Zobrazeno 1 - 10
of 191
pro vyhledávání: '"Thorpe, Matthew P"'
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $\mathrm{W}
Externí odkaz:
http://arxiv.org/abs/2311.08549
Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev $\mathrm{W}^{
Externí odkaz:
http://arxiv.org/abs/2310.12691
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a growing inter
Externí odkaz:
http://arxiv.org/abs/2307.13571
Autor:
Weihs, Adrien, Thorpe, Matthew
Laplace learning is a popular machine learning algorithm for finding missing labels from a small number of labelled feature vectors using the geometry of a graph. More precisely, Laplace learning is based on minimising a graph-Dirichlet energy, equiv
Externí odkaz:
http://arxiv.org/abs/2303.07818
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 obtained via replacing the Laplacian regulariser with a poly-Laplacian r
Externí odkaz:
http://arxiv.org/abs/2209.02305
Autor:
Shadbahr, Tolou, Roberts, Michael, Stanczuk, Jan, Gilbey, Julian, Teare, Philip, Dittmer, Sören, Thorpe, Matthew, Torne, Ramon Vinas, Sala, Evis, Lio, Pietro, Patel, Mishal, Collaboration, AIX-COVNET, Rudd, James H. F., Mirtti, Tuomas, Rannikko, Antti, Aston, John A. D., Tang, Jing, Schönlieb, Carola-Bibiane
Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by
Externí odkaz:
http://arxiv.org/abs/2206.08478
Given an image $u_0$, the aim of minimising the Mumford-Shah functional is to find a decomposition of the image domain into sub-domains and a piecewise smooth approximation $u$ of $u_0$ such that $u$ varies smoothly within each sub-domain. Since the
Externí odkaz:
http://arxiv.org/abs/2202.04965
Autor:
Muniz, Miguel, Loprinzi, Charles L, Orme, Jacob J, Koch, Regina M, Mahmoud, Ahmed M, Kase, Adam M, Riaz, Irbaz B, Andrews, Jack R, Thorpe, Matthew P, Johnson, Geoffrey B, Kendi, Ayse T, Kwon, Eugene D, Nauseef, Jones T, Morgans, Alicia K, Sartor, Oliver, Childs, Daniel S
Publikováno v:
In Cancer Treatment Reviews June 2024 127
Autor:
Thorpe, Matthew, Wang, Bao
Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph. Understanding and certifying the adversarial robustness of machine learning (ML) algorithms has attracted large amounts of attent
Externí odkaz:
http://arxiv.org/abs/2104.10837
In this paper we study the local linearization of the Hellinger--Kantorovich distance via its Riemannian structure. We give explicit expressions for the logarithmic and exponential map and identify a suitable notion of a Riemannian inner product. Sam
Externí odkaz:
http://arxiv.org/abs/2102.08807