An acceleration method for Ten Berge et al.’s algorithm for orthogonal INDSCAL

Abstract

INDSCAL (INdividual Differences SCALing) is a useful technique for investigating both common and unique aspects of K similarity data matrices. The model postulates a common stimulus configuration in a low-dimensional Euclidean space, while representing differences among the K data matrices by differential weighting of dimensions by different data sources. Since Carroll and Chang proposed their algorithm for INDSCAL, several issues have been raised: non-symmetric solutions, negative saliency weights, and the degeneracy problem. Orthogonal INDSCAL (O-INDSCAL) which imposes orthogonality constraints on the matrix of stimulus configuration has been proposed to overcome some of these difficulties. Two algorithms have been proposed for O-INDSCAL, one by Ten Berge, Knol, and Kiers, and the other by Trendafilov. In this paper, an acceleration technique called minimal polynomial extrapolation is incorporated in Ten Berge et al.’s algorithm. Simulation studies are conducted to compare the performance of the three algorithms (Ten Berge et al.’s original algorithm, the accelerated algorithm, and Trendafilov’s). Possible extensions of the accelerated algorithm to similar situations are also suggested.