Spectral Analysis in High-Dimensional Data Space: Insights from Information Geometry

Abstract

This paper explores the application of informatics technologies to “measurement,” a core aspect of research in the natural sciences. Specifically, it focuses on the analysis of spectrum image (SI) data acquired through the combination of scanning transmission electron microscopy (STEM) with electron energy loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDS). The study emphasizes the reliability and limitations of chemical imaging achieved using non-negative matrix factorization (NMF). Through the example of label-free chemical imaging of polymer blends via the STEM-EELS-SI method, the research demonstrates the construction of a sparse, multidimensional descriptor space that captures the intrinsic information embedded in experimental data. This methodology addresses the challenges of NMF and provides a physically interpretable approach to chemical imaging. Lastly, the paper proposes practical recommendations for integrating informatics technologies into measurement processes, enhancing the accuracy and interpretability of data analysis in materials science.