Semi-supervised nonnegative matrix factorization with positive and negative label propagations

Semi-supervised nonnegative matrix factorization (SNMF) methods yield the enhanced representation ability over nonnegative matrix factorization (NMF) by incorporating the label information. Label propagation (LP) is a popular graph-based method used in SNMF to propagate label information from the labeled data to the unlabeled ones. However, label constraint propagation is always ignored to propagate label restrictions for the data. In this paper, a novel SNMF method, namely positive and negative label propagations based SNMF (PNLP-SNMF), is proposed to improve clustering performance by leveraging both positive and negative label information. The proposed method fulfills nonnegative matrix factorization and label constraint propagation in an unified optimization model. By the label indicator, PNLP-SNMF could guide the unlabeled data of the same predicted label to be mapped into the same class and enhance the discriminative ability of the representation in the feature space. Moreover, we further design an effective iterative updating optimization scheme to solve the objective function the the proposed PNLP-SNMF, whose convergence is theoretically proven. Extensive experimental results demonstrate the effectiveness of our proposed method in image clustering tasks by comparing with several state-of-the-art NMF-based methods.