The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Principal component analysis of compositional data
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.
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Cites
LIII. On lines and planes of closest fit to systems of points in space
Pearson, K. (1901) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440109462720 · Cited by 11,934
Analysis of a complex of statistical variables into principal components.
Hotelling, H. (1933) · Journal of Educational Psychology · doi:10.1037/h0071325 · Cited by 9,633
The Statistical Analysis of Compositional Data
Aitchison, J. (1982) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1982.tb01195.x · Cited by 3,405
Self-citationMethods for Statistical Data Analysis of Multivariate Observations.
Sen, P. K., & Gnanadesikan, R. (1978) · Journal of the American Statistical Association · doi:10.2307/2286626 · Cited by 897
MOSIMANN, J. E. (1962) · Biometrika · doi:10.1093/biomet/49.1-2.65 · Cited by 458
Logistic-Normal Distributions: Some Properties and Uses
Aitchison, J., & Shen, S. M. (1980) · Biometrika · doi:10.2307/2335470 · Cited by 375
Self-citationMultivariate Analysis and Multidimensional Geometry
Gower, J. C. (1967) · The Statistician · doi:10.2307/2987199 · Cited by 213
A new approach to null correlations of proportions
Aitchison, J. (1981) · Journal of the International Association for Mathematical Geology · doi:10.1007/bf01031393 · Cited by 186
Self-citationReducing the dimensionality of compositional data sets
Aitchison, J. (1984) · Mathematical Geology · doi:10.1007/bf01029321 · Cited by 91
Self-citation
Cited by
Microbiome Datasets Are Compositional: And This Is Not Optional
Gloor, G. B., Macklaim, J. M., Pawlowsky-Glahn, V., & Egozcue, J. J. (2017) · Frontiers in Microbiology · doi:10.3389/fmicb.2017.02224 · Cited by 3,044
“The replacement for β-diversity exploration of microbiome data is the variance-based compositional principal component (PCA) biplot (Aitchison, 1983; Aitchison and Greenacre, 2002) where the relationship between inter-OTU variance and sample distance can be observed (Gloor et al., 2016b).”
MethodSchild, T., Lomax, B. A., Conti, M., Aridon, G., Harries, D., & Hadler, K. (2025) · Acta Astronautica · doi:10.1016/j.actaastro.2025.02.021 · Cited by 8
Metadata
- Authors
- AITCHISON, J.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1983
- Volume
- 70
- Issue
- 1
- Pages
- 57-65
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2022080111
- Cited by
- 567
- References
- 9
- FWCI
- 4.38
- Type
- journal article
- Language
- en
- Open access
- closed
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