Kernel Locality Preserving Based Dictionary Learning For Sparse Representation

Sparse representation is crucial to the image classification, and it is continuously the focus of the research direction of international and domestic academics. In sparse representation classification, the selection of dictionary is a problem that should not be ignored. Based on sparse representation classification in pattern recognition, concise representation of data can be obtained for sparse representation via dictionary learning. Dictionary learning for sparse representation aims to preserve the local information of original training samples with less dictionary atoms and include more discriminant information in the learned dictionary. At present, this study has become an important research topic of great academic merits and applications values. This thesis focuses on the study of dictionary learning for sparse representation, and the corresponding high efficient algorithms are proposed respectively.The main work and innovations in this thesis are shown as follows:(1)Fisher discrimination dictionary learning for sparse representation (FDDL) can obtain very discriminant sparse dictionary, which will bring high recognition performance for sparse representation classification. However, transforming data into kernel spaces usually can learn nonlinear structure information, which is very useful for discrimination and classification. To make full use of properties of kernel space transformation and to learn more discriminant dictionaries for high recognition performance, two new dictionary learning methods, are proposed for kernel sparse representation classification based on FDDL. First, the original traning data are projected into high dimensional kernel space and then fisher discrimination kernel dictionary learning for kernel sparse representation classification (FDKDL) is proposed. Second, based on FDKDL, kernelized fisher discrimination criterion is imposed on the sparse coefficients, and then kernelized fisher discrimination kernel dictionary learning for kernel sparse representation classification (KFDKDL) is proposed, which makes the obtained dictionary have higher discrimination ability. Experiments of sparse representation based classification on several public image databases demonstrate the effectiveness of the proposed FDKDL and KFDKDL dictionary learning methods.(2)To keep the local information of locality preserving projection, based on FDDL, the locality preserving criterion is imposed on coding coefficients, dictionary learning via locality preserving for sparse representation (LPDL) is proposed. This method makes the coding coefficients of neighboring data points in the dictionary close to each other and preserves the local information of original training samples. Experiments on several public image databases demonstrate the effectiveness of the proposed LPDL dictionary learning methods.(3)With kernel tricks, to further improve the classification performance of learned dictionary, two new dictionary learning methods, based on LPDL, are proposed for kernel sparse representation classification. First, the original training data are projected into a high dimensional kernel space, then locality preserving based kernel dictionary learning for sparse representation (LPKDL) is proposed. Second, the kernelized locality preserving criterion is imposed on the sparse coefficients, and then the kernelized locality preserving based kernel dictionary learning for sparse representation (KLPKDL) is proposed. It uses kernel information of locality preserving based on kernel dictionary learning, which makes the obtained dictionary have higher discrimination ability, and further improve the classification performance. Experiments on several public image databases demonstrate that the proposed FDKDL and KFDKDL dictionary learning methods are superior to other methods on classification performances.