Graph Regularized Nonnegative Matrix Factorization with Sample Diversity for Image Representation

Nonnegative Matrix Factorization (NMF) is an effective algorithm for dimensionality reduction and feature extraction in data mining and computer vision. It incorporates the nonnegativity constraints into the factorization, and thus obtains a parts-based representation. However, the existing NMF variants cannot fully utilize the limited label information and neglect the unlabeled sample diversity. Therefore, we propose a novel NMF method, called Graph Regularized Nonnegative Matrix Factorization with Sample Diversity (GNMFSD), which make use of the label information and sample diversity to facilitate the representation learning. Specifically, it firstly incorporates a graph regularization term that encode the intrinsic geometrical information. Moreover, two reconstruction regularization terms based on labeled samples and virtual samples are also presented, which potentially improve the new representations to be more discriminative and effective. The iterative updating optimization scheme is developed to solve the objective function of GNMFSD and the convergence of our scheme is also proven. The experiment results on standard image databases verify the effectiveness of our proposed method in image clustering.