A NOTE ON THE LOCALLY LINEAR EMBEDDING ALGORITHM
Wojciech Chojnacki, Michael J. Brooks · International Journal of Pattern Recognition and Artificial Intelligence · 2009
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.