A series of graph filtering (GF)-based collaborative filtering (CF) showcases state-of-the-art performance on the recommendation accuracy by using a low-pass filter (LPF) without a training process. However, conventional GF-based CF approaches mostly perform matrix decomposition on the item-item similarity graph to realize the ideal LPF, which results in a non-trivial computational cost and thus makes them less practical in scenarios where rapid recommendations are essential. In this paper, we propose Turbo-CF, a GF-based CF method that is both training-free and matrix decomposition-free. Turbo-CF employs a polynomial graph filter to circumvent the issue of expensive matrix decompositions, enabling us to make full use of modern computer hardware components (i.e., GPU). Specifically, Turbo-CF first constructs an item-item similarity graph whose edge weights are effectively regulated. Then, our own polynomial LPFs are designed to retain only low-frequency signals without explicit matrix decompositions. We demonstrate that Turbo-CF is extremely fast yet accurate, achieving a runtime of less than 1 second on real-world benchmark datasets while achieving recommendation accuracies comparable to best competitors.

翻译：一系列基于图滤波（GF）的协同过滤（CF）方法通过使用无训练过程的低通滤波器（LPF），在推荐准确性上展现出最先进的性能。然而，传统的基于GF的CF方法大多需要对项目-项目相似度图进行矩阵分解以实现理想的LPF，这导致了显著的计算开销，从而在需要快速推荐的场景中实用性不足。本文提出Turbo-CF——一种既无需训练也无需矩阵分解的基于GF的CF方法。Turbo-CF采用多项式图滤波器来规避昂贵的矩阵分解问题，从而能够充分利用现代计算机硬件组件（如GPU）。具体而言，Turbo-CF首先构建边权重得到有效调节的项目-项目相似度图；随后，我们设计了无需显式矩阵分解即可仅保留低频信号的专用多项式LPF。我们证明Turbo-CF兼具极速与高精度特性：在真实世界基准数据集上运行时间低于1秒，同时达到与最优竞争者相当的推荐准确率。