Unifying Graph Convolutional Networks as Matrix Factorization

Zhaocheng Liu, Qiang Liu, Haoli Zhang, Jun Zhu

TL;DR: We unify graph convolutional networks as co-training and unitized matrix factorization.

Abstract: In recent years, substantial progress has been made on graph convolutional networks (GCN). In this paper, for the first time, we theoretically analyze the connections between GCN and matrix factorization (MF), and unify GCN as matrix factorization with co-training and unitization. Moreover, under the guidance of this theoretical analysis, we propose an alternative model to GCN named Co-training and Unitized Matrix Factorization (CUMF). The correctness of our analysis is verified by thorough experiments. The experimental results show that CUMF achieves similar or superior performances compared to GCN. In addition, CUMF inherits the benefits of MF-based methods to naturally support constructing mini-batches, and is more friendly to distributed computing comparing with GCN. The distributed CUMF on semi-supervised node classification significantly outperforms distributed GCN methods. Thus, CUMF greatly benefits large scale and complex real-world applications.

Code: https://github.com/code20190923/CUMF

Keywords: graph convolutional networks, matrix factorization, unification