Geographically annotated social media is extremely valuable for modern information
retrieval. However, when researchers can only access publicly-visible data, one quickly …

Graph learning, when used as a semi-supervised learning (SSL) method, performs well for
classification tasks with a low label rate. We provide a graph-based batch active learning …

We present two graph-based algorithms for multiclass segmentation of high-dimensional
data on graphs. The algorithms use a diffuse interface model based on the Ginzburg …

In this paper we present a computationally efficient algorithm utilizing a fully or seminonlocal
graph Laplacian for solving a wide range of learning problems in binary data classification …

In this paper, we introduce a new (constructive) characterization of tight wavelet frames on
non-flat domains in both continuum setting, ie on manifolds, and discrete setting, ie on …

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn
(AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics …

Geometric, topological and graph theory modeling and analysis of biomolecules are of
essential importance in the conceptualization of molecular structure, function, dynamics, and …

This paper is a republication of an MMS paper [AL Bertozzi and A. Flenner, Multiscale
Model. Simul., 10 (2012), pp. 1090--1118] describing a new class of algorithms for …

We focus on the multi-class segmentation problem using the piecewise constant Mumford-
Shah model in a graph setting. After formulating a graph version of the Mumford-Shah …

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which
can range from hundreds to over a thousand frequencies depending on the sensor. Most …