Modified Locally Linear Embedding based on Neighborhood Radius

As a nonlinear dimensionality reduction technology, locally linear embedding is a kind of very competitive approach with good representational capacity for a broader range of manifolds and high computational efficiency. However, LLE and its variants determine the neighborhood for all points with the same neighborhood size, without considering the unevenly distribution or sparsity of data manifold. This paper presents a new performance index-ratio of neighborhood radius to predict the unevenly distribution or sparsity of data manifold, and a new approach that dynamically determines the neighborhood numbers based on the ratio of neighborhood radius, instead of adopting a fixed number of nearest neighbors per data point. This approach has clear geometry intuition as well as the better performance, compared with LLE algorithm. The conducted experiments on benchmark data sets validate the proposed approach.