Community Detection Guarantees Using Embeddings Learned by Node2Vec
This work addresses the problem of theoretical guarantees for network embeddings, which is incremental as it builds on existing methods like spectral clustering.
The paper tackles the lack of theoretical understanding for node2vec embeddings by proving that k-means clustering on these embeddings provides weakly consistent community recovery in degree-corrected stochastic block models, and demonstrates this empirically.
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.