Validation of non-negative matrix factorization for rapid assessment of large sets of atomic pair distribution function data

Abstract

The use of the non-negative matrix factorization (NMF) technique is validated for automatically extracting physically relevant components from atomic pair distribution function (PDF) data from time-series data such as in situ experiments. The use of two matrix-factorization techniques, principal component analysis and NMF, on PDF data is compared in the context of a chemical synthesis reaction taking place in a synchrotron beam, applying the approach to synthetic data where the correct composition is known and on measured PDFs from previously published experimental data. The NMF approach yields mathematical components that are very close to the PDFs of the chemical components of the system and a time evolution of the weights that closely follows the ground truth. Finally, it is discussed how this would appear in a streaming context if the analysis were being carried out at the beamline as the experiment progressed.

Recent Advances and Applications of Deep Learning Methods in Materials Science

“…This often corresponds to a real physical situation (for example, spectra tend to be positive, as are the weights of chemical constituents). As a result we are finding that the mathematical decomposition often results in interpretable, physically meaningful, components and weights, as shown by Liu et al for PDF data [207]. An extension of this showed that in a spatially resolved study, NMF could be used to extract chemically resolved differential PDFs (similar to the information in EXAFS) from non-chemically resolve PDF measurements [208].…”

Mapping Structural Heterogeneity at the Nanoscale with Scanning Nano-structure Electron Microscopy (SNEM)

“…8 (after masking the Ni region. 2 ), and extract components that are physically-significant, along with the weight matrix [9]. These can then be used as an important set of QoIs.…”

“…Like Pearson analysis, NMF is useful for an exploratory analysis when one does not have prior knowledge on the chemistry or structure of a system [9]. It is related to principle component analysis (PCA) but seems to produce (mathematical) components that explain the variability of the data in the set of PDFs that are more physically meaningful [51], and in particular of interest here, when applied to PDF data [9]. We note that PDF data goes negative, and therefore requires shifting to positive values for this procedure.…”

“…Although it is possible to deconvolve different structural contributions from a spatially-averaged diffraction pattern [9], to get spatially resolved information in a heterogeneous sample, one must reduce the beam-size. At the µm level, automated total scattering data collection with rasterring x-ray beam demonstrated the value in a spatially-resolved structural mapping based on PDF or Bragg peak analysis [10,11,12,13].…”

nmfMapping: a cloud-based web application for non-negative matrix factorization of powder diffraction and pair distribution function datasets

“…Non-negative matrix factorization (NMF) (Paatero & Tapper, 1994) has been a particularly useful, reliable and intuitive unsupervised machine learning (ML) approach for analytically reducing large datasets of physical signals to reveal trends (Brunet et al, 2004;Pauca et al, 2006). More specifically, it can yield isolated structural signals and their relative presence for both PDF (Liu et al, 2021;Geddes et al, 2019) and powder diffraction (Long et al, 2009) data.…”