Stretched non-negative matrix factorization

• Published in: npj computational materials Vol. 10; no. 1; pp. 193 - 15
• Main Authors: Gu, Ran, Rakita, Yevgeny, Lan, Ling, Thatcher, Zach, Kamm, Gabrielle E., O’Nolan, Daniel, Mcbride, Brennan, Wustrow, Allison, Neilson, James R., Chapman, Karena W., Du, Qiang, Billinge, Simon J. L.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 27.08.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/301/1034; 639/301/1034/1037; Algorithms; Characterization and Evaluation of Materials; Chemical reactions; Chemistry; Chemistry and Materials Science; Computational Intelligence; Data analysis; Diffraction; Factorization; Fourier transforms; Independent variables; Materials Science; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Performance evaluation; Real time; Sparsity; Stretching; Temperature; Theoretical
• ISSN: 2057-3960; 2057-3960
• DOI: 10.1038/s41524-024-01377-5

A novel algorithm, stretched NMF, is introduced for non-negative matrix factorization (NMF), accounting for signal stretching along the independent variable’s axis. It addresses signal variability caused by stretching, proving beneficial for analyzing data such as powder diffraction at varying temperatures. This approach provides a more meaningful decomposition, particularly when the component signals resemble those from chemical components in the sample. The stretched NMF model introduces a stretching factor to accommodate signal expansion, solved using discretization and Block Coordinate Descent algorithms. Initial experimental results indicate that the stretched NMF model outperforms conventional NMF for datasets exhibiting such expansion. An enhanced version, sparse-stretched NMF, optimized for powder diffraction data from crystalline materials, leverages signal sparsity for accurate extraction, especially with small stretches. Experimental results showcase its effectiveness in analyzing diffraction data, including success in real-time chemical reaction experiments.