Proportional-Integral-Derivative-Incorporated Latent Factorization of Tensors for Large-Scale Dynamic Network Analysis

A large-scale dynamic network (LDN) involving numerous entities and massive dynamic interactions is an essential data source in many practical industrial applications. It can be represented by a third-order high-dimensional and incomplete (HDI) tensor whose entries are mostly unknown. Yet such a third-order HDI tensor contains wealthy knowledge regarding miscellaneous desired patterns like potential links in an LDN. A stochastic gradient descent-based latent factorization of tensors (LFT) model can extract such knowledge from an HDI tensor. Nevertheless, a stochastic gradient descent-based LFT model commonly suffers from slow convergence that impairs its efficiency on an LDN. To address this issue, this work proposes a Proportional-integral-derivative (PID)-incorporated LFT (PLFT) model. It constructs an adjusted instance error based on the PID control principle, and then substitute it into a stochastic gradient descent algorithm to improve the convergence rate. Experimental results on one LDN generated by a real industrial application show that a PLFT model is able to exceed state-of-the-art models in terms of computational efficiency as well as obtains highly competitive prediction accuracy when handling the task of missing link prediction for a given LDN.