Graph Regularized Discriminative Nonnegative Matrix Factorization

It is well known that both the label information and the local geometry structure information are very important for image data clustering and classification. However, nonnegative matrix factorization (NMF) and its variants do not fully utilize the information or only use one of them. This paper presents a graph regularized discriminative nonnegative matrix factorization (GDNMF) for image data clustering, in which the local geometrical structure and label information of the observed samples are thoroughly considered. In the objective function of NMF, two constraint terms are added to preserve the above information. One is a sparse graph, which is adaptively constructed to obtain the local geometrical structure information. The other is data label information, which is used to capture discriminative information of the original data. By using local and label information, the proposed regularized discriminative nonnegative matrix factorization indeed improves the discrimination power of matrix decomposition. In addition, the F-norm formulation based cost function of regularized discriminative nonnegative matrix factorization is given, and the update rules for the optimization function of regularized discriminative nonnegative matrix factorization are proved. The experiment results on several public image datasets demonstrate the effectiveness of GDNMF algorithm. The innovation of this paper lies in extending unsupervised NMF to semi-supervised case and adaptively capturing the local structure of data based on sparse graph. However, the proposed method does not take into account the challenges of multiview data processing.