Spectral Clustering Based Dimensionality Reduction And Applications

Curse of dimensionality is now a main problem in machine learning, pattern recognition, information retrieval and biological information, which results in more attentions on dimensionality reduction methods. In order to enhance the performance of SAR target recognition, face recognition and hyperspectral remote sensing image classification, this dissertation focuses on the research on spectral clustering based dimensionality reduction algorithm using the intrinsical dimensionality reduction of spectral clustering. Supported by the National Natural Science Foundation of China and the National Science and Technology Ministry of China, some new algorithms are proposed and applied to SAR target recognition, face recognition and hyperspectral remote sensing image classification.The main contributions can be summarized as follows:(1) Based on spectral feature analysis derived from classical NJW spectral clustering, a new dimensionality reduction algorithm based on multi-parameter self-tuning spectral clustering is proposed, which solves the problem of scale parameter. Compared with the traditional feature transformation methods in the applications to handwritten digits recognition and SAR target recognition, the proposed method can achieve better accuracy. Besides, self-tuning parameters not only can get rid of the trouble of selecting a proper global scale parameter, but also are more reasonable than global scale parameter, for self-tuning parameters consider the neighborhood information of each sample.(2) A supervised dimensionality reduction algorithm is proposed based on a new spectral clustering graph cut criterion, scaling cut criterion, which considers the class information of the labeled samples. In order to reduce the computational complexity, as well as enhance the generalization performance of the algorithm, localized k nearest neighbor graph is introduced into when constructing scaling cut criterion. A more reasonable projection matrix can obtained for the use of localized k nearest neighbor graph can relax the variance within class, while enlarge the edge between classes. Experiments on face recognition and hyperspectral remote sensing image classification show that the proposed algorithms can achieve better and more stable results. Optimal dimensionality scaling cut criterion analysis is obtained based on the proposed algorithm, drawing on optimal dimensionality discriminant analysis. The experimental results denote that optimal dimensionality scaling cut criterion analysis can extract the optimal dimension of the original dataset.(3) Kernel scaling cut criterion based supervised dimensionality reduction algorithm is the nonlinear generalization of scaling cut criterion based supervised dimensionality reduction algorithm using kernel technique. When the number of original features is greater than the number of samples, scaling cut criterion based supervised dimensionality reduction has singularity problem, while the proposed algorithm has no limitation of the input feature dimension. Applying the proposed method to SAR target recognition, the experimental results show the promising potential in the field of SAR target recognition of the proposed method.