相关论文: Practical graph isomorphism, II

Graph neural networks (GNNs) have gained prominence in recommendation systems in recent years. By representing the user-item matrix as a bipartite and undirected graph, GNNs have demonstrated their potential to capture short- and…

The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…

We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a…

Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a…

How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

The rapid growth of graph data poses significant challenges in storage, transmission, and particularly the training of graph neural networks (GNNs). To address these challenges, graph condensation (GC) has emerged as an innovative solution.…

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We…

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…

The graph isomorphism problem has a long history in mathematics and computer science, with applications in computational chemistry and biology, and it is believed to be neither solvable in polynomial time nor NP-complete. E. Luks proposed…

In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…

Human mobility analysis at urban-scale requires models to represent the complex nature of human movements, which in turn are affected by accessibility to nearby points of interest, underlying socioeconomic factors of a place, and local…

Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…

In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…

Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to…

Large models have emerged as the most recent groundbreaking achievements in artificial intelligence, and particularly machine learning. However, when it comes to graphs, large models have not achieved the same level of success as in other…

Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…

Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…