Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding

Abstract

We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling,including internal unfolding and external unfolding. We first follow Shepard (1966) and work in a continuum model to gain insight. We then follow Kleindessner and von Luxburg (2014) and work in an asymptotic discrete setting.

final version, focusing on the point model and with discrete-to-continuous convergence, to be published in SIMODS