Semi-Supervised Nonnegative Matrix Factorization via Constraint Propagation

As is well known, nonnegative matrix factorization (NMF) is a popular nonnegative dimensionality reduction method which has been widely used in computer vision, document clustering, and image analysis. However, traditional NMF is an unsupervised learning mode which cannot fully utilize the priori or supervised information. To this end, semi-supervised NMF methods have been proposed by incorporating the given supervised information. Nevertheless, when little supervised information is available, the improved performance will be limited. To effectively utilize the limited supervised information, this paper proposed a novel semi-supervised NMF method (CPSNMF) with pairwise constraints. The method propagates both the must-link and cannot-link constraints from the constrained samples to unconstrained samples, so that we can get the constraint information of the entire data set. Then, this information is reflected to the adjustment of data weight matrix. Finally, the weight matrix is incorporated as a regularization term to the NMF objective function. Therefore, the proposed method can fully utilize the constraint information to keep the geometry of the data distribution. Furthermore, the proposed CPSNMF is explored with two formulations and corresponding update rules are provided to solve the optimization problems. Thorough experiments on standard databases show the superior performance of the proposed method.