A note on the locally linear embedding algorithm

dc.contributor.author	Chojnacki, W.
dc.contributor.author	Brooks, M.
dc.date.issued	2009
dc.description.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.
dc.description.statementofresponsibility	Wojciech Chojnacki, Michael J. Brooks
dc.identifier.citation	International Journal of Pattern Recognition and Artificial Intelligence, 2009; 23(8):1739-1752
dc.identifier.doi	10.1142/S0218001409007752
dc.identifier.issn	0218-0014
dc.identifier.issn	1793-6381
dc.identifier.orcid	Chojnacki, W. [0000-0001-7782-1956]
dc.identifier.orcid	Brooks, M. [0000-0001-9612-5884]
dc.identifier.uri	http://hdl.handle.net/2440/57845
dc.language.iso	en
dc.publisher	World Scientific Publ Co Pte Ltd
dc.source.uri	https://doi.org/10.1142/s0218001409007752
dc.subject	Dimensionality reduction
dc.subject	locally linear embedding
dc.subject	Stiefel manifold
dc.subject	Grassmann manifold
dc.subject	optimization
dc.subject	gauge freedom
dc.subject	gauge fixing
dc.title	A note on the locally linear embedding algorithm
dc.type	Journal article
pubs.publication-status	Published

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