A Proportional-Integral Controller-Incorporated SGD Algorithm for High Efficient Latent Factor Analysis

In industrial big data scenarios, high-dimensional sparse matrices (HDI) are widely used to characterize high-order interaction relationships among massive nodes. The stochastic gradient descent-based latent factor analysis (SGD-LFA) method can effectively extract deep feature information embedded in HDI matrices. However, existing SGD-LFA methods exhibit significant limitations: their parameter update process relies solely on the instantaneous gradient information of current samples, failing to incorporate accumulated experiential knowledge from historical iterations or account for intrinsic correlations between samples, resulting in slow convergence speed and suboptimal generalization performance. Thus, this paper proposes a PILF model by developing a PI-accelerated SGD algorithm by integrating correlated instances and refining learning errors through proportional-integral (PI) control mechanism that current and historical information; Comparative experiments demonstrate the superior representation capability of the PILF model on HDI matrices

An ADRC-Incorporated Stochastic Gradient Descent Algorithm for Latent Factor Analysis

High-dimensional and incomplete (HDI) matrix contains many complex interactions between numerous nodes. A stochastic gradient descent (SGD)-based latent factor analysis (LFA) model is remarkably effective in extracting valuable information from an HDI matrix. However, such a model commonly encounters the problem of slow convergence because a standard SGD algorithm only considers the current learning error to compute the stochastic gradient without considering the historical and future state of the learning error. To address this critical issue, this paper innovatively proposes an ADRC-incorporated SGD (ADS) algorithm by refining the instance learning error by considering the historical and future state by following the principle of an ADRC controller. With it, an ADS-based LFA model is further achieved for fast and accurate latent factor analysis on an HDI matrix. Empirical studies on two HDI datasets demonstrate that the proposed model outperforms the state-of-the-art LFA models in terms of computational efficiency and accuracy for predicting the missing data of an HDI matrix.

A Nonlinear PID-Enhanced Adaptive Latent Factor Analysis Model

High-dimensional and incomplete (HDI) data holds tremendous interactive information in various industrial applications. A latent factor (LF) model is remarkably effective in extracting valuable information from HDI data with stochastic gradient decent (SGD) algorithm. However, an SGD-based LFA model suffers from slow convergence since it only considers the current learning error. To address this critical issue, this paper proposes a Nonlinear PID-enhanced Adaptive Latent Factor (NPALF) model with two-fold ideas: 1) rebuilding the learning error via considering the past learning errors following the principle of a nonlinear PID controller; b) implementing all parameters adaptation effectively following the principle of a particle swarm optimization (PSO) algorithm. Experience results on four representative HDI datasets indicate that compared with five state-of-the-art LFA models, the NPALF model achieves better convergence rate and prediction accuracy for missing data of an HDI data.