Exploratory approaches to seriation by asymmetric multidimensional scaling

Seriation and multidimensional scaling are two techniques aimed at exploring relationships in dominance or proximity data matrices. Rodgers & Thompson (1992) argued that the two approaches can profitably interact in the analysis of asymmetric proximity matrices, they proposed a method that uses seriation to define an empirical ordering of the objects, and symmetric multidimensional scaling to scale the two separate triangles of the proximity matrix defined by this ordering (an approach anticipated by method 3 in Gower (1977)). Following a similar idea, in this paper some procedures are proposed to explore seriation by asymmetric multidimensional scaling. The paper focalizes on skew-symmetric components of a particular class of asymmetric matrices (including e.g. tournament or paired comparison matrices). Two small examples of application are provided to illustrate the procedures respectively in the dichotomous and quantitative case.