Journal of Computer Applications ›› 2020, Vol. 40 ›› Issue (11): 3139-3145.

• Artificial intelligence •

### Multiple birth support vector machine based on Rescaled Hinge loss function

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830046, China
• Received:2020-03-30 Revised:2020-05-25 Online:2020-11-10 Published:2020-06-22
• Supported by:
This work is partially supported by the Key Natural Science Program of Education Department of Xinjiang Autonomous Region (XJEDU2018I002).

### 基于Rescaled Hinge损失函数的多子支持向量机

1. 新疆大学 数学与系统科学学院, 乌鲁木齐 830046
• 通讯作者: 杨志霞(1977-),女,新疆奎屯人,教授,博士,主要研究方向:最优化方法、机器学习;yangzhx@xju.edu.cn
• 作者简介:李卉(1994-),女,新疆库尔勒人,硕士研究生,主要研究方向:机器学习
• 基金资助:
新疆自治区教育厅自然科学重点项目（XJEDU2018I002）。

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.

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