Logratio analysis and compositional distance

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...

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Bibliographic Details
Published in:Mathematical geology 2000-04, Vol.32 (3), p.271-275
Main Authors: AITCHISON, J, BARCELO-VIDAL, C, MARTIN-FERNANDEZ, J. A, PAWLOWSKY-GLAHN, V
Format: Article
Language:English
Subjects:
Cluster analysis
Earth sciences
Earth, ocean, space
Exact sciences and technology
General geology
Studies
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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.[PUBLICATION ABSTRACT]
ISSN:0882-8121
1874-8961
1573-8868
1874-8953
DOI:10.1023/a:1007529726302