Iterative update scheme for nonnegative and sparse linear autoencoders in recommendation

Linear autoencoder models with nonnegative constraints and L1 regularization, such as the sparse linear method (SLIM), have shown remarkable performance while maintaining interpretability. However, their practicality is limited by computationally expensive training processes. This paper proposes a simple yet effective training framework for nonnegative and sparse linear autoencoders. We first develop a simple iterative update scheme (IUS) for SLIM and present a theoretical analysis of its convergence and correctness. To enhance computational efficiency, we then introduce a filtering step that prunes insignificant parameters at each iteration in practice. Based on this training scheme, we derive two model variants by removing the zero-diagonal constraint and utilizing random dropout denoising to replace L2 regularization (i.e., the dropout-based regularization in DLAE), respectively. Experimental results demonstrate that the proposed IUS algorithm reduces training time by 53.8–68.5% and memory usage by 55.6% compared to the alternating direction method of multipliers (ADMM) across six benchmark datasets. The proposed model variants achieve comparable or superior performance to state-of-the-art collaborative filtering models on all real-world datasets. These findings validate the proposed training framework’s capability to enable feasible deployment of SLIM-like models in efficiency-critical and resource-constrained environments.