Application And Optimization Of Nonparallel Hyperplane Support Vector Machine For Binary Classification Problems

Twin Support Vector Machine is a new kind of machine learning method which is based on the classical Support Vector Machine.Different from SVM,TWSVM make decisions based on a pair of nonparallel hyperplanes.Due to its good learning performance,TWSVM has become a popular method,and has received widespread attention.In order to improve the generalization ability of TWSVM,scholars designed a large number of variants.Among them,Nonparallel Hyperplane Support Vector Machine is designed to solve the problem of logical inconsistency issue between the training process and the prediction process of TWSVM.When facing a strange sample,a TWSVM classifier needs to calculate the distance between the sample point and the two hyperplanes,and then classifies it into the category corresponding to the hyperplanes closer to it.However,such comparison idea is not reflected in the training process.By setting constraints related to the distance difference between the sample point and two superplanes,NHSVM model could guarantee the consistency of the training and predicting process.However,we notice that the representations of distance difference in NHSVM model is heavily reliant on the relative position between sample points and the two hyperplane,while the actual data may not satisfy the default position relation.Although the minimization target contains the square of distance from the sample point to its corresponding hyperplane,which seems to weaken above issue to some extent,considering that the optimal solution of a optimization problem is the aggregated result of all items in the objective function,whether misrepresentation exists and the magnitude of such falseness still need to be further explored.Thus,we applied NHSVM model to actual classification tasks,and paid special attention to the results associated with constraints.Results showed that this issue do exists in some datasets.In order to overcome original NHSVM model's defects and make it more in accordance with its design intention,the current paper put forward an improved version called adj-NHSVM model.Compared to the original NHSVM model,the new method modified the optimization problem from two aspects.On the one hand,we add sign parameters to the distance items in constraints to make the model more flexible.On the other hand,we added distance-oriented punishment items to the objective function,which further ensures the close relationship between the sample point and its corresponding hyperplane.Subsequent experiment results show that the revised model performs better than the original one on most datasets,and is also suitable for class imbalance problems.