Generalized GIPSCAL re-revisited: a fast convergent algorithm with acceleration by the minimal polynomial extrapolation

Authors:
Sébastien Loisel;Yoshio Takane
Affiliations:
Department of Mathematics, Heriot-Watt University, Edinburgh, UK EH14 4AS;Department of Psychology, McGill University, Montreal, Canada QC
Venue:
Advances in Data Analysis and Classification
Year:
2011

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Abstract

Generalized GIPSCAL, like DEDICOM, is a model for the analysis of square asymmetric tables. It is a special case of DEDICOM, but unlike DEDICOM, it ensures the nonnegative definiteness (nnd) of the model matrix, thereby allowing a spatial representation of the asymmetric relationships among "objects". A fast convergent algorithm was developed for GIPSCAL with acceleration by the minimal polynomial extrapolation. The proposed algorithm was compared with Trendafilov's algorithm in computational speed. The basic algorithm has been adapted to various extensions of GIPSCAL, including off-diagonal DEDICOM/GIPSCAL, and three-way GIPSCAL.