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Some distance properties of latent root and vector methods used in multivariate analysis
Abstract
This paper is concerned with the representation of a multivariate sample of size n as points P1, P2, …, Pn in a Euclidean space. The interpretation of the distance Δ(Pi, Pj) between the ith and jth members of the sample is discussed for some commonly used types of analysis, including both Q and R techniques. When all the distances between n points are known a method is derived which finds their co-ordinates referred to principal axes. A set of necessary and sufficient conditions for a solution to exist in real Euclidean sapce is found. Q and R techniques are defined as being dual to one another when they both lead to a set of n points with the same inter-point distances. Pairs of dual techniques are derived. In factor analysis the distances between points whose co-ordinrates are the estimated factor scores can be interpreted as D2 with a singular dispersion matrix.
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Cited by
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Metadata
- Authors
- GOWER, J. C.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1966
- Volume
- 53
- Issue
- 3-4
- Pages
- 325-338
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W1999597013
- Cited by
- 4,293
- References
- 0
- FWCI
- 20.87
- Type
- journal article
- Language
- en
- Open access
- closed
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- GOWER, J. C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika. https://doi.org/10.1093/biomet/53.3-4.325
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
