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

Sébastien Loisel; Yoshio Takane

doi:10.1007/s11634-010-0083-2

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

Sébastien Loisel, Yoshio Takane

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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. © 2011 Springer-Verlag.

Original language	English
Pages (from-to)	57-75
Number of pages	19
Journal	Advances in Data Analysis and Classification
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/s11634-010-0083-2
Publication status	Published - Apr 2011

Keywords

Asymmetric square tables
DEDICOM
Diagonal estimation
Dynamical system algorithm
Singular value decomposition (SVD)
Three-way data

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10.1007/s11634-010-0083-2

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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. {\textcopyright} 2011 Springer-Verlag.",

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KW - Asymmetric square tables

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KW - Diagonal estimation

KW - Dynamical system algorithm

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

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