How Powerful is Graph Convolution for Recommendation?
This work provides theoretical insights for researchers in graph-based recommendation, though it is incremental as it builds on existing GCN methods.
The paper tackles the lack of theoretical understanding of graph convolutional networks (GCNs) in collaborative filtering by developing a unified framework based on graph signal processing, showing that GF-CF, a simple baseline derived from this framework, achieves competitive performance, including a 70% gain over LightGCN on Amazon-book.
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.