  Predefined spatial templates to describe the background of $\gamma$-ray
emission from astrophysical processes, like cosmic ray interactions, are used
in previous searches for the $\gamma$-ray signatures of annihilating galactic
dark matter. In this proceeding, we investigate the GeV excess in the inner
Galaxy using an alternative approach, in which the astrophysical components are
identified solely by their spectral and morphological properties. We confirm
the reported GeV excess and derive related parameters for dark matter
interpretation, which are consistent with previous results. We investigate the
morphology of this spectral excess as preferred by the data only. This emission
component exhibits a central Galaxy cusp as expected for a dark matter
annihilation signal. However, Galactic disk regions with a morphology of that
of the hot interstellar medium also host such a spectral component. This points
to a possible astrophysical origin of the excess and requests a more detailed
understanding of astrophysical $\gamma$-ray emitting processes in the galactic
center region before definite claims about a dark matter annihilation signal
can be made.
