Uncertainty quantification of diffusion maps

Nonlinear dimensionality reduction is a critical procedure in data-driven analyses, where data lives in a high-dimensional space and thus imposes high computational costs. Diffusion Maps, as a newer reduction technique, has been successfully applied to various problems. In this paper, we discuss a probabilistic approach to address the errors accrued in the application of Diffusion Maps. We demonstrate how these errors originate in the reduction process and also discuss their implication on the reduced representation. Numerical results from standard examples are included.