Rising importance of p-Laplacian operator in Machine Learning research part6
- Lower bounds for the first eigenvalue of the p-Laplacian on quaternionic Kähler manifolds(arXiv)
Author : Kui Wang, Shaoheng Zhang
Abstract : We study the first nonzero eigenvalues for the p-Laplacian on quaternionic Kähler manifolds. Our first result is a lower bound for the first nonzero closed (Neumann) eigenvalue of the p-Laplacian on compact quaternionic Kähler manifolds. Our second result is a lower bound for the first Dirichlet eigenvalue of the p-Laplacian on compact quaternionic Kähler manifolds with smooth boundary. Our results generalize corresponding results for the Laplacian eigenvalues on quaternionic Kähler manifolds proved in [22]
2. Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian(arXiv)
Author : Jeff Calder, Nadejda Drenska
Abstract : In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning. The overview is focused on a large body of recent work on PDE continuum limits of graph-based learning, which have been used to prove well-posedness of semi-supervised learning algorithms in the large data limit. We highlight some interesting research directions revolving around consistency of graph-based semi-supervised learning, and present some new results on the consistency of p-Laplacian semi-supervised learning using the stochastic tug-of-war game interpretation of the p-Laplacian. We also present the results of some numerical experiments that illustrate our results and suggest directions for future work
