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 · 177 citations
Agricultural and Biological Sciences · Computer Science · Mathematics · #Sensory Analysis and Statistical Methods #Blind Source Separation Techniques #Tensor decomposition and applications

paper · doi:10.1007/bf02310791

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.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• The Approximation of One Matrix by Another of Lower Rank

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