The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Biplots of Compositional Data
Open accessAbstract
Summary: The singular value decomposition and its interpretation as a linear biplot have proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the specific case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to the special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is applied to a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.
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Citations
Cites
The Statistical Analysis of Compositional Data
Aitchison, J. (1986) · doi:10.1007/978-94-009-4109-0 · Cited by 4,383
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
“It is possible to glean substantial qualitative information regarding the quality of the dataset and the relationships between groups with this tool (Aitchison and Greenacre, 2002; Gloor et al., 2016b), and examples are shown in the “Biplot” section of the Supplement.”
MethodGreenacre, M., Groenen, P. J. F., Hastie, T., D’Enza, A. I., Markos, A., & Tuzhilina, E. (2022) · Nature Reviews Methods Primers · doi:10.1038/s43586-022-00184-w · Cited by 1,773
Self-citationIt's all relative: analyzing microbiome data as compositions
Gloor, G. B., Wu, J. R., Pawlowsky-Glahn, V., & Egozcue, J. J. (2016) · Annals of Epidemiology · doi:10.1016/j.annepidem.2016.03.003 · Cited by 323
Reimann, C., Filzmoser, P., Fabian, K., Hron, K., Birke, M., Demetriades, A., Dinelli, E., & Ladenberger, A. (2012) · Science of The Total Environment · doi:10.1016/j.scitotenv.2012.02.032 · Cited by 262
Choi, Y., Lichterman, J. N., Coughlin, L. A., Poulides, N., Li, W., Del Valle, P., Palmer, S. N., Gan, S., Kim, J., Zhan, X., et al. (2023) · Science Immunology · doi:10.1126/sciimmunol.abo2003 · Cited by 132
Metadata
- Authors
- Aitchison, J., & Greenacre, M.
- Venue
- Journal of the Royal Statistical Society Series C: Applied Statistics
- Publisher
- Oxford University Press (OUP)
- Published
- 2002-10-01
- Volume
- 51
- Issue
- 4
- Pages
- 375-392
- ISSN
- 0035-9254 (ISSN-L)
- 1467-9876
- OpenAlex
- W2108303460
- Cited by
- 711
- References
- 1
- FWCI
- 12.38
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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