Convergence Analysis of an SLF-NMU Algorithm for Non-negative Latent Factor Analysis on a High-Dimensional and Sparse Matrix

Abstract

Non-negative latent factor (NLF) models have been frequently applied to information extraction, pattern recognition, and community detection. An NLF model can well represent a high-dimensional and sparse (HiDS) matrix of non-negative data and efficiently acquire useful knowledge from it. A single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) algorithm is highly efficient to build NLF model. However, its convergence ability on such a matrix is still unveiled in theory. This paper presents the convergence property of an SLF-NMU algorithm. We theoretically prove that it can guarantee its convergence to a Karush-Kuhn-Tucher (KKT) stationary point. Empirical studies on two HiDS matrices from practical applications indicate that an SLF-NMU algorithm make an NLF model to converge at a relatively steady state.