收稿日期: 2009-03-18
修回日期: 2009-04-20
网络出版日期: 2009-09-15
基金资助
国家自然科学基金(10671203,70621001,70531040)资助
Improved classification model via MPEC
Received date: 2009-03-18
Revised date: 2009-04-20
Online published: 2009-09-15
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; β 似然估计; filterSQP方法; 鲁棒性
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 . DOI: 10.7523/j.issn.2095-6134.2009.5.003
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
[1] Mangasarian O L. Linear and nonlinear separation of patterns by linear programming
[J]. Operations Research, 1965, 13(3):444-452.
[2] Mangasarian O L. Multisurface method of pattern separation
[J]. IEEE Transactions on Information Theory, 1968,IT-14(6):801-807.
[3] Vapnik V. The nature of statistical learning theory
[M]. New York: Springer, 1995.
[4] Olson T, Pang J S, Priebe C. A likelihood-MPEC approach to target classification
[J]. Mathematical Programming, 2003, 96:1-31.
[5] Priebe C E. Nonhomogeneity analysis using borrowed strength
[J]. Journal of the American Statistical Association, 1996, 91: 1497-1503.
[6] Luo Z Q, Pang J S, Ralph D. Mathematical programs with equilibrium constraints
[M]. Cambridge: Cambridge University Press, 1996.
[7] Scheel H, Scholtes S. Mathematical programs with equilibrium constraints: stationarity, optimality, and sensitivity
[J]. Mathematics of Operations Research, 2000, 25: 1-22.
[8] Scholtes S, Stuhr M. Exact penalization of methematical programs with comple-mentarity constraints
[J]. SIAM Journal on Control and Optimization, 1999, 37: 617-652.
[9] Anitescu M. On using the elasticmode in nonlinear programming approaches to mathematical programs with complementarity constraints
[J]. SIAM Journal on Optimization, 2005, 15: 1203-1236.
[10] Fletcher R, Leyffer S. Solving mathematical program with complementarity constraints as nonlinear programs
[J]. Optimization Methods and Software, 2004, 19(1): 15-40.
[11] Fletcher R, Leyffer S, Ralph D, et al. Local convergence of SQP methods for mathematical programs with eqllilibrillln constraints
[J]. SIAM Journal on Optimization, 2006, 17(1): 259-286.
[12] Fletcher R, Leyffer S. Nonlinear programming without a penalty fllnction
[J]. Mathematical Programming, 2002, 91: 239-270.
[13] Fujisawa H, Eguchi S. Robust estimation in the normal mixture model
[J]. Journal of Statistical Planning and Inference, 2006, 136: 3989-4011.
[14] Zhang Z W, Shi Y, Zhang P, et al. A rough set-based multiple criteria linear programming approach for classification
[J]. Lecture Notes in Computer Science, 2008, 5102: 476-485.
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