Simplification of Graph Convolutional Networks: A Matrix Factorization-based Perspective

TL;DR

This paper simplifies Graph Convolutional Networks by connecting them with Matrix Factorization, proposing a new model UCMF that is more scalable and performs well on large-scale graph tasks.

Contribution

It analyzes the relationship between GCN and MF, and introduces UCMF, a novel, scalable alternative that maintains or improves performance on key graph tasks.

Findings

UCMF achieves comparable or better accuracy than GCN on node classification.

Distributed UCMF outperforms distributed GCN in large-scale settings.

UCMF outperforms several graph embedding models in community detection.

Abstract

In recent years, substantial progress has been made on Graph Convolutional Networks (GCNs). However, the computing of GCN usually requires a large memory space for keeping the entire graph. In consequence, GCN is not flexible enough, especially for large scale graphs in complex real-world applications. Fortunately, methods based on Matrix Factorization (MF) naturally support constructing mini-batches, and thus are more friendly to distributed computing compared with GCN. Accordingly, in this paper, we analyze the connections between GCN and MF, and simplify GCN as matrix factorization with unitization and co-training. Furthermore, under the guidance of our analysis, we propose an alternative model to GCN named Unitized and Co-training Matrix Factorization (UCMF). Extensive experiments have been conducted on several real-world datasets. On the task of semi-supervised node classification, the experimental results illustrate that UCMF achieves similar or superior performances compared with GCN. Meanwhile, distributed UCMF significantly outperforms distributed GCN methods, which shows that UCMF can greatly benefit large scale and complex real-world applications. Moreover, we have also conducted experiments on a typical task of graph embedding, i.e., community detection, and the proposed UCMF model outperforms several representative graph embedding models.