Robust Support Vector Machines And Its Sparse Algorithms Based On Smooth And Nonconvex Loss

The large-scale data classification problem with noise is an important research content in data mining.As a classic data mining technology,support vector machine is widely used in various fields because of its strong generalization ability.Some studies have shown that the support vector machine classification model based on non-convex and non-smooth loss function is robust in the presence of label noise,which can reduce the influence of noise on the classification hyperplane and improve the classification accuracy of the data.However,the use of non-smooth loss functions leads to difficulties in solving this model.Aiming at the above problems,this paper proposes a robust support vector machine model based on smooth and nonconvex loss function,and studies the large-scale data classification problem with label noise,and gives a fast algorithm for solving this model.The research results obtained in this paper mainly include:Firstly,the robust support vector machine classification model based on smooth nonconvex loss function is studied.Although this model is robust to label noise,it needs to solve the quadratic programming by iteratively to obtain the optimal solution of the model.The amount is large and the convergence speed is slow,which is not suitable for training largescale classification problems.In order to solve the above problems,a fast convergence method is presented and verified.The experimental results show the effectiveness of the method.Secondly,based on the idea of least squares,a generalized robust least squares support vector machine model is proposed and solved by a fast convergence algorithm to theoretically explain the robustness of the model.In order to effectively deal with the large-scale classification problem with label noise,a sparsely extended robust least squares support vector machine algorithm and sparse robust support vector machine algorithm are proposed based on the low rank approximation method for kernel matrix.The experimental results show that the proposed algorithm outperforms the related algorithms in terms of convergence speed,test accuracy and training time.Finally,the smooth non-convex loss function of robust support vector machine is improved.A robust support vector machine model with multi-parameter control is proposed.Its robustness is proved in its dual space,and the model is given.The fast convergence solution method is used,and the sparse solution algorithm of the model is given by using the low rank approximation of the kernel matrix.The effectiveness of the algorithm is proved by a large number of experiments.