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.

本文通过图信号处理的角度，研究了基于图卷积网络 (GCNs) 的协作过滤 (CF) 方法的理论，提出了基于图卷积的统一框架，证明了现有的许多 CF 方法都是这个框架的特例，包括邻域方法、低秩矩阵分解、线性自编码器和 LightGCN 等，提出了基于图滤波的协作过滤 (GF-CF) 作为基准模型，在三个知名数据集上实验表明，GF-CF 与基于深度学习的方法相比性能更强，在 Amazon-book 数据集上比 LightGCN 的性能提升了 70%。