Abstract
Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the time-resolved-Raman-sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.
Highlights
In Raman spectroscopy vibrational spectra can be detected
We thereby obtain measured Raman spectra as a function of time, which depicts both main characteristics of an observed process: On the one hand, each measured spectrum is a fingerprint of compounds and represents the intrinsic spectra of the individual species or molecular states involved in the reaction
Assuming M to represent m measurements of n non-negative variables, we interpret the negative matrix factorization (NMF) task as follows: we aim to identify r ingredients which allow for recovery of all m measurements by composition according to respective contributions
Summary
In Raman spectroscopy vibrational spectra can be detected. Analysis of those spectra provides comprehension about chemical and physical properties of molecular structures, which is important in different research areas in biology, medicine and. In the context of Raman data spectral analysis, focusing on the non-negativity of involved matrices becomes reasonable through the model for time-resolved Raman spectral data of Luce et al [5] They introduce an approach to express a series of spectral recordings of a chemical reaction (matrix M) as the matrix product of the component spectra (matrix W) and the evolution of relative concentrations of these reaction components (matrix H). Based on this model and synthetic spectral data, which satisfy the recently much-cited separability assumption, the authors of [5] present an algorithm to detect a factorization WH = M using separable NMF methods. The purpose of this new approach is using adaptable objective function, taking into account only the common structural properties of the sought-for, process defining matrices W and H
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