Research On Multi-class Classification Support Vector Machines

Support vector machine(SVM)was originally designed for binary classifications,and suitable for small-scale dataset learning.How to effectively extend it to solve large-scale multi-class classification problems is an interesting and challenging question for study.In this paper,we first introduce four multi-class classification strategies:one-against-all(OAA),one-against-one(OAO),one-against-one-against-rest(OAOAR)and all-at-once(AAO).We analyze eight classical multi-class classification support vector machines under these four strategies,and the classification illustration diagrams are drawn to understand the principle intuitively.Then,combining L2,p-norm and two kinds of multi-class classification codings(one-hot coding,sine and cosine coding),L2,p-norm multi-class support vector machine(L2,p MSVM)p>1,a new multi-class classification support vector machine based on all-at-once strategy is proposed.The optimization problem of L2,p MSVM is solved by updating variables alternately in iter-ations and sequential minimal optimization-Newton's method(SMO-NM)algorithm.The optimal values of L2,p MSVM's parameters are studied by numerical experiments.Finally,L2,p MSVM is compared with eight classical multi-class classification support vector machines.The experimental results show that when p=2,L2,p MSVM has bet-ter generalization ability,computational complexity and sparsity.When p=2.5,L2,p MSVM has better generalization ability and sparsity than when p=2.