ISSN:
1573-8868
Keywords:
scale invariance
;
permutation invariance
;
perturbation invariance
;
covariance structure
;
subcomposition
;
equivalence classes
;
groups
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Mathematics
Notes:
Abstract Simple perceptions about the nature of compositions lead through logical necessity to certain forms of analysis of compositional data. In this paper the consequences of essential requirements of scale, perturbation and permutation invariance, together with that of subcompositional dominance, are applied to the problem of characterizing change and measures of difference between two compositions. It will be shown that one strongly advocated scalar measure of difference fails these tests of logical necessity, and that one particular form of scalar measure of difference (the sum of the squares of all possible logratio differences in the components of the two compositions), although not unique, emerges as the simplest and most tractable satisfying the criteria.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00891269
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