Performing Locally Linear Embedding with Adaptable Neighborhood Size on Manifold

Abstract

Locally linear embedding approach (LLE) is one of most efficient nonlinear dimensionality reduction approaches with good representational capacity for a broader range of manifolds and high computational efficiency. However, LLE and its variants are based on the assumption that the whole data manifold is evenly distributed so that they fail to nicely deal with most real problems that are unevenly distributed. This paper first proposes an approach to judge whether the manifold is even or not, and then logically divides the unevenly distributed manifold into many evenly distributed sub-manifolds, where the neighourhood size for each sub-manifold is automatically determined based on its structure. It is proved, by visualization and classification experiments on benchmark data sets, that our approach is competitive.