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Cited by 4,293

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Some distance properties of latent root and vector methods used in multivariate analysis

GOWER, J. C.·1966·Biometrika
DOI 10.1093/biomet/53.3-4.325
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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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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
DOI
10.1093/biomet/53.3-4.325
OpenAlex
W1999597013
Cited by
4,293
References
0
FWCI
20.87
Type
journal article
Language
en
Open access
closed

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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.