相关论文: Seeded graph matching for the correlated Gaussian …
Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set…
In this paper, a new information theoretic framework for graph matching is introduced. Using this framework, the graph isomorphism and seeded graph matching problems are studied. The maximum degree algorithm for graph isomorphism is…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein…
Graph matching is an important problem in machine learning and pattern recognition. Herein, we present theoretical and practical results on the consistency of graph matching for estimating a latent alignment function between the vertex sets…
Driven by many real applications, we study the problem of seeded graph matching. Given two graphs $G_1 = (V_1, E_1)$ and $G_2 = (V_2, E_2)$, and a small set $S$ of pre-matched node pairs $[u, v]$ where $u \in V_1$ and $v \in V_2$, the…
There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this…
We present a novel approximate graph matching algorithm that incorporates seeded data into the graph matching paradigm. Our Joint Optimization of Fidelity and Commensurability (JOFC) algorithm embeds two graphs into a common Euclidean space…
Let $G=(V, E)$ be a given edge-weighted graph and let its {\em realization} $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e \in E$ independently with probability $p$. In the {\em stochastic matching} problem, the goal…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
We study the problem of graph coarsening within the Gromov-Wasserstein geometry. Specifically, we propose two algorithms that leverage a novel representation of the distortion induced by merging pairs of nodes. The first method, termed…
This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is…
Data integration is essential across diverse domains, from historical records to biomedical research, facilitating joint statistical inference. A crucial initial step in this process involves merging multiple data sources based on matching…
The maximum energy of the EPR model on a weighted graph is known to be upper-bounded by the sum of the total weight and the value of maximum-weight fractional matching~(MWFM). Recently, Apte, Parekh and Sud~(APS) conjecture that the bound…
Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we…
A matching $M$ is a $\mathscr{P}$-matching if the subgraph induced by the endpoints of the edges of $M$ satisfies property $\mathscr{P}$. As examples, for appropriate choices of $\mathscr{P}$, the problems Induced Matching, Uniquely…
Matching local features across images is a fundamental problem in computer vision. Targeting towards high accuracy and efficiency, we propose Seeded Graph Matching Network, a graph neural network with sparse structure to reduce redundant…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…