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Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal Unfolding and External Unfolding
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DOI：10.1137/24M1691624.png)
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Abstract
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We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling, including internal unfolding and external unfolding. We first follow Shepard [J. Math. Psychol., 3 (1966), pp. 287--315] and work in a continuum model to gain insight. We then follow Kleindessner and von Luxburg [Uniqueness of ordinal embedding, in Conference on Learning Theory, 2014, pp. 40--67] and work in an asymptotic discrete setting.
Keywords:
ordinal embedding
nonmetric multidimensional scaling
internal unfolding
external unfolding
lateration
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