Community Detection Guarantees using Embeddings Learned by Node2Vec

Andrew Davison, Samuel Carlyle Morgan, Owen G. Ward

Keywords: Network Embedding, Node2Vec, Community Detection, Networks

TL;DR: We show theoretical guarantees for community detection using node2vec embeddings of networks.

Abstract:

Embedding the nodes of a large network into an Euclidean space is a common objective in modern
machine learning, with a variety of tools available. These embeddings can then be used as features for
tasks such as community detection/node clustering or link prediction, where they achieve state of the art
performance. With the exception of spectral clustering methods, there is little theoretical understanding
for commonly used approaches to learning embeddings. In this work we examine the theoretical
properties of the embeddings learned by node2vec. Our main result shows that the use of k-means
clustering on the embedding vectors produced by node2vec gives weakly consistent community recovery
for the nodes in (degree corrected) stochastic block models. We also discuss the use of these embeddings
for node and link prediction tasks. We demonstrate this result empirically for both
real and simulated networks, and examine how this relates
to other embedding tools for network data.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 7361