Choquet Integral And Its Application In Classification

Classification problem is one of the typical problems of large data processing.Its main research content is how to determine the boundary between data by model and algorithm,such that the data can be divided correctly.Common methods include decision tree method,support vector machine(SVM),Bayes method and so on.In 1953,French mathematician Gustave Choquet proposed Choquet integral,which is a kind of nonlinear integral and is a generalization of Lebesgue integral.In recent years,Choquet integral has a wide range of applications in decision-making,data fusion,data mining and other fields.Based on the current studies on the data classification of Choquet integral and combined with the idea of the optimal classification boundary of support vector machine.the data classification of Choquet integral is deeply analyzed in the thesis,and the data classification optimization model and algorithm based on Choquet integral are established.The main research works are as follows:(1)The order weighted operator is proposed by generalized the average weighted average operator.Moreover,the data classification optimization model based on order weighted operator is given in the,and the classification ability is analyzed and compared.(2)Through the nature analysis of data classification based on Choquet integral,the weighted axis in n-dimensional space's and the Choquet distance of two points are proposed.The nonlinear constrained optimization data classification model based on Choquet integral is obtained by using the thought of SVM's optimal classification boundary,and the effectiveness of the model is verified by given example.(3)In order to reduce the number of variables of the optimization model in(2),by introducing the ascending dimension mapping under a given weighting axis,the model is transferred in a linear classifying model.By using the genetic algorithm to optimize the values of weighting axis,a new algorithm for solving the optimization model in(2)is built,which can deal with complex data classification.The given experimental data shows the effectiveness of the classification algorithm.