Sparse Graph Regularized Nonnegative Matrix Factorization And Its Application In Face Recognition

Matrix factorization techniques have been frequently applied in many regions, such as information retrieval, computer vision and pattern recogni-tion, and there is great performance. Among them, Non-negative matrix factor-ization (NMF) has been received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be part-based in the human brain. On the other hand, there is a geometric structure among the original data. if we could hold this structure in our new da-ta, which was the low dimensional representation of the original high dimensional ones, it would make the representation more precise. On this idea, the Graph Reg-ularized Non-negative Matrix Factorization (GNMF) was proposed. And it was applied in a lot of problems. in which, GNMF has a good performance. Recent years, sparse optimization received more and more attention. Especially, in infor-mation recovery and image processing, sparse optimization made a new chapter. In this paper, we will propose a new mode based on the sparse optimization and GNMF. And we will apply it in face recognition framework. We test four models in our numerical experiment:NMF, GNMF, Sparse NMF and Sparse GNMF. The algorithm used in experiment is projected gradient method, and we apply smooth-ing method when it comes to sparse models. Also, we create a new regularization of GNMF by the first order difference of picture. Numerical result shows that it has some better performance.