Non-negativity constrained missing data estimation for high-dimensional and sparse matrices

Abstract

Latent factor (LF) models have proven to be accurate and efficient in extracting hidden knowledge from high-dimensional and sparse (HiDS) matrices. However, most LF models fail to fulfill the non-negativity constraints that reflect the non-negative nature of industrial data. Yet existing non-negative LF models for HiDS matrices suffer from slow convergence leading to considerable time cost. An alternating direction method-based non-negative latent factor (ANLF) model decomposes a non-negative optimization process into small sub-tasks. It updates each LF non-negatively based on the latest state of those trained before, thereby achieving fast convergence and maintaining high prediction accuracy and scalability. This paper theoretically analyze the characteristics of an ANLF model, and presents detailed empirical study regarding its performance on several HiDS matrices arising from industrial applications currently in use. Therefore, its capability of addressing HiDS matrices is validated in both theory and practice.