Nonlinear Alignment and Its Local Linear Iterative Solution
Joint Authors
Ma, Zhengming
Zhang, Sumin
Zhan, Zengrong
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-07
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches.
At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold.
There are two contributions in this paper.
First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold.
Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate.
The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations.
The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.
American Psychological Association (APA)
Zhang, Sumin& Ma, Zhengming& Zhan, Zengrong. 2016. Nonlinear Alignment and Its Local Linear Iterative Solution. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1112538
Modern Language Association (MLA)
Zhang, Sumin…[et al.]. Nonlinear Alignment and Its Local Linear Iterative Solution. Mathematical Problems in Engineering No. 2016 (2016), pp.1-14.
https://search.emarefa.net/detail/BIM-1112538
American Medical Association (AMA)
Zhang, Sumin& Ma, Zhengming& Zhan, Zengrong. Nonlinear Alignment and Its Local Linear Iterative Solution. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1112538
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112538