Abstract

We provide a way to infer about existence of topological circularity in high-dimensional data sets in R d from its projection in R 2 obtained through a fast manifold learning map as a function of the high-dimensional dataset X and a particular choice of a positive real σ known as bandwidth parameter. At the same time we also provide a way to estimate the optimal bandwith for fast manifold learning in this setting through minimization of these functions of bandwidth. We also provide limit theorems to characterize the behavior of our proposed functions of bandwidth. 

Keywords: Fast Manifold Learning, Bandwidth Selection, Topological Circularity, Machine Learning