Local Tangent Space Laplacian Eigenmaps

This chapter presents a novel manifold learning algorithm, named Local Tangent Space Laplacian Eigenmaps (LTSLE). The theoretical framework of LTSLE is based on a local tangent space theorem, which is also delivered in this chapter. LTSLE ismotivated by the local geometrical structure of the data and the correspondence between the Laplace-Beltrami operator on a manifold and the Laplacian matrix constructed on a graph. The local similarity between data is characterized by the Euclidean distance in the local tangent space, which corresponds to a Mahalanobis distance calculated in the original data space. Compared to a classic manifold learning method, Laplacian Eigenmaps (LE), LTSLE less depends on the choice of the parameter t of the heat kernel. For efficient projection onto low dimensional subspace, we also introduce a linear version of LTSLE, called LLTSLE. Experimental results on toy problems and real-world applications demonstrate the robustness and effectiveness of the proposed methods. © 2013 Nova Science Publishers, Inc. All Rights Reserved.

Duke Scholars

Author Kaizhu Huang DKU Faculty