Zbl 1101.86309
Aitchison, J.; Barcel??-Vidal, C.; Mart??n-Fern??ndez, J. A.; Pawlowsky-Glahn, V.
Logratio analysis and compositional distance
EN
Math. Geol. 32, No. 3, 271-275 (2000).
00076852
2000
j
86A32
Euclidean distance; permutation invariance; perturbation invariance; scale invariance; subcompositional dominance
Summary: The concept of distance between two compositions is important in the statistical analysis of compositional data, particularly in such activities as cluster analysis and multidimensional scaling. This paper exposes the fallacies in a recent criticism of logratio-based distance measures -- in particular, the misstatements that logratio methods destroy distance structures and are denominator dependent. Emphasis is on ensuring that compositional data analysis involving distance concepts satisfies certain logically necessary invariance conditions. Logratio analysis and its associated distance measures satisfy these conditions.
Comments and authors' reply to this article were given in Math. Geol. 33, No. 7, 845--848, 849--860 (2001).
Zbl 1101.86310; Zbl 1011.86504