Formulating LLE using alignment technique

LLE is a well-known method to nonlinear dimensionality reduction. In this short paper, we present an alternative way to formulate LLE. The alignment technique is exploited to align the local coordinates on the local patches of manifolds to be the global ones. The efficient computation of embedding coordinates-of LLE automatically appears in the proposed framework. (c) 2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.