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Ranking principal components to reflect group structure
Author(s) -
Krzanowski W. J.
Publication year - 1992
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.1180060207
Subject(s) - principal component analysis , mathematics , canonical analysis , ranking (information retrieval) , group (periodic table) , multivariate statistics , linear discriminant analysis , random variate , statistics , multivariate analysis of variance , canonical correlation , degrees of freedom (physics and chemistry) , artificial intelligence , computer science , chemistry , random variable , physics , organic chemistry , quantum mechanics
Canonical variate analysis is the appropriate descriptive technique for multivariate data which have an a priori group structure, but problems arise with this technique when there are more variables than within‐group degrees of freedom because of singularity of matrices. In such cases it is shown through illustrative examples that principal component analysis is a viable substitute provided that the principal components are ranked according to the canonical variate criterion (ratio‐ of between‐ to within‐group variances) rather than the usual criterion of total variance. This ranking can also be used to select components for subsequent discriminant analysis.