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We propose a novel nonnegative matrix factorization (NMF) technique that integrates domain-specific constraints inherent to electron microscopy. This constrained NMF was applied to four-dimensional (4D) scanning transmission electron microscopy (STEM). Using the constrained NMF 4D-STEM data were successfully decomposed into interpretable diffractions and maps that cannot be achieved using principal component analysis (PCA) and primitive NMF. Additionally, hierarchical clustering was optimized based on diffraction similarity, which is a combination of a polar coordinate transformation and cross-correlation. Nanometer-sized crystalline precipitates embedded in an amorphous metallic glass, ZrCuAl, were successfully detected and classified according to their diffraction patterns. The present scheme is broadly applicable across various characterization techniques, including hyperspectral imaging, and effectively mitigates the known artifacts found in conventional machine learning techniques that rely solely on mathematical constraints without domain-specific knowledge.

Rights:

• Creative Commons BY Attribution 4.0 International
  

Keyword: 4D-STEM, unsupervised machine learning, nonnegative matrix factorization, scanning transmission electron microscopy, metallic glass, amorphous, ZrCuAl

Date published: 2025-11-07

Publisher: Springer Science and Business Media LLC

Journal:

• Scientific Reports (ISSN: 20452322) vol. 15 issue. 1 39143

Funding:

• Japan Society for the Promotion of Science JP 22H05145
• Japan Society for the Promotion of Science JP23H04874
• Japan Society for the Promotion of Science 20H02624
• Japan Society for the Promotion of Science 20H02624

Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1038/s41598-025-23541-7

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Updated at: 2025-12-01 12:30:04 +0900

Published on MDR: 2025-12-01 12:23:45 +0900