On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering

Collaborative filtering (CF) is an important research direction in recommender systems that aims to make recommendations given the information on user-item interactions. Graph CF has attracted more and more attention in recent years due to its effectiveness in leveraging high-order information in the user-item bipartite graph for better recommendations. Specifically, recent studies show the success of graph neural networks (GNN) for CF is attributed to its low-pass filtering effects. However, current researches lack a study of how different signal components contributes to recommendations, and how to design strategies to properly use them well. To this end, from the view of spectral transformation, we analyze the important factors that a graph filter should consider to achieve better performance. Based on the discoveries, we design JGCF, an efficient and effective method for CF based on Jacobi polynomial bases and frequency decomposition strategies. Extensive experiments on four widely used public datasets show the effectiveness and efficiency of the proposed methods, which brings at most 27.06% performance gain on Alibaba-iFashion. Besides, the experimental results also show that JGCF is better at handling sparse datasets, which shows potential in making recommendations for cold-start users.