On Alternating Direction Method Of Multipliers For Non-parallel Support Vector Machines

Non-parallel support vector machines are extensions of support vector machines,and they can divide data with cross-prevailing structures.The alternating direction method of multiplier is a simple and effective method and it is suitable for the separable convex programming problem.In recent years,this algorithm has attracted much attention due to its practical application in many fields.Therefore,this paper applies the alternating direction method of multiplier to solve the non-parallel support vector machines,so as to obtain several non-parallel support vector machines based on the alternating direction method of multiplier.The research content of this paper is mainly divided into the following two parts:In the first part,the traditional twin bounded support vector machine is firstly introduced.Then the L2-norm twin bounded support vector machine based on the alternating direction method of multiplier is constructed and its corresponding algorithm is obtained.This paper also proves its convergence.Because the L2-norm regularization term loses the sparseness of the solution and is sensitive to noise and outliers,in order to reduce the sensitivity of the method to noise and outliers,this paper replaces the L2-norm regularization term which in the model with theL1-norm regularization term.So the alternating direction method of multiplier for L1-norm twin bounded support vector machine is constructed and the corresponding algorithm is obtained.In this paper,several numerical experiments on UCI dataset verify the effectiveness of the algorithm.In the second part,the two-sided best fitting hyperplane classifier is firstly introduced.Because it is a non-convex problem,it can solve the original problem by using the concave-convex process.In this paper,according to the separability of the original problem,the original problem is decomposed into two parts of convex and concave.Then the L2-norm two-sided best fitting hyperplane classifier based on the alternating direction method of multiplier is constructed and its corresponding algorithm is obtained.In order to reduce the sensitivity of the method to noise and outliers,this paper also replaces the L2-norm regularization term with the L1-norm regularization term,so as to obtain the L1-norm two-sided best fitting hyperplane classifier based on the alternating direction method of multiplier and its corresponding algorithm.In addition,according to the importance of initialization,this paper also proposes a new initialization method.Several preliminary numerical results on the artificial dataset and the UCI datasets verify the effectiveness of new algorithms,respectively.