Research And Applications Of The SVM Kernel Function Based On Weighted Variables

SVM is widely used to solve the small sample, nonlinear and high-dimensionalpattern recognition problem. Kernel function display a very important role in SVM,linear algorithm can be non-linear and non-linear pattern recognition problem inoriginal input space can be solved by using it. The curse of dimensionality problemcould be avoided cleverly by introducing kernel function into SVM.The application of SVM in classification prediction is the main content of thispaper. Feature vector of sampling is the smallest unit which the kernel function canhandle in traditional SVM, what’s more, this is also the reasons that SVM isinsensitive for attribute dimension. But this kernel function can’t recognize theimportant attributes of the feature vector or useless attributes. To solve this problem,A weighted kernel function based on a variable is proposed in this paper, and theimportance of attribute of feature vector can be identified by kernel function withadding a weight vector.The article is organized as follows:(1) The mathematical model of several classical SVM is introduced and the detailsolving steps are presented. What’s more, an algorithm for solving SVM model isdescribed. Then a brief introduction to the theory of the nature of the kernel functionis given, besides, the features and shortcomings of those kernel functions are analyzed.What’s more, a simulation is done in the MATLAB2011b.(2) A weighted kernel function based on a variable is proposed, the feasibility ofadding weight vector is proved and the practical valves are pointed out here. Tocompare the performance of the kernel function between traditional and improved, atest is done and the results demonstrate that the improved nuclear function have lowsensitivity for data distribution and wide range of applications.(3)Genetic algorithm is adopted to realize parameter optimization and acorresponding improvement is made in genetic manipulation such as encoding andcross. The convergence speeds of algorithm are greatly improved by usingcompetitive primary population.(4) Improved kernel function and optimization method are combined and apply itin the detection of heart disease, and the experiments results proved that improvedkernel function and genetic algorithm have excellent performance and practical value. At last, the content of this thesis is summarized and further feasible researchproblems are discussed.