Community Detection Guarantees Using Embeddings Learned by Node2Vec

TL;DR

This paper provides theoretical guarantees for community detection using node2vec embeddings, showing that k-means clustering on these embeddings can reliably recover communities in stochastic block models.

Contribution

It offers the first theoretical analysis of node2vec embeddings, establishing conditions under which community detection via k-means is consistent.

Findings

k-means on node2vec embeddings achieves weakly consistent community recovery

Empirical validation supports theoretical results

Discussion of embeddings' effectiveness for link prediction

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, and examine how this relates to other embedding tools for network data.