Research On Methods For Reducing SVMs' Solution And For Sparse Signal Reconstruction In CS

Researches on machine learning began in the early of 1960s. It has been widely applied to pattern recognition, signal processing, image processing, data mining, intelligent control and so on. In machine learning, the sparsity of hypothesis functions is expected to improve the generalization performance and the test speed. Moreover the sparse signal reconstruction is a crucial problem in compressed sensing (CS). In this thesis, we focus on the sparse representation of support vectors (SVs) and the reconstruction of sparse signals. The main work of this thesis is included in the following.Support Vector Machine (SVM) behaves well in representing a model sparsely. SVs generated by SVM, however, are redundant. In order to improve the sparsity of SVM's solution, we present a method based on the l1 regularized least-squares programming for generating a set of reduced vectors. The number of reduced vectors should be less than the number of SVs. In order to solve the l1 regularized least-square programming, we use the sequence minimal optimization (SMO) method.Presently SVM has been applied to human face detection, but the number of SVs is rather large, which leads to a slow test speed. In this regard, we introduce the method based the l1 regularized least-squares programming into face detection process to get a fast test speed, and we propose a multi-element sequence optimization (MSO) method based on the SMO method. For the MSO method, the number of elements in the current work set is not fixed to 1 but can be any positive integer. Thus we can achieve a dynamic balance between the speed and classification performance of the algorithm by selecting the element number of the current work set. Firstly, we use SVM to train samples. Secondly, we use our method to generate reduced vectors. Finally the reduced vectors are takes as new SVs and applied to the detection process. Compared to SVM, experiments show that our method can greatly improve the detection speed.In recent years, the sparse signal reconstruction problem in CS has attracted extensive attention of researchers. Here we find that the reconstruction problem is similar to the l1 regularized least-squares programming, so we propose a sequence reconstruction (SR) method based on the MSO method and apply it to the sparse signal reconstruction. Simulation results show that our approach has a faster reconstruction speed compared with existing methods under the condition of ensuring the reconstruction accuracy.