Non-negative matrix factorization for mining big data obtained using four-dimensional scanning transmission electron microscopy.

Scientific instruments for material characterization have recently been improved to yield big data. For instance, scanning transmission electron microscopy (STEM) allows us to acquire many diffraction patterns from a scanning area, which is referred to as four-dimensional (4D) STEM. Here we study a combination of 4D-STEM and a statistical technique called non-negative matrix factorization (NMF) to deduce sparse diffraction patterns from a 4D-STEM data consisting of 10,000 diffraction patterns. Titanium oxide nanosheets are analyzed using this combined technique, and we discriminate the two diffraction patterns from pristine TiO2 and reduced Ti2O3 areas, where the latter is due to topotactic reduction induced by electron irradiation. The combination of NMF and 4D-STEM is expected to become a standard characterization technique for a wide range materials.