Embedding Functional Data: Multidimensional Scaling and Manifold Learning

TL;DR

This paper adapts multidimensional scaling and manifold learning techniques like classical scaling and Isomap to functional data analysis, emphasizing the importance of the ambient metric in these methods.

Contribution

It extends classical scaling and Isomap to the functional data setting, providing a theoretical and methodological framework for their application.

Findings

Demonstrates the adaptation of multidimensional scaling to functional data

Highlights the importance of the ambient metric in functional manifold learning

Provides insights into the use of classical scaling and Isomap for functional data

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.