Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
1970/09/01 by J. Douglas Carroll, Jih-Jie Chang · 4,732 citations
Agricultural and Biological Sciences · Computer Science · Mathematics · Psychology · #Blind Source Separation Techniques #Generalization #Geometry #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Multidimensional scaling #Perception #Psychology #Scalar (mathematics) #Scaling #Sensory Analysis and Statistical Methods #Statistics #Tensor decomposition and applications
paper · doi:10.1007/bf02310791
published in Psychometrika 35(3), 283-319 (Springer Science+Business Media)
openalex publication_date 1970/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract
An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychological space”. A corresponding method of analyzing similarities data is proposed, involving a generalization of “Eckart-Young analysis” to decomposition of three-way (or higher-way) tables. In the present case this decomposition is applied to a derived three-way table of scalar products between stimuli for individuals. This analysis yields a stimulus by dimensions coordinate matrix and a subjects by dimensions matrix of weights. This method is illustrated with data on auditory stimuli and on perception of nations.
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