DeepAI
Log In Sign Up

The multilayer random dot product graph

07/20/2020
by   Andrew Jones, et al.
10

We present an extension of the latent position network model known as the generalised random dot product graph to accommodate multiple graphs with a common node structure, based on a matrix representation of the natural third-order tensor created from the adjacency matrices of these graphs. Theoretical results concerning the asymptotic behaviour of the node representations obtained by spectral embedding are established, showing that after the application of a linear transformation these converge uniformly in the Euclidean norm to the latent positions with a Gaussian error. The flexibility of the model is demonstrated through application to the tasks of latent position recovery and two-graph hypothesis testing, in which it performs favourably compared to existing models. Empirical improvements in link prediction over single graph embeddings are exhibited in a cyber-security example.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/04/2018

On estimation and inference in latent structure random graphs

We define a latent structure model (LSM) random graph as a random dot pr...
12/22/2019

Link prediction in dynamic networks using random dot product graphs

The problem of predicting links in large networks is a crucial task in a...
06/02/2021

Spectral embedding for dynamic networks with stability guarantees

We consider the problem of embedding a dynamic network, to obtain time-e...
05/30/2022

OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs

This work provides the first theoretical study on the ability of graph M...
02/17/2018

Out-of-sample extension of graph adjacency spectral embedding

Many popular dimensionality reduction procedures have out-of-sample exte...
09/16/2017

The generalised random dot product graph

This paper introduces a latent position network model, called the genera...
10/12/2018

Learning Grid-like Units with Vector Representation of Self-Position and Matrix Representation of Self-Motion

This paper proposes a model for learning grid-like units for spatial awa...