We study an analytically irreducible
algebroid germ $(X, 0)$ of complex singularity
by considering the filtrations of its analytic algebra,
and their associated graded rings,
induced by the
{\it divisorial valuations}
associated to the irreducible components
of the exceptional divisor of the normalized blow-up of
the normalization $(\bar{X}, 0)$ of $(X, 0)$, centered at the point $0 \in \bar{X}$.
If $(X, 0)$ is a quasi-ordinary hypersurface singularity, we obtain that
the associated graded ring is a $\C$-algebra of finite type,
namely the coordinate ring of a non necessarily normal affine toric variety
of the form $Z^\Gamma = \mbox{\rm Spec} \C [\Gamma]$, and we show that
the semigroup $\Gamma$ is an analytical invariant of $(X, 0)$.
This provides another
proof of the analytical invariance of the {\it normalized
characteristic monomials} of $(X, 0)$.
If $(X, 0)$ is the algebroid germ of non necessarily normal toric variety,
we apply the same method to prove a local version of the isomorphism
problem for algebroid germs of non necessarily normal toric varieties
(solved by Gubeladze in the algebraic case).