Graph-preserving Nonnegative Matrix Factorization Using Outline Information For Face Recognition

Matrix factorization obtains wide concern on information retrieval,computer version,pattern recognition,and so on.Nonnegative matrix factorization attracts much attention as it follows the basis idea that whole is made of part,and can efficiently discover low dimensional features.In Chapter 1 of the introduction part,we first introduce the existing NMF model and the GNMF model.We then describe the multiple update(MU)algorithm and the projected gradient(PG)algorithm,which can solve both the NMF model as well as the GNMF model.In Chapter 2,we propose a graph regularized nonnegative matrix factorization using outline information(GNMFO)model,and describe the the active set conjugate gradient(ASCG)algorithm to solve the model.In Chapter 3,we do numerical experiment on real world face data sets.We compare the ASCG algorithm with the MU algorithm and the PG algorithm.And we use the ASCG algorithm to solve the GNMFO model,and perform face classification based on the lower dimensional umatrix factor obtained.The main contribution of this thesis is that we enroll the outline information by first-order difference of the original face data to construct the graph-preserving term.This is very easy to fulfill and can improve greatly the classification results for face recognition.Moreover,we make use of the ASCG method to solve the GNMFO model with solid convergent result.Extensive experiments on real-world high-dimensional face data demonstrate that the proposed GNMFO model is robust to provide high classification result.Experimental results also show that our ASCG method is computationally effective and efficient.