Application of machine learning techniques to electron microscopic/spectroscopic image data analysis

The combination of scanning transmission electron microscopy (STEM) with analytical instruments has become one of the most indispensable analytical tools in materials science. A set of microscopic image/spectral intensities collected from many sampling points in a region of interest, in which multiple physical/chemical components may be spatially and spectrally entangled, could be expected to be a rich source of information about a material. To unfold such an entangled image comprising information and spectral features into its individual pure components would necessitate the use of statistical treatment based on informatics and statistics. These computer-aided schemes or techniques are referred to as multivariate curve resolution, blind source separation or hyperspectral image analysis, depending on their application fields, and are classified as a subset of machine learning. In this review, we introduce non-negative matrix factorization, one of these unfolding techniques, to solve a wide variety of problems associated with the analysis of materials, particularly those related to STEM, electron energy-loss spectroscopy and energy-dispersive X-ray spectroscopy. This review, which commences with the description of the basic concept, the advantages and drawbacks of the technique, presents several additional strategies to overcome existing problems and their extensions to more general tensor decomposition schemes for further flexible applications are described.