The Research And Application Of Wavelet Support Vector Machines In Data Modeling

Support vector machine (SVM) based on the Statistical Learning Theory is a new data modeling method in machine learning because of its advantage such as firm mathematic theory foundation, strict theory analysis, global optimization as well as good adaptability and generalization. SVM improves the algorithm generalization effectively and minimizes the empirical risk simultaneously by using Structural Risk Minimization and synthesizing the techniques including the statistical learning and neural networks.Most of the research works focuses on the Support Vector Machine classify theory and application, and the recently research works on Support Vector Machine Regression also show its excellent performance. As a novel theory and method, the training algorithm, practical application and many other topics of SVM are need to be discussed.This paper concentrated on the research work listed below and achieved some creative results.1. Wavelet SVM algorithm based on wavelet kernel function is constructed after studying the kernel function conditions of support vector. Its convergence and commonality as well as generalization are analyzed. The wavelet SVM can be extended easily and experiment results show that it has good function approximation ability.2. Kernel Principal Component Analysis SVM algorithm is studied. A data modeling method based on Kernel Principal Component Analysis and Wavelet Least Square support vector machine is presented. The Kernel Principal Component Analysis method can not only solve the linear correlation of the input and compress data. Cross validation method is used to select parameters of Least Square support vector machine model. The model is applied to prediction of BPA. Results indicate that this method features high learning speed, good approximation and well generalization ability.3. The previous researches show that the Wavelet SVM's generalization capacity is greatly impacted by its parameters, such as kernel parameters and penalty factor. Since there are few analytical methods to choose the Wavelet SVM's parameters, an automatic parameters selection strategy based on quantum-behaved particle swarm optimization (QPSO) algorithm is proposed. In this new method, each particle indicated a group of SVM parameters and the 5-fold cross-validation error is used as the fitness function of QPSO. Simulations of artificial and real data show that the excellently global searching ability of QPSO contributed the task of parameters selection greatly.