Tangent-based manifold approximation with locally linear models

TL;DR

This paper introduces a greedy, tangent-based method for approximating manifolds with affine subspaces, effectively capturing manifold structure while outperforming existing techniques.

Contribution

The paper presents a novel tangent-based greedy algorithm for manifold approximation that improves accuracy and preserves structure better than prior methods.

Findings

The proposed method outperforms state-of-the-art manifold approximation techniques.

It effectively preserves the manifold's structure during approximation.

Experimental results demonstrate superior accuracy and efficiency.

Abstract

In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold's structure. For this purpose, we employ a greedy technique that partitions manifold samples into groups that can be each approximated by a low dimensional subspace. We start by considering each manifold sample as a different group and we use the difference of tangents to determine appropriate group mergings. We repeat this procedure until we reach the desired number of sample groups. The best low dimensional affine subspaces corresponding to the final groups constitute our approximate manifold representation. Our experiments verify the effectiveness of the proposed scheme and show its superior performance compared to state-of-the-art methods for manifold approximation.