Shortest path graph distances are widely used in data science and machine learning, since
they can approximate the underlying geodesic distance on the data manifold. However, the …

Tackling semi-supervised learning problems with graph-based methods has become a trend
in recent years since graphs can represent all kinds of data and provide a suitable …

Let $\mathcal {M}\subseteq\mathbb {R}^ d $ denote a low-dimensional manifold and let
$\mathcal {X}=\{x_1,\dots, x_n\} $ be a collection of points uniformly sampled from $\mathcal …

Laplace learning is a popular machine learning algorithm for finding missing labels from a
small number of labeled feature vectors using the geometry of a graph. More precisely …

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph
infinity Laplacian Page 1 The Annals of Applied Probability 2024, Vol. 34, No. 4, 3870–3910 …

We prove that the dynamics of the MBO scheme for data clustering converge to a viscosity
solution to mean curvature flow. The main ingredients are (i) a new abstract convergence …

We connect adversarial training for binary classification to a geometric evolution equation for
the decision boundary. Relying on a perspective that recasts adversarial training as a …

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 …

We propose a new asymptotic expansion for the fractional p-Laplacian with precise
computations of the errors. Our approximation is shown to hold in the whole range p∈(1,∞) …

In this paper we prove discrete to continuum convergence rates for Poisson Learning, a
graph-based semi-supervised learning algorithm that is based on solving the graph Poisson …