Pairwise constraint propagation via low-rank matrix recovery

As a kind of weaker supervisory information, pairwise constraints can be exploited to guide the data analysis process, such as data clustering. This paper formulates pairwise constraint propagation, which aims to predict the large quantity of unknown constraints from scarce known constraints, as a low-rank matrix recovery(LMR) problem. Although recent advances in transductive learning based on matrix completion can be directly adopted to solve this problem, our work intends to develop a more general low-rank matrix recovery solution for pairwise constraint propagation, which not only completes the unknown entries in the constraint matrix but also removes the noise from the data matrix. The problem can be effectively solved using an augmented Lagrange multiplier method. Experimental results on constrained clustering tasks based on the propagated pairwise constraints have shown that our method can obtain more stable results than state-of-the-art algorithms,and outperform them.