TY - JOUR

T1 - An acceleration method for Ten Berge et al.'s algorithm for orthogonal INDSCAL

AU - Takane, Yoshio

AU - Jung, Kwanghee

AU - Hwang, Heungsun

N1 - Funding Information:
The work reported in this paper has been supported by SSHRC Research Grant 36952 to the first author, and by NSERC Discovery Grant 290439 to the third author.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Dynamical system algorithm

KW - Minimal polynomial extrapolation (MPE)

KW - Multi-way data analysis

KW - Singular value decomposition (SVD) algorithm

UR - http://www.scopus.com/inward/record.url?scp=77954537722&partnerID=8YFLogxK

U2 - 10.1007/s00180-010-0184-6

DO - 10.1007/s00180-010-0184-6

M3 - Article

AN - SCOPUS:77954537722

VL - 25

SP - 409

EP - 428

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

IS - 3

ER -