# Embedding Functional Data: Multidimensional Scaling and Manifold Learning

arXiv: https://arxiv.org/abs/2208.14540 · HTML: https://mlsanity.com/paper/2208.14540/

## 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.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [A review on distance based time series classification](https://mlsanity.com/paper/1806.04509/) (2018)
- [EM Converges for a Mixture of Many Linear Regressions](https://mlsanity.com/paper/1905.12106/) (2019)
- [Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods](https://mlsanity.com/paper/1310.5107/) (2013)
- [Message-passing algorithms for synchronization problems over compact groups](https://mlsanity.com/paper/1610.04583/) (2016)
- [Optimal transport natural gradient for statistical manifolds with continuous sample space](https://mlsanity.com/paper/1805.08380/) (2018)
- [Intrinsic Isometric Manifold Learning with Application to Localization](https://mlsanity.com/paper/1806.00556/) (2018)
- [Minimax Optimal Estimation of KL Divergence for Continuous Distributions](https://mlsanity.com/paper/2002.11599/) (2020)
- [Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning](https://mlsanity.com/paper/1810.09569/) (2018)
- [Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation](https://mlsanity.com/paper/1706.09441/) (2017)
- [Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting](https://mlsanity.com/paper/2011.12478/) (2020)
- [Derivation of human chromatic discrimination ability from an information-theoretical notion of distance in color space](https://mlsanity.com/paper/1611.07272/) (2016)

## 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.