A Proximal Alternating-direction-method-of-multipliers-based Nonnegative Latent Factor Model

A high dimensional and sparse (HiDS) matrix is commonly found in big data-related industrial applications. An alternating direction method of multipliers (ADMM)-based nonnegative latent factor (ANLF) model can efficiently extract latent patterns and knowledge from an HiDS matrix filled with nonnegative data. However, it suffers fluctuations near the local minimum, thereby leading to accuracy loss. To address this issue, this paper proposes a proximal alternating-direction-method-of-multipliers-based nonnegative latent factor (PANLF) model with the following ideas: a) building an augmented Lagrangian function for addressing nonnegativity constraints; b) incorporating proximal regularization into the learning scheme of decision parameters to fast search a local optimum, and c) adopting ADMM to split an optimization task into multiple subtasks where each one is solved based on the results of previously solved ones for fast convergence. Experimental results on four industrial-size HiDS matrices demonstrate that when compared with state-of-the-art models, PANLF possesses higher accuracy with comparable time and space complexity in predicting the missing data of an HiDS matrix.