We formulate a novel extension of nonnegative matrix factorization (NMF) to take into account partial information on source-specific activity in the spectrogram. This information comes in the form of masking coefficients, such as those found in an ideal binary mask. We show that state-of-the-art results in source separation may be achieved with only a limited amount of correct annotation, and furthermore our algorithm is robust to incorrect annotations. Since in practice ideal annotations are not observed, we propose several supervision scenarios to estimate the ideal mask- ing coefficients. First, manual annotations by a trained user on a dedicated graphical user interface are shown to provide satisfactory performance although they are prone to errors. Second, we investigate simple learning strate- gies to predict the Wiener coefficients based on local information around a given time-frequency bin of the spec- trogram. Results on single-channel source separation show that time-frequency annotations allow to disambiguate the source separation problem, and learned annotations open the way for a completely unsupervised learning procedure for source separation with no human intervention.