# NetSMF: Large-Scale Network Embedding as Sparse Matrix Factorization

## TL;DR

NetSMF introduces a scalable large-scale network embedding method by sparsifying the matrix involved in spectral factorization, achieving high efficiency and effectiveness for massive networks.

## Contribution

The paper proposes NetSMF, a novel sparse matrix factorization approach for large-scale network embedding, improving scalability and maintaining embedding quality.

## Key findings

- NetSMF is the only method achieving high efficiency and effectiveness among benchmarks.
- It can generate embeddings for networks with tens of millions of nodes in 24 hours.
- Compared to DeepWalk, NetSMF is significantly faster, reducing computation from months to a day.

## Abstract

We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence implicitly factorizing a matrix with a closed form, and 2)the explicit factorization of such matrix generates more powerful embeddings than existing methods. However, directly constructing and factorizing this matrix---which is dense---is prohibitively expensive in terms of both time and space, making it not scalable for large networks. In this work, we present the algorithm of large-scale network embedding as sparse matrix factorization (NetSMF). NetSMF leverages theories from spectral sparsification to efficiently sparsify the aforementioned dense matrix, enabling significantly improved efficiency in embedding learning. The sparsified matrix is spectrally close to the original dense one with a theoretically bounded approximation error, which helps maintain the representation power of the learned embeddings. We conduct experiments on networks of various scales and types. Results show that among both popular benchmarks and factorization based methods, NetSMF is the only method that achieves both high efficiency and effectiveness. We show that NetSMF requires only 24 hours to generate effective embeddings for a large-scale academic collaboration network with tens of millions of nodes, while it would cost DeepWalk months and is computationally infeasible for the dense matrix factorization solution. The source code of NetSMF is publicly available (https://github.com/xptree/NetSMF).