Research On Robustness Of Support Vector Machine Related Algorithms

support vector machine(SVM),as a data mining method,which has been widely used in various fields of society for its strong generalization ability.However,the support vector machine needs to solve the convex quadratic programming problem(QPP)with inequality constraints.The training time is long and the calculation is complex,so that it cannot handle large-scale data problems.In addition,support vector machine can use kernel functions to deal with nonlinear classifications,such as XOR classification,however,it is not easy to choose the appropriate kernel function.Later,twin support vector machine(TWSVM)is proposed,which not only shortens the training time,but also solves the XOR type data classification,however,the objective function is still based on the L2 norm which is sensitive to noise data.Once the data contains much noise,the performance of the algorithm is greatly influenced.In order to improve the robustness and classification accuracy of the algorithm,in this paper,three innovative algorithms which are based on the algorithm of TWSVM are proposed.The main work is summarized as follows:1.Based on the algorithm of TWSVM,we propose a new robust capped L1-norm twin support vector machine(CTWSVM)algorithm,which not only maintains the original advantages of TWSVM,but also improves the accuracy of the algorithm.In the objective function,we introduce the capped L1-norm to measure the distance from the data point to the classification plane.According to the given threshold,it will decide whether the data point is a noise point.If it is regarded as noise data,it will be “discarded” and excluded from the calculation in order to mitigate the impact of outliers on the classification plane.In addition,we use a new iterative algorithm to solve the problem of capped L1-norm,and theoretically analyze the existence of local optimal and convergence of the algorithm.Through a series of experiments on artificial dataset and UCI dataset,we prove the robustness and feasibility of CTWSVM.2.Based on the algorithm of CTWSVM,we introduce the idea of least squares in order to reduce the training time of the algorithm.Here,we propose a new algorithm called capped L1-LSTSVM,which not only greatly reduces the training cost,but also enhances the robustness of the algorithm.Similarly,we use an effective and simple iterative algorithm to solve the problem,and the experiment on the artificial data set and UCI data set verify the anti-noise ability and feasibility of the algorithm.3.In order to furtherly improve the robustness of the algorithm and increase the flexibility of the algorithm,this paper introduces the capped Lp-norm to the least squares support vector machine(LSTSVM)so that it can be applied to a wider range of data.Similarly,we set the appropriate threshold to eliminate the influence of noise data,and we present some theoretical analysis on the feasibility of the algorithm.Finally,a series of experiments were carried out on artificial datasets and UCI datasets,and different Gaussian noise ratios were introduced into the experiments to compare with other similar classification algorithms to verify the anti-noise ability of the proposed algorithm.