Robust local tangent space alignment

This paper investigates noise manifold learning problem, which is a key issue in applying manifold learning to practical problem. A robust version of LTSA called RLTSA is proposed. The proposed RLTSA algorithm makes LTSA more robust from three aspects: firstly robust PCA algorithm is used instead of the standard SVD to reduce influence of noise on local tangent space coordinates; secondly RLTSA chooses neighborhoods that are approximated well by the local tangent space 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 local alignment errors. Experiments on both synthetic data sets and real data sets demonstrate the effectiveness of our RLTSA when dealing with noise manifold. © 2009 Springer-Verlag Berlin Heidelberg.