Collaborative filtering is one of the most fundamental topics for recommender systems. Various methods have been proposed for collaborative filtering, ranging from matrix factorization to graph convolutional methods. Being inspired by recent successes of graph filtering-based methods and score-based generative models (SGMs), we present a novel concept of blurring-sharpening process model (BSPM). SGMs and BSPMs share the same processing philosophy that new information can be discovered (e.g., new images are generated in the case of SGMs) while original information is first perturbed and then recovered to its original form. However, SGMs and our BSPMs deal with different types of information, and their optimal perturbation and recovery processes have fundamental discrepancies. Therefore, our BSPMs have different forms from SGMs. In addition, our concept not only theoretically subsumes many existing collaborative filtering models but also outperforms them in terms of Recall and NDCG in the three benchmark datasets, Gowalla, Yelp2018, and Amazon-book. In addition, the processing time of our method is comparable to other fast baselines. Our proposed concept has much potential in the future to be enhanced by designing better blurring (i.e., perturbation) and sharpening (i.e., recovery) processes than what we use in this paper.

翻译：协同过滤是推荐系统中最基础的研究课题之一。从矩阵分解到图卷积方法，已有多种方法被提出用于协同过滤。受近期基于图滤波的方法和基于分数的生成模型（SGMs）的成功启发，我们提出了模糊-锐化过程模型（BSPM）这一新颖概念。SGMs和BSPMs共享相同的处理哲学：在原始信息首先被扰动然后恢复至其原始形式的过程中，可以发现新信息（例如，在SGMs情形下能够生成新图像）。然而，SGMs与我们的BSPMs处理不同类型的信息，且它们的最优扰动与恢复过程存在根本性差异。因此，我们的BSPMs具有与SGMs不同的形式。此外，我们的概念不仅在理论上包含了众多现有协同过滤模型，而且在三个基准数据集（Gowalla、Yelp2018和Amazon-book）上，其在召回率（Recall）和归一化折损累计增益（NDCG）指标上均优于这些模型。同时，我们方法的处理时间与其他快速基线方法相当。通过设计比本文所用方法更优的模糊（即扰动）和锐化（即恢复）过程，我们提出的概念在未来具有巨大的提升潜力。