Principal component analysis of compositional data

by: J Aitchison

Biometrika, Vol. 70, No. 1. (1 April 1983), pp. 57-65.

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analysis, component, compositional, datasets, dimensionality, pca, principal, reduction

Abstract

Compositional data, consisting of vectors of proportions, have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. Moreover such data sets frequently display marked curvature so that linear techniques such as standard principal component analysis are likely to prove inadequate. From a critical reexamination of previous approaches we evolve, through adaptation of recently introduced transformation techniques for compositional data analysis, a log linear contrast form of principal component analysis and illustrate its advantages in applications. 10.1093/biomet/70.1.57

@article{citeulike:2294940, abstract = {Compositional data, consisting of vectors of proportions, have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. Moreover such data sets frequently display marked curvature so that linear techniques such as standard principal component analysis are likely to prove inadequate. From a critical reexamination of previous approaches we evolve, through adaptation of recently introduced transformation techniques for compositional data analysis, a log linear contrast form of principal component analysis and illustrate its advantages in applications. 10.1093/biomet/70.1.57}, author = {Aitchison, J. }, citeulike-article-id = {2294940}, doi = {http://dx.doi.org/10.1093/biomet/70.1.57}, journal = {Biometrika}, keywords = {analysis, component, compositional, datasets, dimensionality, pca, principal, reduction}, month = {April}, number = {1}, pages = {57--65}, posted-at = {2008-01-27 14:00:21}, priority = {5}, title = {Principal component analysis of compositional data}, url = {http://dx.doi.org/10.1093/biomet/70.1.57}, volume = {70}, year = {1983} }

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TY - JOUR ID - citeulike:2294940 L3 - citeulike-article-id:2294940 N2 - Compositional data, consisting of vectors of proportions, have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. Moreover such data sets frequently display marked curvature so that linear techniques such as standard principal component analysis are likely to prove inadequate. From a critical reexamination of previous approaches we evolve, through adaptation of recently introduced transformation techniques for compositional data analysis, a log linear contrast form of principal component analysis and illustrate its advantages in applications. 10.1093/biomet/70.1.57 IS - 1 JF - Biometrika EP - 65 TI - Principal component analysis of compositional data VL - 70 SP - 57 KW - analysis KW - component KW - compositional KW - datasets KW - dimensionality KW - pca KW - principal KW - reduction AU - Aitchison, J PY - 1983/04/01/ UR - http://dx.doi.org/10.1093/biomet/70.1.57 ER -

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