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.

翻译：协同过滤（CF）是推荐系统中一项关键研究领域，它利用用户与物品之间的协同相似性提供个性化推荐。鉴于基于节点嵌入的图神经网络（GNN）取得的显著成就，我们探索了嵌入方法固有的表达力上限，并通过将CF任务重述为图信号处理问题来应对挑战。为此，我们提出PolyCF——一种灵活的图信号滤波器，利用多项式图滤波器处理交互信号。PolyCF能够通过一系列广义格拉姆滤波器捕获多个特征空间上的频谱特征，并近似最优多项式响应函数以恢复缺失的交互。通过联合使用图优化目标与成对排序目标来优化卷积核的参数。在三个广泛采用的数据集上的实验表明，PolyCF相较于当前最先进的CF方法具有优越性。此外，综合研究经验性地验证了所提PolyCF中每个组件的有效性。