Improved Laplacian Eigenmaps

This paper presents an improvement to the Laplacian Eigenmaps technique for manifold learning. The Laplace-Beltrami operator on a Riemannian manifold is re-investigated and a discretization scheme based on the theory of Riemannian integration is proposed. The result is a more accurate analogue of the continuous operator for graphs, which by comparison, outperforms the previously reported operators in extracting the structure of the data. The proposed method, similar to Laplacian Eigenmaps, preserves both the local and global structures of the data.

Keywords:

Dimensionality reduction , Laplace-Beltrami operator , manifold learning