Large data and zero noise limits of graph-based semi-supervised learning algorithms
Scalings in which the graph Laplacian approaches a differential operator in the large graph
limit are used to develop understanding of a number of algorithms for semi-supervised …
limit are used to develop understanding of a number of algorithms for semi-supervised …
Rates of convergence for Laplacian semi-supervised learning with low labeling rates
We investigate graph-based Laplacian semi-supervised learning at low labeling rates (ratios
of labeled to total number of data points) and establish a threshold for the learning to be well …
of labeled to total number of data points) and establish a threshold for the learning to be well …
Consistency of Fractional Graph-Laplacian Regularization in Semisupervised Learning with Finite Labels
A Weihs, M Thorpe - SIAM Journal on Mathematical Analysis, 2024 - SIAM
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 …
small number of labeled feature vectors using the geometry of a graph. More precisely …
Continuous-domain assignment flows
F Savarino, C Schnörr - European Journal of Applied Mathematics, 2021 - cambridge.org
Assignment flows denote a class of dynamical models for contextual data labelling
(classification) on graphs. We derive a novel parametrisation of assignment flows that …
(classification) on graphs. We derive a novel parametrisation of assignment flows that …
Discrete-to-continuum rates of convergence for nonlocal p-Laplacian evolution problems
Higher-order regularization problem formulations are popular frameworks used in machine
learning, inverse problems and image/signal processing. In this paper, we consider the …
learning, inverse problems and image/signal processing. In this paper, we consider the …
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
In this work we study statistical properties of graph-based clustering algorithms that rely on
the optimization of balanced graph cuts, the main example being the optimization of …
the optimization of balanced graph cuts, the main example being the optimization of …
Discrete-to-Continuum Rates of Convergence for -Laplacian Regularization
Higher-order regularization problem formulations are popular frameworks used in machine
learning, inverse problems and image/signal processing. In this paper, we consider the …
learning, inverse problems and image/signal processing. In this paper, we consider the …
Rates of Convergence for Regression with the Graph Poly-Laplacian
In the (special) smoothing spline problem one considers a variational problem with a
quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be …
quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be …
A compactness theorem for functions on Poisson point clouds
M Caroccia - Nonlinear Analysis, 2023 - Elsevier
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On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case
We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity
problems extends to the case of functionals defined in terms of the symmetric gradient of the …
problems extends to the case of functionals defined in terms of the symmetric gradient of the …