Collaborative filtering (CF) methods for recommendation systems have been extensively researched, ranging from matrix factorization and autoencoder-based to graph filtering-based methods. Recently, lightweight methods that require almost no training have been recently proposed to reduce overall computation. However, existing methods still have room to improve the trade-offs among accuracy, efficiency, and robustness. In particular, there are no well-designed closed-form studies for \emph{balanced} CF in terms of the aforementioned trade-offs. In this paper, we design SVD-AE, a simple yet effective singular vector decomposition (SVD)-based linear autoencoder, whose closed-form solution can be defined based on SVD for CF. SVD-AE does not require iterative training processes as its closed-form solution can be calculated at once. Furthermore, given the noisy nature of the rating matrix, we explore the robustness against such noisy interactions of existing CF methods and our SVD-AE. As a result, we demonstrate that our simple design choice based on truncated SVD can be used to strengthen the noise robustness of the recommendation while improving efficiency. Code is available at https://github.com/seoyoungh/svd-ae.

翻译：推荐系统中的协同过滤（CF）方法已被广泛研究，涵盖矩阵分解、自编码器以及图滤波等方法。近年来，为降低整体计算开销，研究者提出了几乎无需训练的轻量级方法。然而，现有方法在准确性、效率和鲁棒性之间的权衡仍有改进空间。特别是，针对上述权衡的“均衡”协同过滤问题，目前尚缺乏精心设计的闭式解研究。本文设计了SVD-AE——一种基于奇异值分解（SVD）的简单而有效的线性自编码器，其闭式解可直接通过SVD定义以实现协同过滤。由于闭式解可一次性计算完成，SVD-AE无需迭代训练过程。此外，鉴于评分矩阵存在噪声特性，我们探讨了现有CF方法与SVD-AE对此类噪声交互的鲁棒性。实验表明，基于截断SVD的简单设计不仅能够提升推荐的噪声鲁棒性，同时可提高计算效率。代码已在https://github.com/seoyoungh/svd-ae公开。