The decomposition of any square matrix in symmetric and skew- symmetric components has inspired many methods in asymmetric multidimensional scaling (reviews are provided e.g. in Zielman and Heiser, 1996, Bove and Rocci, 1999, Borg and Groenen, 2005, Saito and Yadohisa, 2005). Separate analyzes of the two components seem preferable when symmetry is much more relevant in the data or when we want to represent separately skew-symmetric residuals of statistical models (e.g. symmetry or quasi-symmetry). In this paper two and three-way methods for the analysis of skew-symmetry are reviewed focalizing on multidimensional models with graphical capabilities.
Bove, G. (2010). Methods for the Analysis of Skew-symmetry in Asymmetric Multidimensional Scaling. In Classification as a Tool for Research. Studies in Classification, Data Analysis, and Knowledge Organization (pp. 271-278). BERLIN HEIDELBERG : Springer-Verlag [10.1007/978-3-642-10745-0_29].
Methods for the Analysis of Skew-symmetry in Asymmetric Multidimensional Scaling
BOVE, Giuseppe
2010-01-01
Abstract
The decomposition of any square matrix in symmetric and skew- symmetric components has inspired many methods in asymmetric multidimensional scaling (reviews are provided e.g. in Zielman and Heiser, 1996, Bove and Rocci, 1999, Borg and Groenen, 2005, Saito and Yadohisa, 2005). Separate analyzes of the two components seem preferable when symmetry is much more relevant in the data or when we want to represent separately skew-symmetric residuals of statistical models (e.g. symmetry or quasi-symmetry). In this paper two and three-way methods for the analysis of skew-symmetry are reviewed focalizing on multidimensional models with graphical capabilities.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
