Semi-supervised graph regularized nonnegative matrix factorization with local coordinate for image representation

Nonnegative matrix factorization(NMF) is a powerful image representation algorithm in pattern recognition and data mining. However, the traditional NMF does not utilize any label information, or fail to guarantee the sparse parts-based representation. In this paper, we put forward a semi-supervised local coordinate NMF (SLNMF) algorithm, which incorporate the available label information and the local coordinate constraint into NMF. Particularly, SLNMF makes the learned coefficients sparse by adding the coordinate constraint, and enhance the discriminative ability of different classes by using the label information constraint. Furthermore, in order to extract the geometric structure of the data space, we propose a new semi-supervised graph regularized NMF with local coordinate constraint (SGLNMF) method, which incorporates the graph regularization into SLNMF to enhance the discriminative abilities of data representations. SGLNMF not only reveals the intrinsic geometrical information of the data space, but also takes into account the local coordinate constraint and the label information. Clustering experiments on several standard image datasets demonstrate the effectiveness of our proposed SLNMF and SGLNMF methods compared to the state-of-the-art methods.