Related papers: Generalized Dirichlet Energy and Graph Laplacians …

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…

The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG) model, which is a variant of the Generalized Random Dot Product Graph (GRDPG), where, in addition, edges can be positive or negative. The setting is extended to a…

A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$. It turns out that whether a graph $G$ is…

Domain generalization (DG) aims to learn a model from source domains and apply it to unseen target domains with out-of-distribution data. Owing to CLIP's strong ability to encode semantic concepts, it has attracted increasing interest in…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…

The increasing amount of graph data places requirements on the efficient training of graph neural networks (GNNs). The emerging graph distillation (GD) tackles this challenge by distilling a small synthetic graph to replace the real large…

Let $G$ be a graph of order $n$ with adjacency matrix $A(G)$. The \textit{energy} of graph $G$, denoted by $\mathcal{E}(G)$, is defined as the sum of absolute value of eigenvalues of $A(G)$. It was conjectured that if $A(G)$ is…

We establish a bridge between spectral clustering and Gromov-Wasserstein Learning (GWL), a recent optimal transport-based approach to graph partitioning. This connection both explains and improves upon the state-of-the-art performance of…

Entity alignment (EA), a pivotal process in integrating multi-source Knowledge Graphs (KGs), seeks to identify equivalent entity pairs across these graphs. Most existing approaches regard EA as a graph representation learning task,…

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…

We propose a novel Graph Neural Network (GNN) model, named DeepStateGNN, for analyzing traffic data, demonstrating its efficacy in two critical tasks: forecasting and reconstruction. Unlike typical GNN methods that treat each traffic sensor…

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a…

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…

We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature…

For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and $D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix of…

We explore the node classification task in the context of graph domain adaptation, which uses both source and target graph structures along with source labels to enhance the generalization capabilities of Graph Neural Networks (GNNs) on…