Constrained nonmetric principal component analysis

  • Yuki Yamagishi
  • Kensuke TaniokaEmail author
  • Hiroshi Yadohisa
Original Paper


Constrained principal component analysis (CPCA) is a useful tool for comprehending the distinctive features of the classes of both subjects and variables in multivariate data. For example, given the class information of variables and subjects as external information, CPCA provides the principal components for the external information of both the variables and subjects. In addition to that, in CPCA, the fit results can be evaluated easily. In this study, we extend CPCA to categorical data via incorporating the notion of optimal scaling. We call our method constrained nonmetric principal component analysis (CNPCA). The advantage of this method is that it can consider the nonlinear relations between categories and estimate the components so that the fit is better than that in CPCA.


Optimal scaling Majorization Orthogonal projection operator 



We are grateful to the Reviewers for their comments which have helped us to improve the manuscript. This work was supported by JSPS KAKENHI Grant Numbers JP17K00060 and JP17K12797.


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Copyright information

© The Behaviormetric Society 2019

Authors and Affiliations

  • Yuki Yamagishi
    • 1
  • Kensuke Tanioka
    • 2
    Email author
  • Hiroshi Yadohisa
    • 3
  1. 1.Graduate School of Culture and Information ScienceDoshisha UniversityKyotoJapan
  2. 2.School of MedicineWakayama Medical UniversityWakayamaJapan
  3. 3.Department of Culture and Information ScienceDoshisha UnviersityKyotoJapan

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