The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
The biplot graphic display of matrices with application to principal component analysis
Abstract
Any matrix of rank two can be displayed as a biplot which consists of a vector for each row and a vector for each column, chosen so that any element of the matrix is exactly the inner product of the vectors corresponding to its row and to its column. If a matrix is of higher rank, one may display it approximately by a biplot of a matrix of rank two which approximates the original matrix. The biplot provides a useful tool of data analysis and allows the visual appraisal of the structure of large data matrices. It is especially revealing in principal component analysis, where the biplot can show inter-unit distances and indicate clustering of units as well as display variances and correlations of the variables.
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Citations
Cites
Singular value decomposition and least squares solutions
Golub, G. H., & Reinsch, C. (1970) · Numerische Mathematik · doi:10.1007/bf02163027 · Cited by 2,929
Cited by
Principal component analysis: A review and recent developments
Jolliffe, I. T., & Cadima, J. (2016) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2015.0202 · Cited by 10,117
Bro, R., & Smilde, A. K. (2014) · Anal. Methods · doi:10.1039/c3ay41907j · Cited by 3,038
What is principal component analysis?
Ringnér, M. (2008) · Nature Biotechnology · doi:10.1038/nbt0308-303 · Cited by 2,407
Cultivar Evaluation and Mega‐Environment Investigation Based on the GGE Biplot
Yan, W., Hunt, L. A., Sheng, Q., & Szlavnics, Z. (2000) · Crop Science · doi:10.2135/cropsci2000.403597x · Cited by 1,977
Ter Braak, C. J. F., & Prentice, I. C. (1988) · Advances in Ecological Research · doi:10.1016/s0065-2504(08)60183-x · Cited by 1,963
Metadata
- Authors
- GABRIEL, K. R.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1971
- Volume
- 58
- Issue
- 3
- Pages
- 453-467
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2104146802
- Cited by
- 3,037
- References
- 1
- FWCI
- 3.42
- Type
- journal article
- Language
- en
- Open access
- closed
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