A Study On Sparse Decomposition And Dictionary Learning Algorithms For Tensor

In reality world, many data presented in the form of high-dimensional tensor such as color images and videos. When we use the matrix and vector to processing high-dimensional data, it will always destroy the structure information of the data, but tensor data processing method can perspective the structural information inherent the data well, this advantage makes high-dimensional data tensor treatment has great potential. In recent years, research on tensor methods and applications has been extended to psychological measurement, medical imaging, computer vision, data mining and signal processing, and many other fields. In nowadays, people always need to process a large amount of data processing, so the research in tensor data has a very important significance and value. This thesis mainly focuses on two aspects.First, we propose a tensor factorization called discriminant sparse non-negative tensor factorization DSNTF (Discriminant Sparse Non-Negative Tensor Factorization), which is an improvement of non-negative tensor factorization NTF (Non-Negative Tensor Factorization) and sparse non-negative tensor factorization SNTF (Sparse Non-Negative Tensor Factorization). In DSNTF, we added both sparse threshold and discrimination coefficient in non-negative tensor factorization; we decompose the tensor data which composed by different classes, by making the within-class scatter as small as possible and between-class scatter as large as possible. Due to the discrimination coefficient, DSNTF can be used in recognition well. We compared the three tensor decomposition; the experiment results show that DSNTF has smaller reconstruction error, and higher recognition rate.Secondly, we propose Kernel based sparse tensor dictionary learning Kernel K-CPD, sparse tensor dictionary learning K-CPD is a improvement of sparse dictionary learning algorithm K-SVD, because it used Candecomp/Parafac Decomposition), so we call it K-CPD. Due to the kernel function, we can map the linearly inseparable data into a high dimensional feature space, making the classification results better. We compared the Kernel K-CPD algorithm and K-CPD algorithms on some face image databases, the experiment results show that the Kernel K-CPD has higher recognition accuracy.