A note on the locally linear embedding algorithm
Date
2009
Authors
Chojnacki, W.
Brooks, M.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
International Journal of Pattern Recognition and Artificial Intelligence, 2009; 23(8):1739-1752
Statement of Responsibility
Wojciech Chojnacki, Michael J. Brooks
Conference Name
Abstract
The paper presents mathematical underpinnings of the locally linear embedding technique for data dimensionality reduction. It is shown that a cogent framework for describing the method is that of optimization on a Grassmann manifold. The solution delivered by the algorithm is characterized as a constrained minimizer for a problem in which the cost function and all the constraints are defined on such a manifold. The role of the internal gauge symmetry in solving the underlying optimization problem is illuminated.