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While robust graph neural networks (GNNs) have been widely studied for graph perturbation and attack, those for label noise have received significantly less attention. Most existing methods heavily rely on the label smoothness assumption to…

Learning low-dimensional representations on graphs has proved to be effective in various downstream tasks. However, noises prevail in real-world networks, which compromise networks to a large extent in that edges in networks propagate…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…

Many algorithms have been proposed to predict missing links in a variety of real networks. These studies focus on mainly both accuracy and efficiency of these algorithms. However, little attention is paid to their robustness against either…

Graph Contrastive Learning (GCL) has shown strong promise for unsupervised graph representation learning, yet its effectiveness on heterophilic graphs, where connected nodes often belong to different classes, remains limited. Most existing…

Today, there are two major understandings for graph convolutional networks, i.e., in the spectral and spatial domain. But both lack transparency. In this work, we introduce a new understanding for it -- data augmentation, which is more…

Graph neural networks (GNNs) learn node representations by passing and aggregating messages between neighboring nodes. GNNs have been applied successfully in several application domains and achieved promising performance. However, GNNs…

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…

Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph…

Graph neural network (GNN) is a powerful learning approach for graph-based recommender systems. Recently, GNNs integrated with contrastive learning have shown superior performance in recommendation with their data augmentation schemes,…

We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level…

Convolutional neural network (CNN)-based feature learning has become state of the art, since given sufficient training data, CNN can significantly outperform traditional methods for various classification tasks. However, feature learning…

Unsupervised graph representation learning is a non-trivial topic. The success of contrastive methods in the unsupervised representation learning on structured data inspires similar attempts on the graph. Existing graph contrastive learning…

Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the…

Temporal Graph Networks (TGNs) have shown remarkable performance in learning representation for continuous-time dynamic graphs. However, real-world dynamic graphs typically contain diverse and intricate noise. Noise can significantly…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could…

In this paper, we study the robust subspace clustering problem, which aims to cluster the given possibly noisy data points into their underlying subspaces. A large pool of previous subspace clustering methods focus on the graph construction…