Related papers: A Spectral Framework for Evaluating Geodesic Dista…

A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…

Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…

Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…

In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…

Modern graph neural networks (GNNs) can be sensitive to changes in the input graph structure and node features, potentially resulting in unpredictable behavior and degraded performance. In this work, we introduce a spectral framework known…

The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations.…

Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…

Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…

Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying…

We present a method for learning "spectrally descriptive" edge weights for graphs. We generalize a previously known distance measure on graphs (Graph Diffusion Distance), thereby allowing it to be tuned to minimize an arbitrary loss…

Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of…

Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has…

This paper proposes a metric to measure the dissimilarity between graphs that may have a different number of nodes. The proposed metric extends the generalised optimal subpattern assignment (GOSPA) metric, which is a metric for sets, to…

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…

In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…

In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…

The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications. Computing exact GED values is typically an NP-hard problem and traditional algorithms…

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…