关键词: 机器学习, 最优化方法, 支持向量机, Rescaled Hinge损失函数, 多子支持向量机

Abstract: As the performance of multi-classification learning model is effected by outliers, a Multiple Birth Support Vector Machine based on Rescaled Hinge loss function (RHMBSVM) was proposed. First, the corresponding optimization problem was constructed by introducing a bounded non-convex Rescaled Hinge loss function. Then, the conjugate function theory was used to make equivalent transformation of the optimization problem. Finally, the variable alternation strategy was used to form an iterative algorithm to solve the non-convex optimization problem. The penalty weight of each sample point was automatically adjusted during the solution process, so that the effect of outliers on K hyperplanes was eliminated, and the robustness was enhanced. The method of 5-fold cross-validation was used to complete the numerical experiment. Results show that, in the case of no outliers in the datasets, the accuracy of the proposed method is 1.11 percentage point higher than that of Multiple Birth Support Vector Machine (MBSVM) and 0.74 percentage point higher than that of Robust Support Vector Machine based on Rescaled Hinge loss function (RSVM-RHHQ); in the case of having outliers in the datasets, the accuracy of the proposed method is 2.10 percentage point higher than that of MBSVM and 1.47 percentage point higher than that of RSVM-RHHQ. Experimental results verify the robustness of the proposed method in solving multi-classification problems with outliers.

Key words: machine learning, optimization method, Support Vector Machine (SVM), Rescaled Hinge loss function, Multiple Birth Support Vector Machine (MBSVM)