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The Journal of Machine Learning Research
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SIAM Journal on Scientific Computing
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Journal of Multivariate Analysis
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ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
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Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Pattern Recognition
Local smoothing for manifold learning
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Using robust dispersion estimation in support vector machines
Pattern Recognition
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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.