Nonmetric linear biplots. (English) Zbl 0939.62058

Summary: A methodology is developed for constructing linear biplots for a class of nonmetric multidimensional scaling methods for multivariate data. The nonlinear transformations of nonmetric scaling manifest themselves in irregularly spaced calibration markers. Two approaches are examined, one based on Procrustean embedding, the other on a modification of the popular regression method. The widespread use of an unmodified regression method in association with nonlinear transformations is questioned. An example is given. The methodology presented here could potentially be developed to give an optimal represention of a matrix in fewer geometric dimensions than its rank.


62H99 Multivariate analysis
62A09 Graphical methods in statistics
91C15 One- and multidimensional scaling in the social and behavioral sciences
62H25 Factor analysis and principal components; correspondence analysis
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