Selection of the number of neighbours of each data point for 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 high dimensional data and attempts to discover nonlinear structure in high dimensional data. The implementation of the algorithm is fairly straightforward, as the algorithm has only two control parameters: the number of neighbours of each data point and the regularisation parameter. The mapping quality is quite sensitive to these parameters. In this paper, we propose a new way for selecting the number of the nearest neighbours of each data point. Our approach is experimentally verified on two data sets: artificial data and real world pictures.