Semi-supervised nonnegative matrix factorization with pairwise constraints for image clustering

Traditional clustering method is a kind of unsupervised learning, which is widely used in practical applications. However, the actual acquired data contains a part of prior information, that is the label of some data is known or the relationship of some pairs of data is known. The clustering method using this information is semi-supervised clustering. The pairwise constraints information is a kind of commonly used prior information, including must-link constraints and cannot-link constraints. Compared with unsupervised clustering algorithms, semi-supervised clustering algorithms have better clustering performance due to the guidance of prior information. Nonnegative matrix factorization (NMF) is an efficient clustering method, but it is an unsupervised method and can not take advantage of pairwise constraints information. To this end, by combining pairwise constraints information with NMF framework, a semi-supervised nonnegative matrix factorization with pairwise constraints (SNMFPC) is proposed in this paper. SNMFPC requires that the low-dimensional representations satisfy these constraints, that is, a pair of must-link data should be close to each other, and a pair of cannot-link data is as distant as possible to each other. Experiments are carried out on several data sets and compared with some semi-supervised methods. The validity of the proposed method is verified.