Friday, April 26, 2024 - 16:15 in V2-210/216 + ZOOM
Principal component analysis and graph Laplacians in high dimensions
A talk in the CRC Seminar series by
Martin Wahl from Universität Bielefeld
| Abstract: |
Laplacian eigenmaps and diffusion maps are nonlinear dimensionality reduction methods that use the eigenvalues and eigenvectors of (un)normalized graph Laplacians. Both methods are applied when the data is sampled from a low-dimensional manifold, embedded in a high-dimensional Euclidean space. From a mathematical perspective, the main problem is to understand these empirical Laplacians as spectral approximations of the underlying Laplace-Beltrami operator. In this talk, we study Laplacian eigenmaps through the lens of kernel principal component analysis. This leads to novel points of view and allows to leverage results for empirical covariance operators in high dimensions.
Zoom Meeting ID: [647 0432 3651]
Passcode: [078107]
$\href{https://uni-bielefeld.zoom.us/...}{\textbf{Join Zoom Meeting}}$
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