Singular value decomposition (SVD) of skew-symmetric matrices was proposed by Gower (Recent Developments in Statistics, Amsterdam: North Holland, 1977) to represent asymmetry of proximity data. Some authors considered the plane (bimension or hedron) determined by the first two singular vectors to detect orderings (seriation) for preference or dominance data. Following these approaches, in this paper some procedures of asymmetric multidimensional scaling useful for seriation are proposed focalizing on a model that is a particular case of rank-2 SVD model. An application to Thurstone’s paired comparison data on the relative seriousness of crime is also presented.
Bove, G. (2013). Asymmetric multidimensional scaling models for seriation. In Statistical Models for Data Analysis (pp. 55-62). BERLIN : Springer [10.1007/978-3-319-00032-9_7].
Asymmetric multidimensional scaling models for seriation
BOVE, Giuseppe
2013-01-01
Abstract
Singular value decomposition (SVD) of skew-symmetric matrices was proposed by Gower (Recent Developments in Statistics, Amsterdam: North Holland, 1977) to represent asymmetry of proximity data. Some authors considered the plane (bimension or hedron) determined by the first two singular vectors to detect orderings (seriation) for preference or dominance data. Following these approaches, in this paper some procedures of asymmetric multidimensional scaling useful for seriation are proposed focalizing on a model that is a particular case of rank-2 SVD model. An application to Thurstone’s paired comparison data on the relative seriousness of crime is also presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
