MESS: Manifold Embedding Motivated Super Sampling

TL;DR

This paper introduces MESS, a framework for generating virtual data points to improve local sampling of high-dimensional manifolds, addressing the curse of dimensionality in machine learning.

Contribution

The paper proposes a novel manifold embedding motivated super sampling method to generate virtual data points, enhancing local sampling in high-dimensional data sets.

Findings

Improves local data density on manifolds

Reduces the impact of the curse of dimensionality

Enhances manifold learning accuracy

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.