Non-negative Matrix Factorization and Its Extensions for Spectral Image Data Analysis

Abstract

Scanning transmission electron microscopy combined with electron energy-loss spectroscopy and energy-dispersive X-ray spectroscopy is useful for analyzing chemical states and elemental components in a new material. Using these instruments, the spectra over the spatial grid points in a region of interest can be observed. This measurement technique is called spectral imaging (SI). Because of the large size of SI data, the analysis cost is a bottleneck in the evaluation process of the material. To reduce the analysis cost, machine learning techniques can be applied, which can automatically extract essential information from the data. This paper reviews our developed machine learning method, which is based on non-negative matrix factorization and its extensions. A spatial orthogonality constraint and a generalized noise model, which includes Gaussian and Poisson noise models, are introduced. Numerical experiments demonstrate the effectiveness and characteristics of our developed methods.