Related papers: Directed Graph Embeddings in Pseudo-Riemannian Man…

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

In this paper we generalize single-relation pseudo-Riemannian graph embedding models to multi-relational networks, and show that the typical approach of encoding relations as manifold transformations translates from the Riemannian to the…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…

We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous…

The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…

Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…

Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…

Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs into Minkowski spacetime using Multidimensional scaling (MDS). First…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat…

Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…