Montag, 11. Mrz 2024, 16:45 - 17:45 iCal

ISOR Colloquium

"Heat kernel PCA with applications to Laplacian Eigenmaps"

Speaker: Martin Wahl (Bielefeld University, Germany)

HS 7 OMP1 (#1.303)
Oskar-Morgenstern-Platz 1, 1090 Wien

Vortrag


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 PCA, and consider the heat kernel as reproducing kernel feature map. This leads to novel points of view and allows to leverage results for empirical covariance operators in infinite dimensions.

Underlying paper: arxiv.org/abs/2402.16481

Zur Webseite der Veranstaltung


Veranstalter

Institut für Statistik und Operations Research


Kontakt

Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631
sabine.sobotka-tompits@univie.ac.at