A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

Abstract

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

MLstructureMining: a machine learning tool for structure identification from X-ray pair distribution functions

“…10,12–14 Here we explore the use of machine learning (ML) to accelerate and automate this process for the case of crystal structure model screening. ML has been successfully employed for various tasks in crystallography and structural analysis, for example, for isolating unique signals from in situ PDF series, 15,16 suggesting space groups 17 and identifying structures ab initio from PDF data. 14,18,19…”