Support Vector Machine Kernel Function Selection Based On Prior Information

Support vector machine is a machine learning method developed from statistical learning theory.It is a major theoretical breakthrough in the development process of many machine learning methods from experience risk to structural risk.It has special advantages to a small sample that is difficult to handle and some nonlinear problems in traditional machine learning methods,it is widely used in the field of artificial intelligence.Support vector machine has good learning ability for nonlinear separable problems because it is a kernel based learning method.The introduction of kernel function makes the support vector machine model don't have to calculate the inner product for the input space,instead,the input space is embedded into the high-dimensional feature space for calculation.This way not only realizes the classification of nonlinear problems,but also reduces the computation complexity.However,the corresponding mapping mode of each kernel function is different,that is,the kernel function contains different measurement characteristics,so kernel function has a very significant influence on the generalization performance of the support vector machine model.Therefore,how to choose kernel function effectively in support vector machine training is an important part of support vector machine research.The kernel function determines the performance of support vector machine model.The keypoint is to make the input sample points relate to each other in the feature space through mapping.However,most of the existing kernel selection studies only to consider the characteristics of the kernel function itself,such as global characteristics,local characteristics,etc.,or select according to experience.Obviously,these kernel selection methods have a series of contingencies and limitations.Therefore,this paper synthetically analyzes the prior information contained in the training samples and the characteristic information of the kernel matrix generated by different kernel functions,and designs the kernel selection mechanism of the support vector machine based on the prior information of the input samples.The main work includes:1.This paper expounds the related theory of support vector machine,and introduces the key point of this paper--kernel function through the corresponding theoretical derivation.Firstly,the definition of kernel function,the properties of kernel function and the commonly used kernel function are described.Secondly,the characteristic information of kernel function is analyzed in detail from Riemann metric distance metric and Angle metric.Finally,this paper elaborates on the research background,theoretical basis and the prior information distribution of specific practical problems to pave the way for the subsequent research contents.2.Due to many actual problems can be expressed by graph theory knowledge,this paper creatively combines the concept of adjacency matrix of undirected graph in graph theory about the input samples,and then it analyzes the generated adjacency matrix to get sample distribution information,it uses the principal component analysis method to obtain the intrinsic dimension of adjacency matrix,it also units the intrinsic dimension of different kernel functions to determine the type of kernel function selected.Finally,through different numerical simulation examples,it is verified that the method proposed in this paper can effectively carry out the kernel selection under the premise of fully considering the prior information of samples,and avoid the blindness of kernel function selection.3.It is often impossible to describe the intrinsic dimensionality of a given sample with integer for practical problems,and it is also difficult to make the generated model have better performance with simple kernel function for complex problems.In this paper,the prior information of samples is estimated with the help of fractal dimension in fractal geometry,and the basis kernel function or mixed kernel function is selected according to the characteristics of self-similarity in fractal.Firstly,the fractal dimension of training samples is calculated by using the method of correlation dimension.Then,the entropy of information is introduced to represent the distribution of training samples,which is used to choose or combine different kinds of kernel functions.This method can not only effectively calculate the prior information of training samples,but also consider the characteristic information of kernel function.4.Considering the above researches are conducted on the basis of the data in UCI,in this article,the data collected during the internship in a company in Shanghai and the face pose classification algorithm based on deep learning and facial five sense points information to test the advantages of the above kernel function selection method.The simulation results show that the classification accuracy of the proposed support vector machine model is higher than that of the deep learning-based method,and the speed of the support vector machine model is much better than that of the deep learning model in terms of running time.Through the simulation of the data in UCI database and the face data extracted in real life,it is proved that the above method is efficient in making full use of the prior information of the sample and the feature information of the kernel function to choose the kernel function.