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2006 NeurIPS NeurIPS 2006

Convergence of Laplacian Eigenmaps

Abstract

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.

🚀 Conference Pioneer - NeurIPS 2006

🌉 Interdisciplinary Bridge - Artificial Intelligence and Mathematics & Optimization

📈 Trend Setter - Geometry

🧭 Keyword Pioneer - spectral method

🐣 Hot Topic Early Bird - spectral method

Authors

Mikhail Belkin, Partha Niyogi

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Core Methods > Embedding Learning Machine Learning > Learning Types > Unsupervised Learning Machine Learning > Optimization & Theory > Theory Mathematics & Optimization > Mathematics > Geometry Mathematics & Optimization > Mathematics > Graph Theory Machine Learning > Core Methods > Dimensionality Reduction

Keywords

dimensionality reduction manifold learning spectral clustering convergence analysis point cloud spectral dimensionality reduction point cloud laplacian spectral method laplacian eigenmap laplace-beltrami operator

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