Research Related To Support Vector Machines

Based on statistical learning theory, support vector machine (Support Vector Machine, SVM) technology has a solid theoretical foundation in mathematics. Generalization ability of the model, the global optimum, non-linear processing, etc. are outstanding, it has become the most active areas of machine learning research priorities.In this paper, the traditional SVMs and emerging nonparallel dual hyperplane SVMs are the main object of study, its methods were related to more in-depth discussion and study. The study involved a new weighted model building for classifier, multi-class classification, parameter selection method, the sample reduction method and so on. Its main tasks are:1. The study of Nonparallel dual hyperplane SVM classifier model. A new weighted least squares twin support vector machine classifier (WLSTSVM) is given, which set up through the weight vector of error variables, to solve the poor robustness problem of the least squares twin support vector machine (LSTSVM) due to the SSE loss function. Expression and derivation are provided in the case of linear and nonlinear, including the corresponding algorithm implementation process. Experiments show that WLSTSVM improves noise immunity and the recognition rates.2. Multi-classification methods for nonparallel dual hyperplane SVM are discussed. A multi-class LSTSVM classifier based on optimal directed acyclic graph (ODAG-LSTSVM) is given. A class separability criterion based on distance measure and the corresponding category number rearrangement method are provided in order to determine the class divisibility, its purpose is to overcome the cumulative errors cased by the traditional DAG structure. Experiments prove that the method has impressive performance in the test accuracy and execution speed.3. The parameter selection methods based on SVM are discussed and studied. The differential evolution algorithm has a good performance in both global optimal solution and the problem of multi-peak, so the mutation strategy and control parameters are discussed. First of all, a mutation strategy based on the quantitative and qualitative change in the law of nature is given, defined the adjusted probability formula for qualitative change; then, follow the principle of survival of the fittest, the adaptive strategies for control parameters are given,which follow the current generation of the best individual fitness function. The optimal solution experiments for classic funtion based on improved DE algorithm get a better average optimal solution and convergence speed. Finally, this improved algorithm is applied to the NPPC’s preferences, given the appropriate algorithm process, the results show good performance in both precision and speed.4. The sample reduction methods based on SVM are studied. Two aspects are included, namely, the sample number reduction and attribute reduction. First, a number reduction method known KD-FFMVM is given, which takes into account the elimination of isolated points, the adverse effects of noise points, and extracts the edge junction samples as much as possible, to prevent the loss of the support vectors; then, based on the analysis of existing attribute reduction methods, nuclear Hebbian algorithm is discussed in order to improve the speed of convergence, the Cauchy distribution probability density function is used to fix the learning rate, which achieves adaptive adjustment, and the effectiveness of the method has been proved; Finally, a SVM classification model based on the reduction strategies is designed, compared with the standard SVM, it can maintain a considerable accuracy while greatly reducing the algorithm training time.