  Tensor factorization models are widely used in many applied fields such as
chemometrics, psychometrics, computer vision or communication networks. Real
life data collection is often subject to errors, resulting in missing data.
Here we focus in understanding how this issue should be dealt with for
nonnegative tensor factorization. We investigate several criteria used for
non-negative tensor factorization in the case where some entries are missing.
In particular we show how smoothness penalties can compensate the presence of
missing values in order to ensure the existence of an optimum. This lead us to
propose new criteria with efficient numerical optimization algorithms.
Numerical experiments are conducted to support our claims.
