Semi-supervised clustering via constrained symmetric non-negative matrix factorization

Semi-supervised clustering based on pairwise constraints has been very active in recent years. The pairwise constraints consist of must-link and cannot-link. Since different types of constraints provide different information, they should be utilized with different strategies in the learning process. In this paper, we investigate the effect of must-link and cannot-link constraints on non-negative matrix factorization (NMF) and show that they play different roles when guiding the factorization procedure. A new semi-supervised NMF model is then proposed with pairwise constraints penalties. Among them, must-link constraints are used to control the distance of the data in the compressed form, and cannot-link constraints are used to control the encoding factor. Meanwhile, the same penalty strategies are applied on symmetric NMF model to handle the similarity matrix. The proposed two models are implemented by an alternating nonnegative least squares algorithm. We examine the performance of our models on series of real similarity data, and compare them with state-of-the-art, illustrating that the new models provide superior clustering performance.