Alternating nonnegative least squares-incorporated regularized symmetric latent factor analysis for undirected weighted networks

An Undirected Weighted Network (UWN) can be precisely quantified as an adjacency matrix whose inherent characteristics are fully considered in a Symmetric Nonnegative Latent Factor (SNLF) model for its good representation accuracy. However, an SNLF model uses a sole latent factor matrix to precisely describe the topological characteristic of a UWN, i.e., symmetry, thereby impairing its representation learning ability. Aiming at addressing this issue, this paper proposes an Alternating nonnegative least squares-incorporated Regularized Symmetric Latent factor analysis (ARSL) model. First of all, equation constraints composed of multiple matrices are built in its learning objective for well describing the symmetry of a UWN. Note that it adopts an L₂-norm-based regularization scheme to relax such constraints for making such a symmetry-aware learning objective solvable. Then, it designs an alternating nonnegative least squares-incorporated algorithm for optimizing its parameters efficiently. Empirical studies on four UWNs demonstrate that an ARSL model outperforms the state-of-the-art models in terms of representation accuracy, as well as achieves promising computational efficiency.