Empirical Graph-Laplace-Approximation of Laplace-Beltrami Operators: Behavior of Eigenspaces

13.06.2022, 10:00  –  Golm, Haus 9, Raum 2.22 (hybrid: Zoom)
Forschungsseminar Statistik

Maximilian Graf

The Laplacian Eigenmaps algorithm as a non-linear dimensionality reduction method was introduced by Belkin and Niyogi in 2001. Key objects are the Graph-Laplace-Matrix and the related Point-Cloud-Laplace-Operator, which can be seen as an approximation of the Laplacian on a manifold, the Laplace-Beltrami-Operator. I will sketch a proof of how its eigenspaces can be approximated by those of the Point-Cloud-Laplacian and how this motivates the Laplacian Eigenmaps algorithm.

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