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https://hdl.handle.net/2440/57845
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DC Field | Value | Language |
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dc.contributor.author | Chojnacki, W. | - |
dc.contributor.author | Brooks, M. | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | International Journal of Pattern Recognition and Artificial Intelligence, 2009; 23(8):1739-1752 | - |
dc.identifier.issn | 0218-0014 | - |
dc.identifier.issn | 1793-6381 | - |
dc.identifier.uri | http://hdl.handle.net/2440/57845 | - |
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.language.iso | en | - |
dc.publisher | World Scientific Publ Co Pte Ltd | - |
dc.source.uri | http://dx.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 | - |
dc.identifier.doi | 10.1142/S0218001409007752 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Chojnacki, W. [0000-0001-7782-1956] | - |
Appears in Collections: | Aurora harvest Computer Science publications |
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