Related papers: FGOT: Graph Distances based on Filters and Optimal…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations…
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…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
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…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
Graph matching is one of the most significant graph analytic tasks, which aims to find the node correspondence across different graphs. Most existing graph matching approaches mainly rely on topological information, whose performances are…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which…
We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…
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…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…