Unsupervised Nonlinear Dimensionality Reduction Based on Tensor Tangent Space Alignment

Nonlinear dimensionality reduction from points underlying low dimension manifolds with outliers in high dimensional space is a challenge problem. In this paper, we proposed a robust dimensionality reduction method which can learn the low dimensional embeddings of manifold from input high dimensional data with large percentage of outliers. The proposed method named tensor tangent space alignment operates locally in neighborhoods and integrates tensor voting for nonlinear manifold inference and an improved tangent space alignment method for dimensionality reduction perfectively. We demonstrate the robust effectiveness of our method on several datasets with different noise levels.