Robust ISOMAP based on neighbor ranking metric

Abstract

ISOMAP is one of classical manifold learning methods that can discover the low-dimensional nonlinear structure automatically in a high-dimensional data space. However, it is very sensitive to the outlier, which is a great disadvantage to its applications. To solve the noisy manifold learning problem, this paper proposes a robust ISOMAP based on neighbor ranking metric (NRM). Firstly, NRM is applied to remove outliers partially, then a two-step strategy is adopted to select suitable neighbors for each point to construct neighborhood graph. The experimental results indicate that the method can effectively improve robustness in noisy manifold learning both on synthetic and real-world data. © 2012 Springer-Verlag.