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.

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