  The effect of errors in variables in quantization is investigated. We prove
general exact and non-exact oracle inequalities with fast rates for an
empirical minimization based on a noisy sample
$Z_i=X_i+\epsilon_i,i=1,\ldots,n$, where $X_i$ are i.i.d. with density $f$ and
$\epsilon_i$ are i.i.d. with density $\eta$. These rates depend on the geometry
of the density $f$ and the asymptotic behaviour of the characteristic function
of $\eta$.
  This general study can be applied to the problem of $k$-means clustering with
noisy data. For this purpose, we introduce a deconvolution $k$-means stochastic
minimization which reaches fast rates of convergence under standard Pollard's
regularity assumptions.
