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Orthogonal canonical variates for discrimination and classification
Author(s) -
Krzanowski W. J.
Publication year - 1995
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180090608
Subject(s) - principal component analysis , orthogonality , canonical correlation , data matrix , mathematics , linear discriminant analysis , random variate , canonical analysis , multivariate statistics , data set , matrix (chemical analysis) , partial least squares regression , statistics , pattern recognition (psychology) , artificial intelligence , computer science , random variable , clade , biochemistry , chemistry , geometry , materials science , composite material , gene , phylogenetic tree
Abstract A new set of derived variables is proposed for exhibiting group separation in multivariate data on for preprocessing such data prior to discriminant analysis. The technique combines optimal features of canonical variate analysis and principal component analysis: the derived variables are linear combinations of the original variables that optimize the canonical variate criterion (ratio of between‐group to within‐group variance) but subject to the orthogonality constraints of principal components. In this formulation the canonical variates can be derived even when the within‐group matrix is singular (i.e. when there are more variables than objects in the data matrix). A simple computational algorithm for extraction of these variables is proposed. The methods are illustrated on several data sets and compared with alternative techniques such as principal component analysis and partial least squares.