A more topologically stable locally linear embedding algorithm based on R*-tree

Abstract

Locally linear embedding is a popular manifold learning algorithm for nonlinear dimensionality reduction. However, the success of LLE depends greatly on an input parameter - neighborhood size, and it is still an open problem how to find the optimal value for it. This paper focuses on this parameter, proposes that it should be self-tuning according to local density not a uniform value for all the data as LLE does, and presents a new variant algorithm of LLE, which can effectively prune "short circuit" edges by performing spatial search on the R*-Tree built on the dataset. This pruning leads the original fixed neighborhood size to be a self-tuning value, thus makes our algorithm have more topologically stableness than LLE does. The experiments prove that our idea and method are correct. © 2008 Springer-Verlag Berlin Heidelberg.