A Nonlinear Proportional Integral Derivative-Incorporated Stochastic Gradient Descent-based Latent Factor Model

Abstract

Recommender system (RS) commonly describes its user-item preferences with a high-dimensional and sparse (HiDS) matrix. A latent factor (LF) model relying on stochastic gradient descent (SGD) is frequently adopted to extract useful information from such an HiDS matrix. In spite of its efficiency, an SGD-based LF model commonly takes many iterations to converge. When processing a large-scale HiDS matrix, its computational efficiency should be further improved by further accelerating its convergence rate as well as maintaining its learning ability. To address this issue, this paper innovatively proposes novel SGD algorithm which incorporates a nonlinear proportional integral derivative (NPID) controller into its learning scheme for building an LF model. The main idea is to adopt an NPID controller to model the learning residual achieved in the past iterations, thereby adjusting the learning direction and step size of the current iteration, thereby making a resultant model converge fast. With the NPID-incorporated SGD algorithm, this study proposes an NPID-SGD-based LF (NSLF) model. Experimental results on two HiDS matrices demonstrate that compared with a standard SGD-based LF model, the proposed model achieves higher computational efficiency and prediction accuracy for missing data of an HiDS matrix.