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|Title:||A note on the locally linear embedding algorithm|
|Citation:||International Journal of Pattern Recognition and Artificial Intelligence, 2009; 23(8):1739-1752|
|Publisher:||World Scientific Publ Co Pte Ltd|
|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|
|Appears in Collections:||Computer Science publications|
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