Applying Ricci Flow to High Dimensional Manifold Learning

TL;DR

This paper introduces RF-ML, a novel manifold learning algorithm that uses Ricci flow to account for curvature, improving neighborhood preservation in high-dimensional data reduction.

Contribution

The paper proposes a new Ricci flow-based algorithm for manifold learning that enhances neighborhood preservation by incorporating curvature information.

Findings

RF-ML improves neighborhood preservation over traditional methods.

Ricci flow effectively smooths manifold curvature during dimension reduction.

Experimental results demonstrate superior performance of RF-ML in high-dimensional datasets.

Abstract

Traditional manifold learning algorithms often bear an assumption that the local neighborhood of any point on embedded manifold is roughly equal to the tangent space at that point without considering the curvature. The curvature indifferent way of manifold processing often makes traditional dimension reduction poorly neighborhood preserving. To overcome this drawback we propose a new algorithm called RF-ML to perform an operation on the manifold with help of Ricci flow before reducing the dimension of manifold.