Related papers: The multilayer random dot product graph

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position…

We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…

We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…

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…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

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…

Joint spectral embeddings facilitate analysis of multiple network data by simultaneously mapping vertices in each network to points in Euclidean space where statistical inference is then performed. In this work, we consider one such joint…

Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot…

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels…

Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this…

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…

A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…

We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…

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…

The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph…