A nonlinear dimension reduction method with both distance and neighborhood preservation

Abstract

Dimension reduction is an important task in the field of machine learning. Local Linear Embedding (LLE) and Isometric Map (ISOMAP) are two representative manifold learning methods for dimension reduction. Both the two methods have some shortcomings. The most significant one is that they preserve only one specific feature of the underlying datasets after dimension reduction, while ignoring other meaningful features. In this paper, we propose a new method to deal with this problem, it is called G lobal and L ocal feature P reserving E mbedding, GLPE in short. GLPE can preserve both the neighborhood relationships and the global pairwise distances of high-dimensional datasets. Experiments on both artificial and real-life datasets validate the effectiveness of the proposed method. © 2013 Springer-Verlag Berlin Heidelberg.