  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.
