相关论文: Laplace Learning in Wasserstein Space

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…

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…

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…

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…

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…

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…

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…

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…

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.…

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…

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…

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,…

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…

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…

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…

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…

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…

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…

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…