改进的基于均衡约束数学规划的分类模型

doi:10.7523/j.issn.2095-6134.2009.5.003

中国科学院大学学报 ›› 2009, Vol. 26 ›› Issue (5): 599-608.DOI: 10.7523/j.issn.2095-6134.2009.5.003

改进的基于均衡约束数学规划的分类模型

丁飞^1,2, 尹红霞^2,3

1. 中国科学院研究生院数学科学学院,北京 100049;
2. 中国科学院虚拟经济与数据科学研究中心,北京 100080;
3. 明尼苏达州立大学数学与统计系,曼凯托,美国 56001

收稿日期:2009-03-18 修回日期:2009-04-20 发布日期:2009-09-15
通讯作者: 丁飞
基金资助:
国家自然科学基金(10671203,70621001,70531040)资助 

Improved classification model via MPEC

DING Fei^1,2, YIN Hong-Xia^2,3

1. School of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China;
2. Research Center on Fictitious Economy and Date Science, Chinese Academy of Sciences, Beijing 100080, China;
3. Department of Mathematics and Statistics, Minnesota State University Mankato, Mankato, MN 56001, USA

Received:2009-03-18 Revised:2009-04-20 Published:2009-09-15

摘要/Abstract

摘要：

对基于均衡约束数学规划(MPEC)的数据分类模型进行改进.在确定数据所服从分布的密度函数(高斯混合模型来模拟)的参数时,使用β似然估计来代替原模型中的最大似然估计.新模型可以克服似然函数可能出现无界的现象,在计算上有更好的鲁棒性.对于所得MPEC分类模型,使用filterSQP方法将其作为非线性规划求解.数值试验显示了新模型的有效性.

关键词: 均衡约束数学规划, &beta, 似然估计, filterSQP方法, 鲁棒性

Abstract:

In this paper, we provide an improved form of MPEC model for data classification first proposed in Ref.[1]. We use β likelihood estimation instead of maximum likelihood estimation to estimate the parameters of data's probability distribution function (modeled by Gaussian mixture models). Our new model can avoid the contingent of unboundedness of the maximum likelihood function and excessive sensitivity of the maximum likelihood estimator to outliers, showing more robustness. Then we use filterSQP method to solve our β likelihood MPEC model as nonlinear program. Efficiency of the model is shown by primal numerical tests.

Key words: MPEC, β likelihood estimation, filterSQP, robustness

中图分类号:

O221.2

丁飞, 尹红霞. 改进的基于均衡约束数学规划的分类模型[J]. 中国科学院大学学报, 2009, 26(5): 599-608.

DING Fei, YIN Hong-Xia. Improved classification model via MPEC[J]. , 2009, 26(5): 599-608.

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改进的基于均衡约束数学规划的分类模型

Improved classification model via MPEC

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