  The key challenge of time-resolved Raman spectroscopy is the identification
of the constituent species and the analysis of the kinetics of the underlying
reaction network. In this work we present an integral approach that allows for
determining both the component spectra and the rate constants simultaneously
from a series of vibrational spectra. It is based on an algorithm for
non-negative matrix factorization which is applied to the experimental data set
following a few pre-processing steps. As a prerequisite for physically
unambiguous solutions, each component spectrum must include one vibrational
band that does not significantly interfere with vibrational bands of other
species. The approach is applied to synthetic "experimental" spectra derived
from model systems comprising a set of species with component spectra differing
with respect to their degree of spectral interferences and signal-to-noise
ratios. In each case, the species involved are connected via monomolecular
reaction pathways. The potential and limitations of the approach for recovering
the respective rate constants and component spectra are discussed.
