  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.
