Constrained clustering: Effective constraint propagation with imperfect oracles

Abstract—While spectral clustering is usually an unsuper-vised operation, there are circumstances in which we have prior belief that pairs of samples should (or should not) be assigned with the same cluster. Constrained spectral clustering aims to exploit this prior belief as constraint (or weak supervision) to influence the cluster formation so as to obtain a structure more closely resembling human perception. Two important issues re-main open: (1) how to propagate sparse constraints effectively, (2) how to handle ill-conditioned/noisy constraints generated by imperfect oracles. In this paper we present a unified framework to address the above issues. Specifically, in contrast to existing constrained spectral clustering approaches that blindly rely on all features for constructing the spectral, our approach searches for neighbours driven by discriminative feature selection for more effective constraint diffusion. Crucially, we formulate a novel data-driven filtering approach to handle the noisy constraint problem, which has been unrealistically ignored in constrained spectral clustering literature. Keywords-Constrained clustering, constraint propagation, feature selection, imperfect oracles, spectral clustering. I