Sparse Nonnegative Matrix Factorization Based On Iterative Support Detection For Face Recognition

As an important branch of biometric features recognition, face recognition technology has become a hot research issue in the field of pattern recognition and received more and more attention. It has been successfully applied by the government, the Customs and the Public Security, and gradually applied in high-risk areas such as banking and financial industry. Due to the deep influence generated by face recognition technology, a range of algorithms, which include Principle Component Analysis(PCA), face recognition algorithm based on Neural Network, Support Vector Machine(SVM) and Nonnegative Matrix Factorization(NMF), have been presented by researchers since the1990 s, and each of these algorithms has different specialties and advantages to confront with different complex matters.Compared with other face recognition algorithms, NMF has the following two advantages: first, by introducing the nonnegative constraint, the calculation results can simulate the human’s perceiving habits which shows “the whole is constituted by parts”;second, NMF algorithm has the natural sparsity which can deal with the distractions like illumination, occlusion or overturning. However, there are also some shortcomings such as less obvious local features, large relative error and slow convergence speed, which lead to imperfect results for NMF in the application of face recognition. In order to improve performance of NMF algorithm, the main work of this paper are as follows:A first novel approach called spare NMF based on Iterative Support Detection(SNMF/ISD) is proposed in this paper. Compared with Basis Pursuit(BP) which is one kind of algorithms applied in Compressive Sensing, ISD can obtain better results which have less number of iterations, lower reconstruction error and stronger sparsity than BP,thus we can extend this method from one-dimension vector space to matrix space, and utilize ISD method to improve a previous NMF algorithm SNMF/ANLS in order to generate a new NMF algorithm called SNMF/ISD which performs better results than other NMF algorithms. In addition, the convergence proof of SNMF/ISD will be given in the following part.The introducers of SNMF/ANLS have only used one branch of their algorithms named SNMF/R(imposing sparsity on coefficient matrix) and applied it to biomedical application. In this paper, we use not only the other branch of SNMF/ANLS called SNMF/L(imposing sparsity on feature matrix), but also our new algorithm SNMF/ISD to carry out face recognition experiments on several face database. Then we make a comparison between SNMF/ISD and the other three NMF algorithms with intuitive plots and forms,which shows that algorithm SNMF/ISD can obtain smaller reconstruction error together with strong sparseness. Moreover, with nearest neighbor classifier, testing data and training data are classified, and a comparison result on recognition rate for different algorithms in different feature space is presented. The experiment results confirms that SNMF/ISD can achieve more robust recognition effects against other previous NMF algorithms.