Research And Implementation Of Model Selection And Parametric Optimization Based On SVM

Support vector machine (SVM) is a machine learning tool which is based on a small mount of samples to be separated. Its basic principle is to find a linear classifier between two classificatory samples to distinguish them while eusure the distance of the two classes is largest. But in practical application, samples can hardly be separated by a linear classifer. These samples should be mapped to another higher dimensional space, and in this space the samples could be separated linearly. The transformation is implemented by a mapping function which is called kernel function.Parameters of kernel functions are supposed to be set whether the kernel functions are constructed from classificatory datas or they are just classical ones. How to set these parameters in order to have the best classific result? How do these parameters have impact on classific accuracy? Which kernel funtion should be used if there are not only one kernel funcionts to chonse? The selection of the kernel fuctions and parametric configuration has a direct impact on the result of classifying. Some experiments had been done to examine and analyse these pertinent questions.Observe the impact of different parametric configuration through experiments. Change parameters and examine the corresponding change of classificatory result. If these samples have not only one suitable kernel funtions, use all of them in experiment. The experimental results show us that parameters and kernel functions have great influence on classificatory accuracy. The purpose of classification is not only to separate samples but also obtain optimal result. To reach this goal we have to find a way to set parameters and choose kernels.In this thesis an error funcition is constructed to quantify classific errors. Since small classificatory errors equal to high classificatory accuray, obtain the smallest value of error function means achieving the highest precision. The problem of how to have the highest accuracy is translated into how to minimize the error function. Use error function's derivative to seek its minimal value and this mathod can also be used to find suitable parameters for kernel functions. Implement this method on classificatory samples to slove parametric configuration problem, and this is also the way to optimaize kernel function's parameters. This process is called parametric optimization.Different kernel functions use the same method to get their parameters, arter this step every kernel function will achieve its highest classifactory precision. Compare the value of these classific accuracies and find out the kernel function correspond to the maximal value. In this way we could complete the task of choosing kernel functions. This step is called model selection. Arfter the process of parametric optimization and model selection we could obtain the best classificatory accuracy. Experiments'results manifest the correctness of the method proposed in the thesis.