Dependence of locally linear embedding on the regularization parameter

This paper deals with a method, called locally linear embedding (LLE). It is a nonlinear dimensionality reduction technique that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional data and attempts to discover a nonlinear structure (including manifolds) in high-dimensional data. In practice, the nonlinear manifold learning methods are applied in image processing, text mining, etc. The implementation of the LLE algorithm is fairly straightforward, because the algorithm has only two control parameters: the number of neighbors of each data point and the regularization parameter. The mapping quality is quite sensitive to these parameters. In this paper, we propose a new way of selecting a regularization parameter of a local Gram matrix.