Non-Negative Latent Factor Model Based on β-Divergence for Recommender Systems

Luo Xin, Ye Yuan, Mengchu Zhou, Zhigang Liu, Mingsheng Shang

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


Non-negative latent factor (NLF) models well represent high-dimensional and sparse (HiDS) matrices filled with non-negative data, which are frequently encountered in industrial applications like recommender systems. However, current NLF models mostly adopt Euclidean distance in their objective function, which represents a special case of a {{β }} -divergence function. Hence, it is highly desired to design a {{β }} -divergence-based NLF ( {{β }} -NLF) model that uses a {{β }} -divergence function, and investigate its performance in recommender systems as {{β }} varies. To do so, we first model {{β }} -NLF's learning objective with a {{β }} -divergence function. Subsequently, we deduce a general single latent factor-dependent, non-negative and multiplicative update scheme for {{β }} -NLF, and then design an efficient {{β }} -NLF algorithm. The experimental results on HiDS matrices from industrial applications indicate that by carefully choosing the value of {{β }} , {{β }} -NLF outperforms an NLF model with Euclidean distance in terms of accuracy for missing data prediction without increasing computational time. The research outcomes show the necessity of using an optimal {{β }} -divergence function in order to achieve the best performance of an NLF model on HiDS matrices. Hence, the proposed model has both theoretical and application significance.

Original languageEnglish (US)
Article number8809405
Pages (from-to)4612-4623
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number8
StatePublished - Aug 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • big data
  • high-dimensional and sparse (HiDS) matrix
  • industrial application
  • learning algorithm
  • non-negative latent factor (NLF) analysis
  • recommender system
  • β-divergence


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