Embedding Functional Data: Multidimensional Scaling and Manifold Learning
This work provides tools for analyzing functional data, which is incremental as it extends existing multivariate techniques to a new domain.
The authors adapted multidimensional scaling and manifold learning methods, specifically classical scaling and Isomap, to functional data analysis, demonstrating their application and emphasizing the importance of the ambient metric.
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.