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 this https URL

通过设计一种基于奇异向量分解（SVD）的线性自编码器，该研究提出了一种简单而有效的 SVD-AE 算法，该算法不需要迭代训练过程，可以通过 SVD 的闭式解进行计算，提高了推荐系统的噪声容忍性和效率。