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Type: Journal article
Title: A note on the locally linear embedding algorithm
Author: Chojnacki, W.
Brooks, M.
Citation: International Journal of Pattern Recognition and Artificial Intelligence, 2009; 23(8):1739-1752
Publisher: World Scientific Publ Co Pte Ltd
Issue Date: 2009
ISSN: 0218-0014
Statement of
Wojciech Chojnacki, Michael J. Brooks
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.
Keywords: Dimensionality reduction; locally linear embedding; Stiefel manifold; Grassmann manifold; optimization; gauge freedom; gauge fixing
RMID: 0020094705
DOI: 10.1142/S0218001409007752
Appears in Collections:Computer Science publications

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