Isometric Multi-Manifolds Learning

TL;DR

This paper introduces a novel multi-manifolds learning algorithm, M-Isomap, which accurately preserves intra- and inter-manifold geodesics, extending Isomap's capabilities to data distributed on multiple manifolds.

Contribution

The paper proposes M-Isomap, a new algorithm that effectively learns data on multiple manifolds, and revises the existing D-C Isomap for multi-manifold learning, demonstrating improved performance.

Findings

M-Isomap preserves intra- and inter-manifold geodesics accurately.

Revised D-C Isomap can learn multi-manifolds data effectively.

Experimental results show the proposed methods outperform previous approaches.

Abstract

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to multi-manifolds learning. In this paper, we first proposed a new multi-manifolds learning algorithm (M-Isomap) with help of a general procedure. The new algorithm preserves intra-manifold geodesics and multiple inter-manifolds edges precisely. Compared with previous methods, this algorithm can isometrically learn data distributed on several manifolds. Secondly, the original multi-cluster manifold learning algorithm first proposed in \cite{DCIsomap} and called D-C Isomap has been revised so that the revised D-C Isomap can learn multi-manifolds data. Finally, the features and effectiveness of the proposed multi-manifolds learning algorithms are demonstrated and compared through experiments.