Uniqueness of ordinal embedding

author: Matthäus Kleindessner, Department of Informatics, University of Hamburg
published: July 15, 2014,   recorded: June 2014,   views: 2701


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Ordinal embedding refers to the following problem: all we know about an unknown set of points x1,…,xn∈Rd are ordinal constraints of the form ∥xi−xj∥<∥xk−xl∥; the task is to construct a realization y1,…,yn∈Rd that preserves these ordinal constraints. It has been conjectured since the 1960ies that upon knowledge of all ordinal constraints a large but finite set of points can be approximately reconstructed up to a similarity transformation. The main result of our paper is a formal proof of this conjecture.

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