MESS: Manifold Embedding Motivated Super Sampling

Abstract: Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this manifold assumption one generally requires the manifold to be locally sampled to a certain density such that features of the manifold can be observed. However, for increasing intrinsic dimensionality of a data set the required data density introduces the need for very large data sets, resulting in one of the many faces of the curse of dimensionality. To combat the increased requirement for local data density we propose a framework to generate virtual data points that faithful to an approximate embedding function underlying the manifold observable in the data.