Principal component analysis with external information on both subjects and variables

Yoshio Takane, Tadashi Shibayama

Research output: Contribution to journalArticlepeer-review

98 Citations (Scopus)


A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.

Original languageEnglish
Pages (from-to)97-120
Number of pages24
Issue number1
Publication statusPublished - 1991 Mar 1
Externally publishedYes


  • GMANOVA (growth curve models)
  • QR decomposition
  • dual scaling
  • generalized singular value decomposition (GSVD)
  • orthogonal projection operator
  • redundancy analysis
  • trace-orthogonality
  • two-way CANDELINC
  • vector preference models

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics


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