Multidimensional scaling on metric measure spaces

  title={Multidimensional scaling on metric measure spaces},
  author={Henry Adams and Mark Blumstein and Lara Kassab},
  journal={Rocky Mountain Journal of Mathematics},
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its optimality properties and goodness of fit. Further, we present a notion of MDS on infinite metric measure spaces that generalizes these optimality properties. As a consequence we can study the MDS embeddings of the geodesic circle $S^1$ into $\mathbb{R}^m$ for all $m… 

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