Curvature-aware manifold learning

PATTERN RECOGNITION

卷:83

Article

Li, Yangyang^1,2 

[1] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab MADIS, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Beijing 100049, Peoples R China

关键词: Manifold learning;    Riemannian curvature;    Second fundamental form;    Hessian operator;   

DOI  :  10.1016/j.patcog.2018.06.007

来源: Elsevier

【 摘 要 】

One of the fundamental assumptions of traditional manifold learning algorithms is that the embedded manifold is globally or locally isometric to Euclidean space. Under this assumption, these algorithms divided manifold into a set of overlapping local patches which are locally isometric to linear subsets of Euclidean space. Then the learnt manifold would be a flat manifold with zero Riemannian curvature. But in the general cases, manifolds may not have this property. To be more specific, the traditional manifold learning does not consider the curvature information of the embedded manifold. In order to improve the existing algorithms, we propose a curvature-aware manifold learning algorithm called CAML. Without considering the local and global assumptions, we will add the curvature information to the process of manifold learning, and try to find a way to reduce the redundant dimensions of the general manifolds which are not isometric to Euclidean space. The experiments have shown that CAML has its own advantage comparing to other traditional manifold learning algorithms in the sense of the neighborhood preserving ratios (NPR) on synthetic databases and classification accuracies on image set classification. (C) 2018 Elsevier Ltd. All rights reserved.

【 授权许可】

Free