Constrained non-negative matrix factorization enabling real-time insights of $\textit{in situ}$ and high-throughput experiments
This work addresses the need for more interpretable and accurate real-time analysis in time-sensitive data collection, such as in situ materials characterization, though it appears incremental by building on existing NMF methods with constraints.
The paper tackles the problem of canonical Non-negative Matrix Factorization (NMF) methods not ensuring components or weights represent true physical processes in real-time analysis of streaming spectral data, by introducing a constrained NMF method that uses known or assumed priors to significantly improve the revelation of underlying phenomena, as demonstrated on synthetic examples and measured X-ray diffraction and pair distribution function data.
Non-negative Matrix Factorization (NMF) methods offer an appealing unsupervised learning method for real-time analysis of streaming spectral data in time-sensitive data collection, such as $\textit{in situ}$ characterization of materials. However, canonical NMF methods are optimized to reconstruct a full dataset as closely as possible, with no underlying requirement that the reconstruction produces components or weights representative of the true physical processes. In this work, we demonstrate how constraining NMF weights or components, provided as known or assumed priors, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch based method for efficiently applying constrained NMF and demonstrate this on several synthetic examples. When applied to streaming experimentally measured spectral data, an expert researcher-in-the-loop can provide and dynamically adjust the constraints. This set of interactive priors to the NMF model can, for example, contain known or identified independent components, as well as functional expectations about the mixing of components. We demonstrate this application on measured X-ray diffraction and pair distribution function data from $\textit{in situ}$ beamline experiments. Details of the method are described, and general guidance provided to employ constrained NMF in extraction of critical information and insights during $\textit{in situ}$ and high-throughput experiments.