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arXiv · 2401.12590

PolyCF: Towards the Optimal Spectral Graph Filters for Collaborative Filtering

Yifang Qin·Wei Ju·Xiao Luo·Yiyang Gu·Zhiping Xiao·Ming Zhang
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Abstract

Collaborative Filtering (CF) is a pivotal research area in recommender systems that capitalizes on collaborative similarities between users and items to provide personalized recommendations. With the remarkable achievements of node embedding-based Graph Neural Networks (GNNs), we explore the upper bounds of expressiveness inherent to embedding-based methodologies and tackle the challenges by reframing the CF task as a graph signal processing problem. To this end, we propose PolyCF, a flexible graph signal filter that leverages polynomial graph filters to process interaction signals. PolyCF exhibits the capability to capture spectral features across multiple eigenspaces through a series of Generalized Gram filters and is able to approximate the optimal polynomial response function for recovering missing interactions. A graph optimization objective and a pair-wise ranking objective are jointly used to optimize the parameters of the convolution kernel. Experiments on three widely adopted datasets demonstrate the superiority of PolyCF over current state-of-the-art CF methods. Moreover, comprehensive studies empirically validate each component's efficacy in the proposed PolyCF.

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Yifang Qin, Wei Ju, Xiao Luo, Yiyang Gu, Zhiping Xiao, Ming Zhang. 2024-01-23. PolyCF: Towards the Optimal Spectral Graph Filters for Collaborative Filtering. https://arxiv.org/abs/2401.12590

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