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Author Mitteroecker, Philipp ♦ Bookstein, Fred
Source SpringerLink
Content type Text
Publisher Springer US
File Format PDF
Copyright Year ©2011
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Life sciences; biology
Subject Keyword Canonical variate analysis ♦ Linear discriminant function ♦ Ordination ♦ Principal component analysis ♦ Procrustes ♦ Selection gradient ♦ Ecology ♦ Evolutionary Biology ♦ Developmental Biology ♦ Animal Genetics and Genomics ♦ Human Genetics
Abstract Linear discriminant analysis (LDA) is a multivariate classification technique frequently applied to morphometric data in various biomedical disciplines. Canonical variate analysis (CVA), the generalization of LDA for multiple groups, is often used in the exploratory style of an ordination technique (a low-dimensional representation of the data). In the rare case when all groups have the same covariance matrix, maximum likelihood classification can be based on these linear functions. Both LDA and CVA require full-rank covariance matrices, which is usually not the case in modern morphometrics. When the number of variables is close to the number of individuals, groups appear separated in a CVA plot even if they are samples from the same population. Hence, reliable classification and assessment of group separation require many more organisms than variables. A simple alternative to CVA is the projection of the data onto the principal components of the group averages (between-group PCA). In contrast to CVA, these axes are orthogonal and can be computed even when the data are not of full rank, such as for Procrustes shape coordinates arising in samples of any size, and when covariance matrices are heterogeneous. In evolutionary quantitative genetics, the selection gradient is identical to the coefficient vector of a linear discriminant function between the populations before vs. after selection. When the measured variables are Procrustes shape coordinates, discriminant functions and selection gradients are vectors in shape space and can be visualized as shape deformations. Except for applications in quantitative genetics and in classification, however, discriminant functions typically offer no interpretation as biological factors.
ISSN 00713260
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2011-02-25
Publisher Place Boston
e-ISSN 19342845
Journal Evolutionary Biology
Volume Number 38
Issue Number 1
Page Count 15
Starting Page 100
Ending Page 114


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Source: SpringerLink