The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of
interest in the past few decades. This article is a tour of some of the recent developments …

We study the convergence of the graph Laplacian of a random geometric graph generated
by an iid sample from am-dimensional submanifold MM in R^ d R d as the sample size n …

Gaussian processes are a versatile framework for learning unknown functions in a manner
that permits one to utilize prior information about their properties. Although many different …

An emerging way to deal with high-dimensional noneuclidean data is to assume that the
underlying structure can be captured by a graph. Recently, ideas have begun to emerge …

The development of Internet of Things (IoT) technologies has led to the widespread adoption
of monitoring networks for a wide variety of applications, such as smart cities, environmental …

In this paper we improve the spectral convergence rates for graph-based approximations of
weighted Laplace-Beltrami operators constructed from random data. We utilize regularity of …

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 …

This paper establishes the consistency of spectral approaches to data clustering. We
consider clustering of point clouds obtained as samples of a ground-truth measure. A graph …

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 …

Nonlocal Modeling, Analysis, and Computation : Back Matter Page 1 Bibliography [1] L.
ABDELOUHAB, J. BONA, M. FELLAND, AND J.-C. SAUT, Nonlocal models for nonlinear …