相关论文: Hypergraph $p$-Laplacian equations for data interp…

We propose a scalable method for semi-supervised (transductive) learning from massive network-structured datasets. Our approach to semi-supervised learning is based on representing the underlying hypothesis as a graph signal with small…

Modern machine learning paradigms, such as deep learning, occur in or close to the interpolation regime, wherein the number of model parameters is much larger than the number of data samples. In this work, we propose a regularity condition…

Learning a new task from a handful of examples remains an open challenge in machine learning. Despite the recent progress in few-shot learning, most methods rely on supervised pretraining or meta-learning on labeled meta-training data and…

Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift.…

We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…

Normalization is a vital process for any machine learning task as it controls the properties of data and affects model performance at large. The impact of particular forms of normalization, however, has so far been investigated in limited…

Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the…

The success of many machine learning (ML) methods depends crucially on having large amounts of labeled data. However, obtaining enough labeled data can be expensive, time-consuming, and subject to ethical constraints for many applications.…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…

We introduce a novel formulation for guided super-resolution. Its core is a differentiable optimisation layer that operates on a learned affinity graph. The learned graph potentials make it possible to leverage rich contextual information…

In this paper we are concerned with a class of optimization problems involving the $p(x)$-Laplacian operator, which arise in imaging and signal analysis. We study the well-posedness of this kind of problems in an amalgam space considering…

The interconnectedness and interdependence of modern graphs are growing ever more complex, causing enormous resources for processing, storage, communication, and decision-making of these graphs. In this work, we focus on the task graph…

The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…

Semi-supervised learning with manifold regularization is a classical framework for jointly learning from both labeled and unlabeled data, where the key requirement is that the support of the unknown marginal distribution has the geometric…

In this paper we study numerical approximations of the evolution problem for the nonlocal $p$-Laplacian with homogeneous Neumann boundary conditions. First, we derive a bound on the distance between two continuous-in-time trajectories…

Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…

Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed from random data points. The data points are sampled from a distribution supported on a smooth manifold. The family of equations that we study…

In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…