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Singularity and Nonnormality in the Classification of Compositional Data

Mathematical Geology

By:
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DOI: 10.1023/A:1021705120065

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Abstract

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore-Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Singularity and Nonnormality in the Classification of Compositional Data
Series title:
Mathematical Geology
DOI:
10.1023/A:1021705120065
Volume
30
Issue:
1
Year Published:
1998
Language:
English
Publisher:
Springer
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
5
Last page:
20
Number of Pages:
16