DeepAI
Log In Sign Up

Graph Encoder Embedding

09/27/2021
by   Cencheng Shen, et al.
57

In this paper we propose a lightning fast graph embedding method called graph encoder embedding. The proposed method has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC – an unattainable feat for any existing graph embedding method. The speedup is achieved without sacrificing embedding performance: the encoder embedding performs as good as, and can be viewed as a transformation of the more costly spectral embedding. The encoder embedding is applicable to either adjacency matrix or graph Laplacian, and is theoretically sound, i.e., under stochastic block model or random dot product graph, the graph encoder embedding asymptotically converges to the block probability or latent positions, and is approximately normally distributed. We showcase three important applications: vertex classification, vertex clustering, and graph bootstrap; and the embedding performance is evaluated via a comprehensive set of synthetic and real data. In every case, the graph encoder embedding exhibits unrivalled computational advantages while delivering excellent numerical performance.

READ FULL TEXT

page 4

page 5

page 7

page 8

10/02/2013

Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding

Vertex clustering in a stochastic blockmodel graph has wide applicabilit...
12/23/2019

Spectral embedding of regularized block models

Spectral embedding is a popular technique for the representation of grap...
08/06/2019

An Efficient JPEG Steganographic Scheme Design Using Domain Transformation of Embedding Cost

Although the recently proposed JPEG steganography using Block embedding ...
04/26/2019

Optimal Bayesian Estimation for Random Dot Product Graphs

We propose a Bayesian approach, called the posterior spectral embedding,...
07/28/2016

Limit theorems for eigenvectors of the normalized Laplacian for random graphs

We prove a central limit theorem for the components of the eigenvectors ...
10/10/2019

Efficient Estimation for Random Dot Product Graphs via a One-step Procedure

We propose a one-step procedure to efficiently estimate the latent posit...
01/17/2022

Detection of Correlated Alarms Using Graph Embedding

Industrial alarm systems have recently progressed considerably in terms ...