Research Of Face Recognition Algorithm Based On Nonnegative Tensor Factorization

In recent decades, face recognition technology have received much attention in the field of biometric identification, many algorithms have been proposed such as principal component analysis(PCA), independent component analysis(ICA), isometric mapping(ISOMAP) etc. and applied in our real life.Nonnegative matrix factorization algorithm is proposed by Lee and Seung in 1999, which is a kind of nonnegative data processing method. When the algorithm has been put forward, it has caused the research upsurge and has been applied to many fields. Because a face image can be regarded as a matrix and the elements of the matrix are nonnegative, so NMF method can also be applied to the field of face recognition and then achieved remarkable results.Whether the linear or nonlinear face recognition algorithms and the popular NMF algorithm, these algorithms will reduce the high dimensional face image data to the low dimensional space, which can destroy the original geometric of the face image. And in the process of data dimensionality reduction and feature extraction, face image information may be lost, and it may lead to the occurrence of the curse of dimensionality and small sample situation. But as the multiple linear extension of nonnegative matrix factorization, the nonnegative tensor factorization can avoid the above shortcomings to some extent.Aiming at the problem above, first we describe the related knowledge of NMF. On this basis, this thesis introduces the tensor concept and the algebra basic operations of tensor. The objective function of the NTF based on different distance and the commonly used nonnegative tensor factorization algorithm: the multiplicative iterative algorithm and the alternating nonnegative least squares algorithm are described. Then we give the iterative rules of the above algorithms. From the derivation process we can see: the NTF algorithm will not turn the matrix into vector in the process of decomposition, which will not damage the internal structure of the matrix, thus reducing the loss of information.On the basis of the above theoretical study, a face recognition algorithm based on nonnegative tensor factorization is proposed. This method considers the constraints on the spatial arrangement of the face image pixel data and retains the redundancy among the ranks of the face data, which is more conducive to the restoration and recognition of image. We verify the validity and efficiency of the method from several different aspects. From the different iterations, training sample number and characteristic dimension, we also show the NTF algorithm has higher efficiency than the NMF or PCA algorithm and it can represent the local mode of human face better. Then it has a higher recognition rate.