Relaxed Symmetric Non-negative Latent Factor Analysis for Large-scale Undirected Weighted Networks

Abstract

A large-scale undirected weighted network (LUWN) is described by a symmetric high-dimensional and sparse (SHiDS) matrix. To correctly represent its symmetry, existing models adopt a strong symmetry assumption, i.e., reducing the solution space to adopt a unique latent factor matrix to describe an SHiDS matrix’s symmetry. Yet it may impair a resultant model’s representativeness to its numerical features. Aiming at addressing this issue, this work proposes a Relaxed Symmetric Non-negative latent factor analysis (RSN) model that adopts three-fold ideas: a) Introducing a triple equation constraint into its learning objective for relaxing the strong symmetry assumption, thereby greatly improving its representativeness to the numerical features of an SHiDS matrix; b) Adopting the framework of Alternating Direction Method of Multipliers to fast realize its learning objective subject to multiple constraints; and c) utilizing a data density-oriented principle during its modeling and optimization, thereby precisely representing an SHiDS matrix’s imbalanced data. Empirical studies on four industrial SHiDS matrices describing real LUWNs demonstrate that RSN outperforms state-of-the-art models in representing an SHiDS matrix precisely, as well as achieves highly competitive computational efficiency. Hence, this work greatly advances the area of LUWN analysis.