How Powerful is Graph Convolution for Recommendation?

TL;DR

This paper analyzes the effectiveness of graph convolutional networks in recommendation systems through graph signal processing, introduces a unified framework, and proposes a simple, efficient baseline that outperforms some existing deep learning methods.

Contribution

It provides a theoretical framework linking GCN-based collaborative filtering to graph signal processing and introduces GF-CF, a computationally efficient baseline with strong empirical results.

Findings

GF-CF achieves competitive or better performance than deep learning methods.

GF-CF outperforms LightGCN by 70% on Amazon-book dataset.

Many existing CF methods are special cases of the proposed framework.

Abstract

Graph convolutional networks (GCNs) have recently enabled a popular class of algorithms for collaborative filtering (CF). Nevertheless, the theoretical underpinnings of their empirical successes remain elusive. In this paper, we endeavor to obtain a better understanding of GCN-based CF methods via the lens of graph signal processing. By identifying the critical role of smoothness, a key concept in graph signal processing, we develop a unified graph convolution-based framework for CF. We prove that many existing CF methods are special cases of this framework, including the neighborhood-based methods, low-rank matrix factorization, linear auto-encoders, and LightGCN, corresponding to different low-pass filters. Based on our framework, we then present a simple and computationally efficient CF baseline, which we shall refer to as Graph Filter based Collaborative Filtering (GF-CF). Given an implicit feedback matrix, GF-CF can be obtained in a closed form instead of expensive training with back-propagation. Experiments will show that GF-CF achieves competitive or better performance against deep learning-based methods on three well-known datasets, notably with a $70\%$ performance gain over LightGCN on the Amazon-book dataset.