Selecting a Regularisation Parameter in the Locally Linear Embedding Algorithm

Abstract: This paper deals with a method, called locally linear embedding. It is a nonlinear dimensionality reduction technique that computes low-dimensional, neighbourhood preserving embeddings of highdimensional data and attempts to discover nonlinear structure in high-dimensional data. The implementation of the algorithm is fairly straightforward, because the algorithm has only two control parameters: the number of neighbours of each data point and the regularization parameter. The mapping quality is quite sensitive to these parameters. In this paper, we propose a new algorithm for selecting a regularization parameter of a local Gram matrix. Our approach is experimentally verified on an artificial data set.