Alternating-Direction-Method of Multipliers-Based Adaptive Nonnegative Latent Factor Analysis

Abstract

Large scale interaction data are frequently found in industrial applications related with Big Data. Due to the fact that few interactions commonly happen among numerous nodes in real scenes, such data can be quantified into a High-Dimensional and Incomplete (HDI) matrix where most entries are unknown. An alternating-direction-method-based nonnegative latent factor model can perform efficient and accurate representation leaning to an HDI matrix, while its multiple hyper-parameters greatly limit its scalability for real applications. Aiming at implementing a highly-scalable and efficient latent factor model, this paper adopts the principle of particle swarm optimization and the tree-structured parzen estimator algorithm to facilitate the hyper-parameter adaptation mechanism, thereby building an Alternating-direction-method-based Adaptive Nonnegative Latent Factor (A ² NLF) model. Its theoretical convergence is rigorously proved. Empirical studies on several nonnegative HDI matrices from real applications demonstrate that the proposed A ² NLF model obtains higher computational and storage efficiency than several state-of-the-art models, along with significant accuracy gain. Its hyper-parameter adaptation is implemented smoothly, thereby greatly boosting its scalability in real problems.