Dong Cheng, Vittorio Murino, Mário Figueiredo
This paper proposes a new approach to model-based clustering under prior knowl- edge. The proposed formulation can be interpreted from two different angles: as penalized logistic regression, where the class labels are only indirectly observed (via the probability density of each class); as ﬁnite mixture learning under a group- ing prior. To estimate the parameters of the proposed model, we derive a (gener- alized) EM algorithm with a closed-form E-step, in contrast with other recent approaches to semi-supervised probabilistic clustering which require Gibbs sam- pling or suboptimal shortcuts. We show that our approach is ideally suited for image segmentation: it avoids the combinatorial nature Markov random ﬁeld pri- ors, and opens the door to more sophisticated spatial priors (e.g., wavelet-based) in a simple and computationally efﬁcient way. Finally, we extend our formulation to work in unsupervised, semi-supervised, or discriminative modes.