Non-Negative Latent Factor Model Based on β-Divergence for Recommender Systems

Non-negative latent factor (NLF) models well represent high-dimensional and sparse (HiDS) matrices filled with non-negative data, which are frequently encountered in industrial applications like recommender systems. However, current NLF models mostly adopt Euclidean distance in their objective function, which represents a special case of a β-divergence function. Hence, it is highly desired to design a β-divergence-based NLF ( β-NLF) model that uses a β-divergence function, and investigate its performance in recommender systems as β varies. To do so, we first model β-NLF's learning objective with a β-divergence function. Subsequently, we deduce a general single latent factor-dependent, non-negative and multiplicative update scheme for β-NLF, and then design an efficient β-NLF algorithm. The experimental results on HiDS matrices from industrial applications indicate that by carefully choosing the value of β, β-NLF outperforms an NLF model with Euclidean distance in terms of accuracy for missing data prediction without increasing computational time. The research outcomes show the necessity of using an optimal β-divergence function in order to achieve the best performance of an NLF model on HiDS matrices. Hence, the proposed model has both theoretical and application significance.