基于线性判别分析的Choquet积分的符号模糊测度提取
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摘要
在解决分类问题时,建立在Choquet积分上的分类器以其非线性和不可加性的特点,扮演着越来越重要的角色。由于Choquet积分中的符号模糊测度可以描述各特征对结果的影响,因此Choquet积分在解决数据分类及融合问题方面具有显著的优势。但是,关于Choquet积分符号模糊测度值的求解,学术界一直缺乏有效的方法。目前最常用的方法是遗传算法,但是遗传算法在解决符号模糊测度值的优化问题时存在算法较为复杂、耗时较长等缺陷。由于符号模糊测度值在Choquet积分分类器中是决定性的重要参数,因此设计出一种有效的符号模糊测度提取方法十分必要。文中提出基于线性判别分析的Choquet积分符号模糊测度的提取方法,推导出在分类问题下Choquet积分的符号模糊测度值的解析式表达,其能够有效、快速地得出关键性参数。分别在人工数据集及基准实际数据集上进行测试与验证,实验结果表明所提方法能有效解决Choquet积分分类器中符号模糊测度的优化问题。
For solving classification problems,Choquet integral classifier plays an increasingly important role by its nonlinear and nonadditivity.Especially,in the domain of solving the problem of data classification and fusion,Choquet integral has obvious advantages,because its signed fuzzy measure provides an effective representation to describe the interaction among contributions from predictive attributes to objective attributes.However,there is lack of an effective method to extract the signed fuzzy measure of Choquet integral.Currently,the most common used method is genetic algorithm,but the genetic algorithm is complex and time-consuming.Since the values of signed fuzzy measure are critical parameters in the Choquet integral classifier,it is necessary to design an efficient extraction method.Based on linear discriminant analysis,this paper proposed an extraction method for retrieving the values of signed fuzzy measure in the Choquet integral based on linear discriminant analysis,and derived the analytic expression of the signed measure value in Choquet integral under the classification problem,so that the key parameters can be obtained quickly and efficiently.This method was tested and validated on artificial data sets and benchmark data sets,respectively.The experiment results show that this method can effectively solve the optimization problem of signed fuzzy measure in Choquet integral classifier.
For solving classification problems,Choquet integral classifier plays an increasingly important role by its nonlinear and nonadditivity.Especially,in the domain of solving the problem of data classification and fusion,Choquet integral has obvious advantages,because its signed fuzzy measure provides an effective representation to describe the interaction among contributions from predictive attributes to objective attributes.However,there is lack of an effective method to extract the signed fuzzy measure of Choquet integral.Currently,the most common used method is genetic algorithm,but the genetic algorithm is complex and time-consuming.Since the values of signed fuzzy measure are critical parameters in the Choquet integral classifier,it is necessary to design an efficient extraction method.Based on linear discriminant analysis,this paper proposed an extraction method for retrieving the values of signed fuzzy measure in the Choquet integral based on linear discriminant analysis,and derived the analytic expression of the signed measure value in Choquet integral under the classification problem,so that the key parameters can be obtained quickly and efficiently.This method was tested and validated on artificial data sets and benchmark data sets,respectively.The experiment results show that this method can effectively solve the optimization problem of signed fuzzy measure in Choquet integral classifier.
引文
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[2] WANG Z,KLIR G J.Fuzzy measure theory[J].Plenum Berlin,1992,35(1-2):3-10.
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[4] TEHRANI A F,CHENG W,HULLERNRIER E.Preference learning using the Choquet integral:The case of multipartite ranking[C]∥IEEE Transactions on Fuzzy Systems.IEEE,2012:1102-1113.
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[6] CHEN J F,HE Q.Determination of fuzzy measure in Choquet fuzzy integral fusion model[J].Journal of Hebei University,2006,26(4):354-357.(in Chinese)陈俊芬,何强.Choquet模糊积分融合模型中模糊测度的确定[J].河北大学学报,2006,26(4):354-357.
[7] LI T S.Research on multi classifier fusion model based on Choquet integral[D].Hebei:Hebei University,2010.(in Chinese)李铁松.基于Choquet积分的多分类器融合模型研究[D].河北:河北大学,2010.
[8] WANG Z,YANG R,SHI Y.A new nonlinear classification model based on cross-oriented Choquet integrals[C]∥International Conference on Information Science and Technology Nanjing.China,2011:176-181.
[9] FANG H,RIZZO M L,WANG H,et al.A new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm[J].Pattern Recognition,2010,43(4):1393-1401.
[10]GRACISCH M,MUROFUSHI T,SUGENO M.Fuzzy measures and integral[M]∥Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference.Netherlands:Springer,1995.
[11]YAGER R R.Evaluating Choquet integrals whose arguments are probability distributions[J].IEEE Transactions on Fuzzy Systems,2016,24(4):957-965.
[12]XU K,WANG Z,HENG P A,et al.Classification by nonlinear integral projections[J].IEEE Transactions on Fuzzy Systems,2003,11(2):187-201.
[13]YANG R,WANG Z,HENG P A,et al.Classification of Heterogeneous fuzzy data by Choquet integral with fuzzy-valued integrand[J].IEEE Transactions on Fuzzy Systems,2007,15(5):931-942.
[14]KOCHI N,WANG Z.Solving nonlinear programming problems based on the Choquet integral by agenetic algorithm[J]Journal of Intelligent and Fuzzy Systems,2015,29(1):437-442.
[15]BUSTINCE H,GALAR M.A new approach to interval-values Choquet integrals and the problem of ordering in interval-values fuzzy set applications[J].IEEE Transactions on Fuzzy Systems,2013,21(6):1150-1162.
[16]WANG Z.A new genetic algorithm for nonlinear multi-regressions based on generalized Choquet integrals.[C]∥12th IEEE International Conference on Fuzzy Systems.IEEE,2003:819-821.
[2] WANG Z,KLIR G J.Fuzzy measure theory[J].Plenum Berlin,1992,35(1-2):3-10.
[3] XU K,WANG Z,HENG P A,et al.Classification by nonlinear integrals projections[C]∥IEEE Transactions on Fuzzy Systems.IEEE,2003:187-201.
[4] TEHRANI A F,CHENG W,HULLERNRIER E.Preference learning using the Choquet integral:The case of multipartite ranking[C]∥IEEE Transactions on Fuzzy Systems.IEEE,2012:1102-1113.
[5] WANG H X.On Choquet integral and set-valued Choquet integral with their applications in finance[D].Beijing:Beijing University of Technology.2013.(in Chinese)王洪霞.Choquet积分和集值Choquet积分及其在金融中的应用[D].北京:北京工业大学,2013.
[6] CHEN J F,HE Q.Determination of fuzzy measure in Choquet fuzzy integral fusion model[J].Journal of Hebei University,2006,26(4):354-357.(in Chinese)陈俊芬,何强.Choquet模糊积分融合模型中模糊测度的确定[J].河北大学学报,2006,26(4):354-357.
[7] LI T S.Research on multi classifier fusion model based on Choquet integral[D].Hebei:Hebei University,2010.(in Chinese)李铁松.基于Choquet积分的多分类器融合模型研究[D].河北:河北大学,2010.
[8] WANG Z,YANG R,SHI Y.A new nonlinear classification model based on cross-oriented Choquet integrals[C]∥International Conference on Information Science and Technology Nanjing.China,2011:176-181.
[9] FANG H,RIZZO M L,WANG H,et al.A new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm[J].Pattern Recognition,2010,43(4):1393-1401.
[10]GRACISCH M,MUROFUSHI T,SUGENO M.Fuzzy measures and integral[M]∥Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference.Netherlands:Springer,1995.
[11]YAGER R R.Evaluating Choquet integrals whose arguments are probability distributions[J].IEEE Transactions on Fuzzy Systems,2016,24(4):957-965.
[12]XU K,WANG Z,HENG P A,et al.Classification by nonlinear integral projections[J].IEEE Transactions on Fuzzy Systems,2003,11(2):187-201.
[13]YANG R,WANG Z,HENG P A,et al.Classification of Heterogeneous fuzzy data by Choquet integral with fuzzy-valued integrand[J].IEEE Transactions on Fuzzy Systems,2007,15(5):931-942.
[14]KOCHI N,WANG Z.Solving nonlinear programming problems based on the Choquet integral by agenetic algorithm[J]Journal of Intelligent and Fuzzy Systems,2015,29(1):437-442.
[15]BUSTINCE H,GALAR M.A new approach to interval-values Choquet integrals and the problem of ordering in interval-values fuzzy set applications[J].IEEE Transactions on Fuzzy Systems,2013,21(6):1150-1162.
[16]WANG Z.A new genetic algorithm for nonlinear multi-regressions based on generalized Choquet integrals.[C]∥12th IEEE International Conference on Fuzzy Systems.IEEE,2003:819-821.