Research On Structured Fuzzy Twin Support Vector Machine Algorithm With Different Loss Functions

Twin support vector machine is a learning algorithm inspired by generalized eigenvalue support vector machine.Now it has become one of the important research contents of machine learning.Due to the good classification performance and fast learning ability of the twin support vector machine,it has attracted more and more researchers' attention.The twin support vector machine has been studied in depth,and many different twin support vector machine algorithms have been proposed.However,in order to measure the pros and cons of the model,some of the proposed algorithms mainly use the hinge loss function.And this loss function is easy to cause noise sensitivity and resampling instability.In order to further improve the performance of twin support vector machines,this paper analyzes and studies several different loss functions,and presents the advantages and disadvantages of these functions.On this basis,based on the L1 loss function and Pinball loss function,and by introducing structural information and fuzzy membership,structural fuzzy twin support vector machines with different loss functions were studied.The details are as follows:(1)The loss functions in the field of classification and regression are analyzed and studied,including 0-1 loss function,hinge loss function,Pinball loss function,L1 loss function and L2 loss function.For each loss function,the problems and their characteristics are given.At the same time,the advantages of L1 loss function and Pinball loss function are expounded.(2)The structure fuzzy twin support vector machine algorithm based on L1 loss is studied.In the L1 loss twin support vector machine,in order to obtain two non-parallel hyperplanes,this method only considers the separability between the classes of the samples,and ignores the potential structural information within the sample classes.In addition,the algorithm does not consider the impact of different samples on the classification decision surface,which makes the method's generalization performance and anti-noise performance low.To this end,based on the L1 loss twin support vector machine,the structural fuzzy twin support vector machine model based on L1 loss is constructed by introducing the structural information in the samples and the role of different samples into this twin support vector machine.By solving this model,a structural fuzzy twin support vector machine algorithm based on L1 loss is proposed.(3)The structural fuzzy twin support vector machine algorithm based on Pinball loss is studied.In order to further improve the performance of the twin support vector machine,a structural fuzzy twin support vector machine model of Pinball loss is constructed based on the generalized function of L1 loss,namely the Pinball loss function,and considering the structural information in the samples and the different functions of each sample.Using optimization method to solve the model,a fuzzy twin support vector machine algorithm based on Pinball loss structure is proposed.The algorithm solves the sensitivity of the noise data to the algorithm and has the stability of resampling.(4)The UCI standard data set and artificial data set are selected,and the proposed algorithm is tested by using the five-fold cross-validation method.The proposed algorithm is compared with the typical twin support vector machine algorithm.At the same time,experiments on different methods of obtaining structural information and fuzzy membership are carried out.