Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding
Statistics Theory
2025-06-19 v3 Statistics Theory
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.
Keywords
Cite
@article{arxiv.2310.00211,
title = {Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding},
author = {Ery Arias-Castro and Clément Berenfeld and Daniel Kane},
journal= {arXiv preprint arXiv:2310.00211},
year = {2025}
}
Comments
final version, focusing on the point model and with discrete-to-continuous convergence, to be published in SIMODS