A PID-incorporated Latent Factorization of Tensors Approach to Dynamically Weighted Directed Network Analysis

Hao Wu, Xin Luo, Meng Chu Zhou, Muhyaddin J. Rawa, Khaled Sedraoui, Aiiad Albeshri

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


A large-scale dynamically weighted directed network (DWDN) involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications, like in a terminal interaction pattern analysis system (TIPAS). It can be represented by a high-dimensional and incomplete (HDI) tensor whose entries are mostly unknown. Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN. A latent factorization-of-tensors (LFT) model proves to be highly efficient in extracting such knowledge from an HDI tensor, which is commonly achieved via a stochastic gradient descent (SGD) solver. However, an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs. To address this issue, this work proposes a proportional-integral-derivative (PID)-incorporated LFT model. It constructs an adjusted instance error based on the PID control principle, and then substitutes it into an SGD solver to improve the convergence rate. Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models, the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.

Original languageEnglish (US)
Pages (from-to)533-546
Number of pages14
JournalIEEE/CAA Journal of Automatica Sinica
Issue number3
StatePublished - Mar 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Information Systems
  • Control and Optimization
  • Artificial Intelligence


  • Big data
  • high dimensional and incomplete (HDI) tensor
  • latent factorization-of-tensors (LFT)
  • machine learning
  • missing data
  • optimization
  • proportional-integral-derivative (PID) controller


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