Symmetric and Nonnegative Latent Factor Models for Undirected, High-Dimensional, and Sparse Networks in Industrial Applications

Undirected, high-dimensional, and sparse (HiDS) networks are frequently encountered in industrial applications. They contain rich knowledge regarding various useful patterns. Nonnegative latent factor (NLF) models are effective and efficient in extracting useful knowledge from directed networks. However, they cannot describe the symmetry of an undirected network. For addressing this issue, this paper analyzes the extraction process of NLFs on asymmetric and symmetric matrices, respectively, thereby innovatively achieving the symmetric and nonnegative latent factor (SNLF) models for undirected, HiDS networks. The proposed SNLF models are equipped with: 1) high efficiency; 2) nonnegativity; and 3) symmetry. Experimental results on real networks show that the SNLF models are able to: 1) describe the symmetry of the target network rigorously; 2) ensure the nonnegativity of resultant latent factors; and 3) achieve high computational efficiency when addressing data analysis tasks like missing data estimation.