How Powerful is Graph Convolution for Recommendation?

• URL: http://arxiv.org/abs/2108.07567v1
• Date: Tue, 17 Aug 2021 11:38:18 GMT
• Title: How Powerful is Graph Convolution for Recommendation?
• Authors: Yifei Shen, Yongji Wu, Yao Zhang, Caihua Shan, Jun Zhang, Khaled B. Letaief, Dongsheng Li
• Abstract summary: Graph convolutional networks (GCNs) have recently enabled a popular class of algorithms for collaborative filtering (CF) In this paper, we endeavor to obtain a better understanding of GCN-based CF methods via the lens of graph signal processing.
• Score: 21.850817998277158
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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