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Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly…

Machine Learning · Computer Science 2021-10-22 Alireza Sadeghi , Meng Ma , Bingcong Li , Georgios B. Giannakis

In this paper we analyze the graph-based approach to semi-supervised learning under a manifold assumption. We adopt a Bayesian perspective and demonstrate that, for a suitable choice of prior constructed with sufficiently many unlabeled…

Statistics Theory · Mathematics 2021-06-15 Daniel Sanz-Alonso , Ruiyi Yang

Consider a set of $n$ data points in the Euclidean space $\mathbb{R}^d$. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high…

Machine Learning · Computer Science 2022-02-04 Benyamin Ghojogh , Fakhri Karray , Mark Crowley

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves…

Machine Learning · Statistics 2013-06-07 Cristina Garcia-Cardona , Arjuna Flenner , Allon G. Percus

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…

Computer Vision and Pattern Recognition · Computer Science 2014-03-12 Fabio Anselmi , Joel Z. Leibo , Lorenzo Rosasco , Jim Mutch , Andrea Tacchetti , Tomaso Poggio

This work proposes an overview of the recent semi-supervised learning approaches and related works. Despite the remarkable success of neural networks in various applications, there exist a few formidable constraints, including the need for…

Machine Learning · Computer Science 2024-08-09 Gyeongho Kim

We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled data and finite labeled data. Previous work has conjectured that Lipschitz learning is well-posed in this limit, but is insensitive to the…

Analysis of PDEs · Mathematics 2019-08-20 Jeff Calder

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

Machine Learning · Computer Science 2022-10-24 Marshall Mueller , Shuchin Aeron , James M. Murphy , Abiy Tasissa

Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization.…

Machine Learning · Computer Science 2019-06-14 Chia-Wen Kuo , Chih-Yao Ma , Jia-Bin Huang , Zsolt Kira

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Machine Learning · Computer Science 2025-03-10 Leonel Rozo , Miguel González-Duque , Noémie Jaquier , Søren Hauberg

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

Machine Learning · Computer Science 2021-05-26 Parisa Abdolrahim Poorheravi , Vincent Gaudet

We propose a meta-learning method for semi-supervised learning that learns from multiple tasks with heterogeneous attribute spaces. The existing semi-supervised meta-learning methods assume that all tasks share the same attribute space,…

Machine Learning · Computer Science 2023-11-10 Tomoharu Iwata , Atsutoshi Kumagai

We explain Poisson learning on graph-based semi-supervised learning to see if it could avoid the problem of global information loss problem as Laplace-based learning methods on large graphs. From our analysis, Poisson learning is simply…

Machine Learning · Statistics 2022-03-14 Canh Hao Nguyen

We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning…

Machine Learning · Computer Science 2025-02-14 Sawyer Jack Robertson , Chester Holtz , Zhengchao Wan , Gal Mishne , Alexander Cloninger

Semi-supervised learning is becoming increasingly important because it can combine data carefully labeled by humans with abundant unlabeled data to train deep neural networks. Classic methods on semi-supervised learning that have focused on…

Computer Vision and Pattern Recognition · Computer Science 2019-09-20 Ahmet Iscen , Giorgos Tolias , Yannis Avrithis , Ondrej Chum

Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on…

Machine Learning · Computer Science 2025-08-12 Shay Deutsch , Lionel Yelibi , Alex Tong Lin , Arjun Ravi Kannan

High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing…

Optimization and Control · Mathematics 2026-05-07 Willem Diepeveen , Melanie Weber

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is…

Machine Learning · Computer Science 2023-06-26 Kion Fallah , Alec Helbling , Kyle A. Johnsen , Christopher J. Rozell

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

Machine Learning · Statistics 2024-10-21 Weichun Xia , Jiaxin Jiang , Lei Shi