  A main task in data analysis is to organize data points into coherent groups
or clusters. The stochastic block model is a probabilistic model for the
cluster structure. This model prescribes different probabilities for the
presence of edges within a cluster and between different clusters. We assume
that the cluster assignments are known for at least one data point in each
cluster. In such a partially labeled stochastic block model, clustering amounts
to estimating the cluster assignments of the remaining data points. We study
total variation minimization as a method for this clustering task. We implement
the resulting clustering algorithm as a highly scalable message-passing
protocol. We also provide a condition on the model parameters such that total
variation minimization allows for accurate clustering.
