A Proportional Integral Controller-Enhanced Non-Negative Latent Factor Analysis Model
Ye Yuan, Siyang Lu, Xin Luo · IEEE/CAA Journal of Automatica Sinica · 2025
A non-negative latent factor (NLF) model is able to be built efficiently via a single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) algorithm for performing precise representation to high-dimensional and incomplete (HDI) matrix from many kinds of big-data-related applications. However, an SLF-NMU algorithm updates a latent factor relying on the current update increment only without considering past learning information, making a resultant model suffer from slow convergence. To address this issue, this study proposes a proportional integral (PI) controller-enhanced NLF (PI-NLF) model with two-fold ideas: 1) Designing an increment refinement (IR) mechanism, which formulates the current and past update increments as the proportional and integral terms of a PI controller, thereby assimilating the past update information into the learning scheme smoothly with high efficiency; 2) Deriving an IR-based SLF-NMU (ISN) algorithm, which updates a latent factor following the principle of an IR mechanism, thus significantly accelerating an NLF model's convergence rate. The simulation results on eight HDI matrices collected by real applications validate that a PI-NLF model outstrips several leading-edge models in both computational efficiency and accuracy when estimating missing data within an HDI matrix. The proposed PI-NLF model can be effectively applied to applications involving HDI matrix like e-commerce system, social network, and cloud service system. The code is available at https://github.com/yuanyeswu/PINLF/blob/mainIPINLF-code.zip.