Ordinal Regression Algorithm Based On Nonparallel Support Vector Machine

Ordinal regression(OR for short)solves a class of multi-class classification which are the multi-class problem with order.It has a wide range of applications in many fields,such as credit rating,face recognition,medical research and social science.Support vector machine(SVM for short)is a powerful tool for solving classification problems.It has achieved sig-nificant classification effects in solving the problem for binary classification.Therefore,how to extend the binary support vector machine to the ordinal regression problem has important research significance.The main content of this thesis roughly divided into the following three parts:The first part is to promote v-nonparallel support vector machine(v-NPSVM for short)to obtain a new ordinal regression called v-nonparallel support vector ordinal regression(v-NPSVOR for short).Compared with NPSVOR,the algorithm changes the parameter ? to the variable ?k,k?{1,...,q},which reduces the difficulty of selecting parameter;The second part is to gen-eralize the sparse linear nonparallel support vector machine(L1-NPSVM for short)to obtain a new ordinal regression called L1-nonparallel support vector ordinal regression(L1-NPSVOR for short).The algorithm adds the objective function in NPSVOR to 1/2bl2,so that not only the solution of the decision variable bk is unique but also the dual problem reduces equality constraints;The third part is to promote the improved twin support vector machine(ITSVM for short)to obtain a new ordinal regression called stable nonparallel support vector ordinal regression(SNPSVOR for short).The algorithm changes the first inequality constraint in L1-NPSVOR to an equality constraint,which reduces the influence of the data set with outliers to some extent.Numerical experiments show the effectiveness of the above three algorithms.