Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
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In the past few years, the problem of nonlinear dimensionality reduction arises in many fields of information processing. The local tangent space alignment (LTSA) is one of the effective and efficient algorithms to perform nonlinear dimensionality reduction. It has a number of attractive features: simple geometric intuitions, straightforward implementation, and global optimization. However, LTSA may fail on the manifold with nonuniformly distributed noise or large curvatures. In this paper, LTSA is improved by introducing various dimensional local coordinates to represent the local geometry for each neighborhood. The modified LTSA (MLTSA) is much stable and theoretical analysis is given to show the improvement of MLTSA on noisy manifold. We also illustrate the effectiveness of our method on both synthetic and real-world data sets.