Research On Kernel Function Of Support Vector Machine Based On Sample Information And Fractal Interpolation

Support vector machine is a learning algorithm that has just emerged in the past three decades and is widely used.It is widely used in various fields to deal with small sample data and solve nonlinear inseparable problems.It is a kernel learning algorithm based on the similarity relationship criterion.At the same time,support vector machines have a solid and solid theoretical foundation compared to other methods.The support vector machine calculates the inner product or distance relationship between the input spatial data through the kernel function method,and establishes a similar relationship between the two pieces of data,so that the linearly inseparable original spatial data is transformed into the relationship between the data and has a high dimensionality data.The high-dimensional data space obtained by using the kernel function itself is a relationship matrix expressing the similarity measurement characteristics between data,so the matrix may have linearly separable characteristics.Support vector machine predicts and analyzes the similar characteristics of the test sample and the training sample through statistical theory when predicting the label of the input data.Therefore,how to construct an appropriate kernel function is decisive for the accuracy of support vector prediction.The kernel function is to express the spatial relationship and measurement characteristics of the original spatial data.The kernel function is a function that adjusts the similarity measurement relationship between data,and expresses the similarity measurement relationship between data through the kernel function,thereby increasing the separability of the data.Therefore,the merits and demerits of the classification prediction result lies in the kernel function.Therefore,the characteristics between the data may be close to the above curve,but these functions cannot properly describe the characteristics of the data.Therefore,in the experimental operation,the coincidence point of the curve characteristics and the data characteristics is difficult to grasp.At the same time,the variation range of different data features is different,but the degree of influence on the data labels varies between data features.Therefore,this paper conducts a comprehensive analysis of the influence of different features of the data on the data label into the weight relationship between the features,and the fit between the data characteristic curve and the kernel function curve,and based on the sample features to establish a kernel function algorithm suitable for the data.The main research content of this article:1.Introduction to support vector machine theory.Through the development and theoretical derivation of the support vector machine,the core of the current support vector machine,the kernel function,is derived.The definition,properties,common kernel functions,multi-core kernel functions and the curve characteristics of kernel functions are described for kernel functions,and the essence of kernel functions is discovered,and the similarity measurement relationship between data is adjusted.Set the stage for future research.2.There are certain differences between data features.Different features have different impacts on the determination of data labels.Simple normalization processing cannot deal with the differences between features.By establishing a spatial overlap rate method,the distinction between different features on data labels is calculated,and information entropy is used to weight different data features.In order to better reflect the separability of data,adjust the difference between different types of data,increase the sparsity between similar measures,and introduce the L1 norm on the basis of the original L2 norm to further increase the compactness and heterogeneity of similar data.The sparseness of data,and then achieve the purpose of linear separability,reducing the cross section between heterogeneous data.3.In actual problems,the similarity measurement relationship between data is not a fixed curve form,and the complexity of different data varies greatly,but most data is relatively complicated.For a complex data,a simple kernel function determined by an elementary function cannot Meet the complexity of the data.This paper uses complex data to establish a kernel function through interpolation.Among many interpolation functions,the complexity of fractal interpolation is relatively controllable,and the complexity is relatively high,which can meet the needs of most data.In this paper,an iterative function system is established based on the relationship between similarity measurement characteristics between data and data labels to further determine the kernel function of the corresponding data.And through the experimental method described the compatibility between the kernel function and the data.This method greatly increases the match between the data and the kernel function,and fully exerts the leading role of the potential information of the data.Using UCI data to carry out experimental simulations,demonstrate the different differentiation between the features in the above method,and verify that the above method fully exerts the potential information existing in the data in the kernel function,and the feasibility of the above method.