Construction And Application Of Gegenbauer Correction Kernel In Support Vector Machine

Kernel function is a function that satisfies Mercer positive definite kernel condition and is related to the operation of vectorized sample inner product.It is used to measure the similarity of samples in feature space.The kernel function is introduced into the SVM classification algorithm,which can map the low-dimensional and non separable samples to the high-dimensional space to realize the linear classification,which avoids the dimension disaster when directly calculating the high-dimensional distribution of samples,and reduces the complexity of model application.As a function approximator,Gegenbauer orthogonal polynomials have excellent performance in resisting redundancy of feature space data.At the same time,the kernel function constructed by Gegenbauer orthogonal polynomial is semi parametric,which can greatly simplify the optimization of kernel parameters.The disadvantage of Gegenbauer is that when describing the similarity between samples,Gegenbauer will give a certain degree of similarity to all the compared samples globally.Sometimes,Gegenbauer will give a larger similarity to the remote samples or a smaller similarity to the closer samples,which leads to the lack of learning due to incomplete feature information in the model training.In order to solve the problem of under learning of Gegenbauer kernel function support vector machine,based on the integration idea of multi-core learning,Gegenbauer kernel function is combined with Laplace kernel function and Cauchy kernel function respectively according to different information expression ways.Because these two kernel functions can only describe the local features of samples,there will be a certain degree of loss of similarity for edge features which are far away from the center of the sample but with high importance.Compared with Gegenbauer,the Gegenbauer kernel function can only describe the global characteristics of the sample,but ignore the local expression ability of good feature information.It is used as the weight function of Gegenbauer kernel function,which plays a correction role to a certain extent,so that the Gegenbauer kernel function can accurately describe the sample similarity information,so as to improve the learning ability of support vector machine.Through comparative experiments on UCI data,it is verified that the classification effect of the modified Gegenbauer kernel is better than before.At the same time,several common kernel functions are optimized in learning ability and generalization ability..Finally,based on the above improved Gegenbauer modified kernel support vector classification model,it is applied to the lung X-ray image classification of kaggle machine learning platform.After the general preprocessing of the image,because the support vector machine is a non-end-to-end classification model,it is necessary to extract the image features for calculation.By analyzing the features of lung X-ray image,such as uncertainty,multimodality and fuzziness,texture features of X-ray image are extracted based on statistical method.By using borderline smot algorithm to solve the problem of category imbalance among various kinds of image data,through the empirical analysis in several modified Gegenbauer kernel support vector machines,the final classification accuracy and the time spent in analyzing the pictures,compared with the neural network algorithm selected by other players in the kaggle competition,the results obtained are also relatively good,and its classification accuracy rate also has It has certain application value.