Related papers: Manifold structure in graph embeddings
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
A graph drawing in the plane is called an almost embedding if images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of almost embeddings: winding number, cyclic and triodic Wu…
An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study…
Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
Knowledge Graph embedding provides a versatile technique for representing knowledge. These techniques can be used in a variety of applications such as completion of knowledge graph to predict missing information, recommender systems,…
We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graphs representation learning has been a very active research area in recent years. The goal of graph representation learning is to generate graph representation vectors that capture the structure and features of large graphs accurately.…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…