Embedding distributional data
Ery Arias-Castro, Wanli Qiao · The Annals of Statistics · 2025
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for Euclidean data to be applicable to distributional data. We focus on classical scaling and Isomap—prototypical methods that have played important roles in these areas—and showcase their use in the context of distributional data analysis. In the process, we highlight the crucial role that the ambient metric plays.