A fast self-adaptive intuitionistic fuzzy latent factor model

Latent factor (LF) model is an efficient method for extracting potential useful information from high-dimensional and incomplete (HDI) matrices. Gradient descent (GD) is a classical learning algorithm and often applied in LF models. However, the standard GD-based LF models rely heavily on learning rate setting, while existing adaptive GD algorithms still update the learning rates corresponding to all parameters uniformly with solidified static rules. This rigidity hinders the model's capacity for parameter-specific learning rate adjustments, thereby prolonging training time and increasing computational expense. Motivated by this discovery, we propose a dynamic single-latent-factor-dependent and self-adaptive intuitionistic fuzzy updating (SLF-SIFU) algorithm and an intuitionistic fuzzy latent factor (IFLF) model. Its main ideas are two fold- ideas: 1) use intuitionistic fuzzy numbers (IFNs) to dynamically model the uncertain relationship between learning rates and gradients during each iteration of each latent factor parameter for guiding learning rate update; 2) decouple the GD algorithm to separate gradient magnitude and direction information, which prevent the extremely large gradient from invalidating the learning rate and causing oscillatory convergence. Experiments on four widely-used HDI datasets show that the IFLF model outperforms state-of-the-art LF models in terms of accuracy and convergence speed with good generalizability.