  We perform a geometric analysis for the sky map of the IceCube TeV-PeV
neutrino excess and test its compatibility with the sky map of decaying dark
matter signals in our galaxy. Using both Kolmogorov-Smirnov and the
likelihood-ratio tests, we have found that the observed event sky map prefers
to have a combination of the galactic dark matter and a homogeneous background
contributions, compared to a purely galactic dark matter origin. For the
assumption that the galactic dark matter is responsible for all neutrino
excess, the current data can also exclude a wide range of dark matter profiles
except flatter profiles such as the isothermal one. We also consider several
representative decaying dark matter spectra, which can provide a good fit to
the observed spectrum at IceCube with a dark matter lifetime of around 12
orders of magnitude longer than the age of the universe.
