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11/01/2022
Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Motivated by the challenge of sampling Gibbs measures with nonconvex pot...
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11/05/2021
Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
We investigate identifying the boundary of a domain from sample points i...
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08/18/2021
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
In this work we build a unifying framework to interpolate between densit...
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06/19/2020
Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates
We propose a new framework, called Poisson learning, for graph based sem...
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06/04/2020
Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates
We study graph-based Laplacian semi-supervised learning at low labeling ...
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12/20/2019
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
We consider dynamics driven by interaction energies on graphs. We introd...
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06/22/2019
Mumford-Shah functionals on graphs and their asymptotics
We consider adaptations of the Mumford-Shah functional to graphs. These ...
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10/10/2018
Properly-weighted graph Laplacian for semi-supervised learning
The performance of traditional graph Laplacian methods for semi-supervis...
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05/23/2018
Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms
Scalings in which the graph Laplacian approaches a differential operator...
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01/30/2018
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator
We study the convergence of the graph Laplacian of a random geometric gr...
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07/19/2017
Analysis of p-Laplacian Regularization in Semi-Supervised Learning
We investigate a family of regression problems in a semi-supervised sett...
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09/27/2016
A Transportation L^p Distance for Signal Analysis
Transport based distances, such as the Wasserstein distance and earth mo...
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09/15/2016
Transport-based analysis, modeling, and learning from signal and data distributions
Transport-based techniques for signal and data analysis have received in...
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12/15/2015
Multiple penalized principal curves: analysis and computation
We study the problem of finding the one-dimensional structure in a given...
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08/08/2015
A variational approach to the consistency of spectral clustering
This paper establishes the consistency of spectral approaches to data cl...
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11/24/2014
Consistency of Cheeger and Ratio Graph Cuts
This paper establishes the consistency of a family of graph-cut-based al...
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03/25/2014