A fast two‐stage algorithm for non‐negative matrix factorization in smoothly varying data. Issue 2 (24th February 2023)

• Record Type: Journal Article
• Authors: Gu, Ran; Billinge, Simon J. L.; Du, Qiang
• Is Part Of: Acta crystallographica. Volume 79:Issue 2(2023)
• Page Start: 203
• Page End: 216
• Publication Date: 2023-02-24
• Subjects: non‐negative matrix factorization -- smoothly varying data -- pair distribution function -- interior point method; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273323000761
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : A fast two‐stage algorithm developed for highly efficient and accurate non‐negative matrix factorization in smoothly varying data, such as atomic pair distribution function data, is reported. 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.