A Second-Order Symmetric Non-Negative Latent Factor Model for Undirected Weighted Network Representation

Abstract

Precise representation to undirected weighted network (UWN) is the foundation of understanding connection patterns inside a massive node set. It can be addressed via a Symmetric Non-negative Latent Factor (SNLF) model with a non-convex learning objective. However, existing SNLF models commonly adopt a first-order learning algorithm that cannot well handle such a non-convex objective, thereby leading to inaccurate UWN representation. Aiming at addressing this issue, this study incorporates an efficient second-order learning algorithm into an SNLF model, thereby establishing a Second-order Symmetric Non-negative Latent Factor (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> NLF) model with two-fold ideas: a) applying the single latent factor-related mapping function to the non-negativity constrained optimization parameters to achieve an unconstrained learning objective, and b) optimizing this learning objective with its optimization parameters through an efficient second-order learning algorithm to achieve accurate representation to the target UWN with affordable computational burden. Empirical studies indicate that owing to its efficient incorporation of the second-order optimization technique, the proposed S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> NLF model outperforms state-of-the-art SNLF models when they are used to gain highly accurate representation to UWNs emerging from real applications.