Convergence of Laplacian Eigenmaps

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Mikhail Belkin, Partha Niyogi


Geometrically based methods for various tasks of machine learning have attracted considerable attention over the last few years. In this paper we show convergence of eigenvectors of the point cloud Laplacian to the eigen- functions of the Laplace-Beltrami operator on the underlying manifold, thus establishing the first convergence results for a spectral dimensionality re- duction algorithm in the manifold setting.