Embedding Functional Data: Multidimensional Scaling and Manifold Learning
Statistics Theory
2022-09-01 v1 Machine Learning
Metric Geometry
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2208.14540,
title = {Embedding Functional Data: Multidimensional Scaling and Manifold Learning},
author = {Ery Arias-Castro and Wanli Qiao},
journal= {arXiv preprint arXiv:2208.14540},
year = {2022}
}