Related papers: Geometry of Graph Edit Distance Spaces
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…
In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search.…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to transform one graph to another. It is NP-hard to compute in general, and a…
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…
In this survey we present a generalization of the notion of metric space and some applications to discrete structures as graphs, ordered sets and transition systems. Results in that direction started in the middle eighties based on the…
End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can topologically be represented by a…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…
A graph G on n vertices is said to be extendable if G can be modified to form a new graph H on more than n vertices, while preserving the degrees of the vertices common to G and H. The added vertices all have the same degree and we define…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…
Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
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…