We investigate a family of regression problems in a semisupervised setting. The task is to
assign real-valued labels to a set of n sample points provided a small training subset of N …

In the manifold setting, we provide a series of spectral convergence results quantifying how
the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions …

The performance of traditional graph Laplacian methods for semi-supervised learning
degrades substantially as the ratio of labeled to unlabeled data decreases, due to a …

For data sampled from an arbitrary density on a manifold embedded in Euclidean space, the
Continuous k-Nearest Neighbors (CkNN) graph construction is introduced. It is shown that …

This paper proposes and analyzes a novel clustering algorithm, called learning by
unsupervised nonlinear diffusion (LUND), that combines graph-based diffusion geometry …

This paper considers a Bayesian approach to graph-based semi-supervised learning. We
show that if the graph parameters are suitably scaled, the graph-posteriors converge to a …

We consider the problem of recovering a function input of a differential equation formulated
on an unknown domain M. We assume to have access to a discrete domain …

Graph Laplacians computed from weighted adjacency matrices are widely used to identify
geometric structure in data, and clusters in particular; their spectral properties play a central …

Graph-based semi-supervised regression (SSR) involves estimating the value of a function
on a weighted graph from its values (labels) on a small subset of the vertices; it can be …

We consider adaptations of the Mumford–Shah functional to graphs. These are based on
discretizations of nonlocal approximations to the Mumford–Shah functional. Motivated by …