Clustering with Prior Information

A fundamental issue in clustering concerns one’s ability (and limitation) to detect clusters, assuming they are built-in to the model that generates the data [1, 4]. Results for the planted partition graph models suggest that clusters can be recovered with arbitrary accuracy if sufficient data (link density) is available [2]. More recently, this problem of cluster detectability has been addressed theoretically for sparse graphs, by formulating it through a certain Ising–Potts Hamiltonian [6]. It was shown that clustering in the sparse planted partition model is characterized by a phase transition from detectable to undetectable regimes as one increases the overlap between the clusters [6]. Specifically, for sufficiently large inter–cluster coupling, the underlying (planted) cluster structure has no impact on the optimal (minimum–energy) configuration of the Hamiltonian.