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Embedding Functional Data: Multidimensional Scaling and Manifold Learning

arXiv 2208.14540 ↗First posted 30 Aug 2022math.ST cs.LG math.MGcited by 0

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Abstract (arXiv)

We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical methods that have played important roles in these area -- and showcase their use in the context of functional data analysis. In the process, we highlight the crucial role that the ambient metric plays.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 132 references that are in the map. First posted on arXiv 30 Aug 2022.

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References · 15

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
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  12. 2018Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learningcited by 9
3 more
  1. 2017Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximationcited by 4
  2. 2020Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Settingcited by 3
  3. 2016Derivation of human chromatic discrimination ability from an information-theoretical notion of distance in color spacecited by 1

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