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

Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…

Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…

Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…

We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…

Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional…

Learning node representations that incorporate information from graph structure benefits wide range of tasks on graph. The majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given…

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…

Network embedding is aimed at mapping nodes in a network into low-dimensional vector representations. Graph Neural Networks (GNNs) have received widespread attention and lead to state-of-the-art performance in learning node representations.…

Representation learning is the first step in automating tasks such as research paper recommendation, classification, and retrieval. Due to the accelerating rate of research publication, together with the recognised benefits of…

Minimal parametrization of 3D lines plays a critical role in camera localization and structural mapping. Existing representations in robotics and computer vision predominantly handle independent lines, overlooking structural regularities…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewire or infer a GNN's graph to maximize the GNN's predictive…

Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…

Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph…

We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations…

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the…