Semi-supervised non-negative matrix factorization for image clustering with graph Laplacian

Non-negative matrix factorization (NMF) plays an important role in multivariate data analysis, and has been widely applied in information retrieval, computer vision, and pattern recognition. NMF is an effective method to capture the underlying structure of the data in the parts-based low dimensional representation space. However, NMF is actually an unsupervised method without making use of supervisory information of data. In recent years, semi-supervised learning has received a lot of attentions, because partial label information can significantly improve learning quality of the algorithms. In this paper, we propose a novel semi-supervised non-negative matrix factorization (SEMINMF) algorithm, which not only utilizes the local structure of the data characterized by the graph Laplacian, but also incorporates the label information as the fitting constraints to learn. Hence, it can learn from labeled and unlabeled data. By this means our SEMINMF can obtain a more discriminative powerful representation space. Experimental results show the effectiveness of our proposed novel method in comparison to the state-of-the-art algorithms on several real world applications.