Robust L-Isomap with a Novel Landmark Selection Method

Abstract

Isomap is a widely used nonlinear method for dimensionality reduction. Landmark-Isomap (L-Isomap) has been proposed to improve the scalability of Isomap. In this paper, we focus on two important issues that were not taken into account in L-Isomap, landmark point selection and topological stability. At first, we present a novel landmark point selection method. It first uses a greedy strategy to select some points as landmark candidates and then removes the candidate points that are neighbours of other candidates. The remaining candidate points are the landmark points. The selection method can promote the computation efficiency without sacrificing accuracy. For the topological stability, we define edge density for each edge in the neighbourhood graph. According to the geometrical characteristic of the short-circuit edges, we provide a method to eliminate the short-circuit edge without breaking the data integrity. The approach that integrates L-Isomap with these two improvements is referred to as Robust L-Isomap (RL-Isomap). The effective performance of RL-Isomap is confirmed through several numerical experiments.