Adaptive PID-Incorporated Nonnegative Latent Factor Analysis

Abstract

High-dimensional and incomplete (HDI) data are ubiquitous for representing the intricate interactions among a vast number of nodes arising from diverse real application scenarios. Nonnegative latent factor (NLF) models have demonstrated their effectiveness in extracting critical latent features from HDI data by leveraging a single latent factor (LF)-dependent, nonnegative, and multiplicative update (SLF-NMU) algorithm. However, the SLF-NMU algorithm always leads NLF models to converge sluggishly as it updates an LF based only on the current updated information. To address this critical issue, we present APNLF, which innovatively adopts an adaptive proportional–integral–derivative (PID) controller to enable the learning process of SLF-NMU to be more efficient. The proposed APNLF encompasses the following twofold ideas: 1) establishing a PID-increment-based SLF-NMU (PSN) algorithm, which updates an LF by comprehensively modeling the current, past, and future update increment information guided by the principle of a PID controller; and 2) designing an effective fuzzy reasoning rule to implement all hyperparameters adaptation, which boosts model’s applicability in practical applications. Moreover, APNLF’s convergence analysis is provided in theory. Experiments on five HDI datasets demonstrate that the APNLF model outperforms the state-of-the-art models in efficiency and accuracy on an HDI matrix. The source code is available at https://github.com/Aaaaapplege/APNLF-Development