Robust local tangent space alignment via iterative weighted PCA

Recently manifold learning has attracted extensive interest in machine learning and related communities. This paper investigates the noise manifold learning problem, which is a key issue in applying manifold learning algorithm to practical problems. We propose a robust version of LTSA algorithm called RLTSA. The proposed RLTSA algorithm makes LTSA more robust from three aspects: firstly robust PCA algorithm based on iterative weighted PCA is employed instead of the standard SVD to reduce the influence of noise on local tangent space coordinates; secondly RLTSA chooses neighborhoods that are well approximated by the local coordinates to align with the global coordinates; thirdly in the alignment step, the influence of noise on embedding result is further reduced by endowing clean data points and noise data points with different weights into the local alignment errors. Experiments on both synthetic data sets and real data sets demonstrate the effectiveness of our RLTSA when dealing with noise manifold. & 2011 Elsevier B.V. All rights reserved.