Curvature-aware manifold learning

doi:10.1016/j.patcog.2018.06.007

CSpace

	Curvature-aware manifold learning
	Li, Yangyang 1,2
	2018-11-01
发表期刊	PATTERN RECOGNITION
ISSN	0031-3203
卷号	83 页码:273-286
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.
关键词	Manifold learning Riemannian curvature Second fundamental form Hessian operator
DOI	10.1016/j.patcog.2018.06.007
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB1000902] ; NSFC[61232015] ; NSFC[61472412] ; NSFC[61621003] ; Beijing Science and Technology Project: Machine Learning based Stomatology; Tsinghua-Tencent-AMSS-Joint Project: WWW Knowledge Structure and its Application
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS记录号	WOS:000442172200021
出版者	ELSEVIER SCI LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31084
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Yangyang
作者单位	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
推荐引用方式 GB/T 7714	Li, Yangyang. Curvature-aware manifold learning[J]. PATTERN RECOGNITION,2018,83:273-286.
APA	Li, Yangyang.(2018).Curvature-aware manifold learning.PATTERN RECOGNITION,83,273-286.
MLA	Li, Yangyang."Curvature-aware manifold learning".PATTERN RECOGNITION 83(2018):273-286.