Joint Optimization for Pairwise Constraint Propagation.

Constrained spectral clustering (SC) based on pairwise constraint propagation has attracted much attention due to the good performance. All the existing methods could be generally cast as the following two steps, i.e., a small number of pairwise constraints are first propagated to the whole data under the guidance of a predefined affinity matrix, and the affinity matrix is then refined in accordance with the resulting propagation and finally adopted for SC. Such a stepwise manner, however, overlooks the fact that the two steps indeed depend on each other, i.e., the two steps form a "chicken-egg" problem, leading to suboptimal performance. To this end, we propose a joint PCP model for constrained SC by simultaneously learning a propagation matrix and an affinity matrix. Especially, it is formulated as a bounded symmetric graph regularized low-rank matrix completion problem. We also show that the optimized affinity matrix by our model exhibits an ideal appearance under some conditions. Extensive experimental results in terms of constrained SC, semisupervised classification, and propagation behavior validate the superior performance of our model compared with state-of-the-art methods.