Nonnegative matrix factorization incorporating domain specific constraints for four dimensional scanning transmission electron microscopy

Modern electron microscopy enables the acquisition of extremely large datasets, necessitating optimized machine learning techniques, such as dimensionality reduction and clustering, to extract material insights. We propose a novel nonnegative matrix factorization (NMF) technique that integrates domain-specific constraints inherent to electron microscopy, including spatial resolution and continuous intensity features without downward-convex peaks. This constrained NMF was applied to four-dimensional (4D) scanning transmission electron microscopy (STEM). Using the constrained NMF, both simulated and actual experimental data were successfully decomposed into interpretable diffractions and maps that cannot be achieved using principal component analysis (PCA) and primitive NMF methods. Additionally, hierarchical clustering was optimized based on diffraction similarity, which is a combination of a polar coordinate transformation and uniaxial cross-correlation. Then, 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.