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https://hdl.handle.net/2440/57845
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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 1793-6381 |
Statement of Responsibility: | 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 |
DOI: | 10.1142/S0218001409007752 |
Published version: | http://dx.doi.org/10.1142/s0218001409007752 |
Appears in Collections: | Aurora harvest Computer Science publications |
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