The diffusion geometry of fibre bundles: horizontal diffusion maps (Q2659718)

In the paper under review, one introduces the framework of horizontal diffusion maps, designed for analyzing complex data sets with non-scalar or functional pairwise relations. In this framework, a data set with pairwise structural correspondences is modeled as a locally trivial (not necessarily principal or vector) fibre bundle equipped with a connection. This setting shows the sub-Riemannian structure of high-dimensional data sets, and provides a nonparametric learning framework for data sets with structural correspondences.