Related papers: Manifold structure in graph embeddings

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

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…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…

Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…

In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…