Embedding distributional data
The Annals of Statistics · 2025 · Volume 53 · Issue 2
Abstract
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.
Keywords
62B11, 62H25, 62R10, 62R10, 62R20, 62R30, classical scaling, dimensionality reduction, distributional data analysis (DDA), embedding problem, Fisher metric, Functional data analysis (FDA), information geometry, ISOMAP, multidimensional scaling, Optimal transport, Principal Component Analysis, RKHS metric, Wasserstein metric
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