Convergence Analysis of a Fast Non-negative Latent Factor Model

A fast non-negative latent factor (FNLF) model adopts a single latent factor-dependent, non-negative, multiplicative and momentum-incorporated update (SLF-NM2 U) algorithm, which can ensure fast convergence on a high-dimensional and sparse (HiDS) matrix according to empirical studies in prior researches. However, it is crucial to investigate the theoretical proof regarding the reason why incorporation of a generalized momentum method into an SLF-NM2 U algorithm can ensure the fast convergence of an FNLF model, which has not been addressed in previous work. Therefore, this paper aims to unveil how a generalized momentum method improves the convergence rate of an FNLF model in the discrete time case by combining physical analysis. The FNLF model is superior to the NLF model in terms of the convergence rate and the prediction accuracy of missing data. This conclusion is obtained by empirically research on the HiDS matrix in industrial applications, which also provides empirical basis for theoretical proof.