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Biometrika 1985 72(2):241-252; doi:10.1093/biomet/72.2.241
© 1985 by Biometrika Trust
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Canonical and principal components of shape

JOHN N. DARROCH and JAMES E. MOSIMANN

School of Mathematical Sciences, Flinders University Adelaide, S.A., 5042, Australia
Division of Computer Research and Technology, National Institute of Health Bethesda, Maryland 20014, U.S.A.

Canonical components of shape, discriminant functions of shape and principal components of shape are defined from log shape vectors. Several results relate these components to the corresponding components of log measurement and to a particular size variable referred to as residual log size. The latter variable accounts for the variation which cannot be attributed to shape. Canonical components of shape are determined for Anderson's data for three species of iris, as well as for data on red-winged blackbirds in Florida. While the three species differ strongly in shape as well as in size, male and female blackbirds differ strongly in size but not much in shape. Principal components of shape are illustrated with the blackbird data and the most constant principal component is found to be interesting.

Key Words: Canonical component • Discriminant function • Growth-invariant discriminant function • Tris data • Principal component • Shape • Size


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