An outlier-insensitive Linear Pursuit Embedding algorithm

Abstract

Dimension reduction techniques with the flexibility to learn a broad class of nonlinear manifold have attracted increasingly close attention since meaningful low-dimensional structures are always hidden in large number of high-dimensional natural data, such as global climate patterns, images of a face under different viewing conditions, etc. In this paper, we introduce L1-Norm linear pursuit embedding (L1-LPE) algorithm, aims to find a more robust linear method in presence of outliers and unexpected samples when dealing with high-dimensional nonlinear manifold problems. To achieve this goal, a new method based on a rather different geometric intuition L1-Norm is proposed to describe the local geometric structure. L1-LPE and L2-LPE is studied and compared in this paper and experiments on both toy problems and real data problems are presented.