【摘要】 SVM的损失函数可以保证分类结果的高置信度,但同时是一个无界的凸函数,导致受噪声的影响较大。为了提高SVM在噪声环境下的分类效果,提出使用结合了pinball和LS损失函数的ML loss来降低对噪声的敏感性,将其应用到SVM中得到MLSVM模型。根据LS损失函数具有结构风险最小化的特性和等式约束来简化求解过程,然后使用pinball损失函数根据分类样本之间的最大分位数距离来确定分类超平面,再使用拉格朗日函数等方法求解MLSVM的目标函数和分类超平面。在数据集上的实验表明,相比于hinge SVM等模型,MLSVM可以降低对数据中噪声的敏感性,提升对含噪数据的分类性能。更多还原

【Abstract】 The loss function of SVM is able to guarantee the high confidence of classification results,but it is also an unbounded convex function which is greatly affected by noise. In order to improve the classification effect of SVM in noisy environment,this paper proposed ML loss combined with pinball and LS loss functions to reduce the sensitivity to noise,which was applied to SVM to obtain MLSVM model. The algorithm simplified the solution process according to the characteristics of LS loss function with structural risk minimization and equality constraints,then used pinball loss function to determine the classification hyperplanes according to the max quantile distance between classification samples and used Lagrange function and other methods to work out the objective function and classification hyperplanes of MLSVM. Experiments on datasets show that compared with hinge SVM and other models,MLSVM is capable of reducing the sensitivity to noise in data and improving the recognition performance of noise-containing data.更多还原