A Study On The Multiscale Kernel SVM Algorithm And Its Application

With its remarkable advantages, such as global optimization and the strong ability of generalization, the method of support vector machine (SVM) has lead to comprehensive applications and researches. This thesis has been focused on some typical problems in this field.The selection of SVM parameters is known to be very important for the performance of the machine. However, existing searching methods are either too complicated or time consuming. Thus, a sample set shrinking strategy is designed to overcome these limitations. Before training, this method takes some of the non-support-vector samples out of the training set, leaving enough support vectors to formulate the decision hyperplane; therefore efficiently reduce the set size. When doing the parameter searching job in the smaller new set, a model can be founded with a comparatively nice performance as the former one. That is to say, with half the time consumed, a model can be constructed with testing accuracy just slightly changed.In the rest part of the article, a study of the kernels is carried on to explore the inherent characteristics of the feature mapping. Firstly, a comparison is given between the existing kernels, such as the linear kernels and the Gaussian kernels. Then, we focus on the construction of a new type of kernels. It has been pointed out that the kernel function of SVM is equivalent to the reproducing kernel of a certain Reproducing Kernel Hilbert Space (RKHS). Therefore, a family of kernels, called the Mercer Kernel, is introduced with primary conclusions of its related RKHS. Furthermore, we are inspired by the idea of multiresolution analysis (MRA) to form a special kind of Mercer Kernel, which is thus defined as multiscale kernel (MSK). Equipped with a sufficient condition of its positive definiteness, the MSK is used as a kernel function of the SVM's feature mapping. After a discussion on the tuning of parameters, an efficient algorithm is proposed for the classification SVM. According to the experiments, SVMs with MSK perform slightly better than the Gaussian SVMs.