SDNMF: Semisupervised discriminative nonnegative matrix factorization for feature learning

As one of the most effective feature learning methods, Nonnegative Matrix Factorization (NMF) has been widely used in many scientific fields, such as computer vision, data mining, and bioinformatics. However, NMF is an unsupervised method that cannot fully utilize the label information of data. Thus, its performance is limited in some recognition and classification problems. To remedy this shortcoming, this paper proposes a Semisupervised Discriminative NMF (SDNMF) method. First, we design a Soft-Labeled NMF (SLNMF) model by introducing a soft-label matrix-based regression term into the original NMF, so that the relationship between the soft-label matrix and low-dimensional features can be constructed to improve the discriminative ability of low-dimensional features. Second, to effectively estimate the soft-label matrix, a Label Propagation (LP) model is adopted to fully explore the spatial distribution relationship between the labeled and unlabeled samples. Third, an Adaptive Graph Learning (AGL) model is proposed to exploit the geometric relationship of samples well, which could enhance the performance of LP. Finally, the above three models (i.e., SLNMF, LP, and AGL) are integrated into a unified framework for effective feature learning, which can not only effectively explore the structural relationship matrix between data, but also predict the labels for unknown samples. Moreover, an iterative optimization algorithm is presented to solve our objective function. The convergence and computational complexity analysis of the proposed SDNMF method are also provided. Extensive experiments are conducted on several standard data sets. Compared with related methods, the experimental results verify that the proposed SDNMF method achieves better performance.