Study On Hybrid Kernel Function And Fuzzy System Identification Based On Support Vector Machines

Support vector machines (SVM) based on the statistical learning theory is a new machine learning tool. It has some advantages such as good and strong generalization ability, global optimization, and unrelated to peacekeeping, and now it has been successfully applied in pattern recognition, text classification, fuzzy identification, intelligent control, medical image processing and some other fields.Kernel function maps low-dimensional input vector to high dimensional space to solve the curse of dimensionality and nonlinear problems effectively. To better describe quantities of complex nonlinear systems existing in the real world, reseachers have proposed some different forms of fuzzy model with nonlinear mapping. Fuzzy grid, fuzzy clustering, neural networks are commonly used in the fuzzy model to generated identification of fuzzy rules. However, they easily result into various problems:the curse of dimensionality, sensitivity to outliers and noise problems. To overcome these shortcomings, reseachers attached a new identification method to employ the advantages of SVM and fuzzy systems. Therefore, it is important to study the kernel function and fuzzy recognition technology based on support vector machine.This paper focuses on the application of SVM in kernel function and the fuzzy identification. The main elements are listed as follows:1. Constructing a hybrid kernel and parameters optimization. Gaussian kernel function has been widely used in the field of machine learning, but it has some shortcomings, such as, its unique parameter can't reflect the importance of different sample characteristics and the kernel broadband is a constant, poor global character. In order to make use of the advantages of kernel function, we construct a hybrid kernel function which based on Gaussian kernel function and has advantages of local and overall. Meanwhile, we propose an optimal parameter selection algorithm to select multiple parameters.2. The study on improved GK fuzzy clustering algorithm. As a good data analysis tool, the GK fuzzy clustering can automatically detect different cluster shape. However, it has many shortcomings. For example, the number of clustering is constant and reselecting the cluster center is necessary, further, the covariance should be non-zero in the formula. Thus, develop an improved GK fuzzy clustering algorithm to overcome these disadvantages.3. The study on a new fuzzy identification algorithm. The equivalence of the SVR lacking constants and mamdani fuzzy model has been analyzed. Further, an identification algorithm has been proposed. In this proposed algorithm, the data can be classified through using the improved GK algorithm, fuzzy rules can be extracted by using SVR and the parameters can be optimized by using gradient descent algorithm.