A Fuzzy PID-Incorporated Stochastic Gradient Descent Algorithm for Fast and Accurate Latent Factor Analysis

A stochastic gradient descent (SGD)-based latent factor analysis (LFA) model can obtain superior performance when performing representation to a high-dimensional and incomplete (HDI) matrix, which is encountered in various big data-related applications cause of the great demand for describing the highly complex interactions among tremendous nodes. However, an SGD-based LFA model is often stacked by slow convergence since a standard SGD algorithm updates a single latent factor depending on the stochastic gradient of current instance learning error, which disregards the past learning information. To address this critical issue, this paper innovatively proposes a Fuzzy PID-incorporated SGD (FPS) algorithm with the following two-fold ideas: a) refining the instance learning error by modeling the past update information guided by the principle of a PID controller efficiently, and b) designing a fuzzy reasoning process to implement the gain parameter adaptation in a PID controller effectively. With it, an FPS-based LFA model is further built for fast and accurate latent factor analysis on an HDI matrix. Experiments conducted on six HDI datasets reveal that the proposed FPS-based LFA model surpasses state-of-the-art LFA models in computational efficiency and accuracy when estimating missing data within an HDI matrix.