Constrained nonmetric principal component analysis
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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.
KeywordsOptimal 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.
- Bock RD (1960) Methods and applications of optimal scaling, Psychometric Laboratory Report, University of North CarolinaGoogle Scholar
- Nishisato S, Lawrence DR (1989) Dual scaling of multiway data matrices: several variants. In: Coppi R, Bolasco S (eds) Multiway data analysis. North-Holland, Amsterdam, pp 317–326Google Scholar
- Murakami T, Kiers HAL, ten Berge JMF (1999) Non-metric principal component analysis for categorical variables with multiple quantifications (unpublished manuscript)Google Scholar
- Young FW, de Leeuw J, Takane Y (1980) Quantifying qualitative data. In: Lantermann ED, Feger H (eds) Similarity and choice. Huber, BernGoogle Scholar