  We present a new model-based integrative method for clustering objects given
both vectorial data, which describes the feature of each object, and network
data, which indicates the similarity of connected objects. The proposed general
model is able to cluster the two types of data simultaneously within one
integrative probabilistic model, while traditional methods can only handle one
data type or depend on transforming one data type to another. Bayesian
inference of the clustering is conducted based on a Markov chain Monte Carlo
algorithm. A special case of the general model combining the Gaussian mixture
model and the stochastic block model is extensively studied. We used both
synthetic data and real data to evaluate this new method and compare it with
alternative methods. The results show that our simultaneous clustering method
performs much better. This improvement is due to the power of the model-based
probabilistic approach for efficiently integrating information.
