基于案例学习的多层次聚类指标客观权重极大熵挖掘模型
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摘要
本文针对待聚类对象的多层次聚类指标权重配置问题进行了研究。首先运用向量空间模型将聚类对象表征为包含多个层次聚类属性指标的特征空间向量并基于余弦距离测算底层属性指标的相似程度,然后根据聚类指标的层次结构以及相应各层指标的权重系数综合测算对象之间的相似程度,最后根据历史聚类案例中相同类别对象之间相似度较大,不同类别对象之间相似度较小等特点,构建了基于案例学习的多层次聚类指标客观权重极大熵挖掘模型。通过案例分析以及与其他方法的比较研究,证明了本模型的可行性与有效性,为多层次聚类指标客观赋权问题提供了一种新的研究思路。
The weight of characteristic attribute index is a significant influence factor during the process of multiple criteria clustering decision aids.Hence,many researches have focused on this important research area.Historical clustering information can effectively provide importance measures for each index with regard to clustering the objects which are to be evaluated.Learning of previous cases can not only contributes to the reveal of the objective law of clustering but also dig out the weight of each attribute index.However,this significant information has been overlooked by many previous researches which can definitely lead to the inaccurate weight calculation.Case learning,in this paper,is defined as the method proposed by the self-reasoning of the results of typical case sets and calculating some of the key parameters,so as to construct the proper decision-making models which can be applied to the evaluation of new objects in the future.To make the most of the existing clustering cases,the objects which are to be clustered as multidimensional attributes are defined by using space vector model.Based on the fact that objects in the same category are more similar than those in different categories,cosine distance is introduced to measure the similarity among different objects.Maximum entropy model is also employed to estimate the expected contribution of different indexes located in diverse levels to the category of the whole object.An illustrative example about weight allocation of attribute indexes in criminal cases is presented in this paper to show how the new approach is applied in the practical clustering decision problem.The feasibility and validity of the newly-proposed method is demonstrated through the comparison analysis with other similar methods.As a decision support,the proposed model can also provide a novel standpoint for weight calculation of objects with multi-level attribute indexes.
The weight of characteristic attribute index is a significant influence factor during the process of multiple criteria clustering decision aids.Hence,many researches have focused on this important research area.Historical clustering information can effectively provide importance measures for each index with regard to clustering the objects which are to be evaluated.Learning of previous cases can not only contributes to the reveal of the objective law of clustering but also dig out the weight of each attribute index.However,this significant information has been overlooked by many previous researches which can definitely lead to the inaccurate weight calculation.Case learning,in this paper,is defined as the method proposed by the self-reasoning of the results of typical case sets and calculating some of the key parameters,so as to construct the proper decision-making models which can be applied to the evaluation of new objects in the future.To make the most of the existing clustering cases,the objects which are to be clustered as multidimensional attributes are defined by using space vector model.Based on the fact that objects in the same category are more similar than those in different categories,cosine distance is introduced to measure the similarity among different objects.Maximum entropy model is also employed to estimate the expected contribution of different indexes located in diverse levels to the category of the whole object.An illustrative example about weight allocation of attribute indexes in criminal cases is presented in this paper to show how the new approach is applied in the practical clustering decision problem.The feasibility and validity of the newly-proposed method is demonstrated through the comparison analysis with other similar methods.As a decision support,the proposed model can also provide a novel standpoint for weight calculation of objects with multi-level attribute indexes.
引文
[1]衣博.历史建筑价值评价中专家调查法的信度效度检验研究[D].哈尔滨:东北林业大学,2015.
[2]Xu Z.On consistency of the weighted geometric mean complex judgement matrix in AHP[J].European Journal of Operational Research,2000,126(3):683-687.
[3]陈伟,夏建华.综合主、客观权重信息的最优组合赋权方法[J].数学的实践与认识,2007,37(1):17-22.
[4]陆明生.多目标决策中的权系数[J].系统工程理论与实践,1986,6(4):77-78.
[5]程明熙.处理多目标决策问题的二项系数加权和法[J].系统工程理论与实践,1983,3(4):23-26.
[6]王宗军.多目标权系数赋值方法及其选择策略[J].系统工程与电子技术,1993,(6):35-41.
[7]魏明,堵俊,季巍,等.多层次模糊综合评价方法在生态补水方案选择中的应用[J].环境保护前沿,2014,4(6):220-224.
[8]韩小孩,张耀辉,孙福军,等.基于主成分分析的指标权重确定方法[J].四川兵工学报,2012,33(10):124-126.
[9]程启月.评测指标权重确定的结构熵权法[J].系统工程理论与实践,2010,30(7):1225-1228.
[10]熊文涛,齐欢,雍龙泉.一种新的基于离差最大化的客观权重确定模型[J].系统工程,2010,28(5):95-98.
[11]上官廷华,冯荣耀,柳宏川.一种基于熵和均方差法综合赋权的K-means算法[J].计算机与现代化,2010,(4):34-36.
[12]李方方,李秀芳.基于多目标规划理论的财险公司定价决策模型[J].中南财经政法大学学报,2015,(1):48-54.
[13]丁涛,吴华清,梁樑.360度评估体系中权重调整方法研究[J].中国管理科学,2016,24(7):149-154.
[14]程砚秋.基于区间相似度和序列比对的群组G1评价方法[J].中国管理科学,2015,(s1):204-210.
[15]金佳佳,徐伟宣,汪群峰,等.考虑专家判断信息的灰色关联极大熵权重模型[J].中国管理科学,2012,20(2):135-143.
[16]王跃进,孟宪颐.绿色产品多级模糊评价方法的研究[J].中国机械工程,2000,11(9):1016-1019.
[17]谢延红,宁玉富,刘建军,等.多层不确定综合评价方法及应用[C]//中国青年信息与管理学者大会,2011.
[18]Zhang L,Xu Y,Yeh C H,et al.City sustainability evaluation using multi-criteria decision making with objective weights of interdependent criteria[J].Journal of Cleaner Production,2016,131:491-499.
[19]Boroushaki S.Entropy-based weights for multi-criteria spatial decision-making[J].Yearbook of the Association of Pacific Coast Geographers,2017,79:168-187.
[20]Chen Y,Kilgour D M,Hipel K W.A case-based distance method for screening in multiple-criteria decision aid[J].Omega,2008,36(3):373-383.
[21]Greco S,Mousseau V.Robust ordinal regression for multiple criteria group decision:UTAGMS-GROUP and UTADISGMS-GROUP[J].Decision Support Systems,2012,52(3):549-561.
[22]Ma L C.Screening alternatives graphically by an extended case-based distance approach[J].Omega,2012,40(1):96-103.
[23]Salton G.A vector space model for automatic indexing[J].Communications of the Acm,1974,18(11):613-620.
[24]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社,2002.
[25]胡毓达.实用多目标最优化[M].上海:上海科学技术出版社,1990.
[2]Xu Z.On consistency of the weighted geometric mean complex judgement matrix in AHP[J].European Journal of Operational Research,2000,126(3):683-687.
[3]陈伟,夏建华.综合主、客观权重信息的最优组合赋权方法[J].数学的实践与认识,2007,37(1):17-22.
[4]陆明生.多目标决策中的权系数[J].系统工程理论与实践,1986,6(4):77-78.
[5]程明熙.处理多目标决策问题的二项系数加权和法[J].系统工程理论与实践,1983,3(4):23-26.
[6]王宗军.多目标权系数赋值方法及其选择策略[J].系统工程与电子技术,1993,(6):35-41.
[7]魏明,堵俊,季巍,等.多层次模糊综合评价方法在生态补水方案选择中的应用[J].环境保护前沿,2014,4(6):220-224.
[8]韩小孩,张耀辉,孙福军,等.基于主成分分析的指标权重确定方法[J].四川兵工学报,2012,33(10):124-126.
[9]程启月.评测指标权重确定的结构熵权法[J].系统工程理论与实践,2010,30(7):1225-1228.
[10]熊文涛,齐欢,雍龙泉.一种新的基于离差最大化的客观权重确定模型[J].系统工程,2010,28(5):95-98.
[11]上官廷华,冯荣耀,柳宏川.一种基于熵和均方差法综合赋权的K-means算法[J].计算机与现代化,2010,(4):34-36.
[12]李方方,李秀芳.基于多目标规划理论的财险公司定价决策模型[J].中南财经政法大学学报,2015,(1):48-54.
[13]丁涛,吴华清,梁樑.360度评估体系中权重调整方法研究[J].中国管理科学,2016,24(7):149-154.
[14]程砚秋.基于区间相似度和序列比对的群组G1评价方法[J].中国管理科学,2015,(s1):204-210.
[15]金佳佳,徐伟宣,汪群峰,等.考虑专家判断信息的灰色关联极大熵权重模型[J].中国管理科学,2012,20(2):135-143.
[16]王跃进,孟宪颐.绿色产品多级模糊评价方法的研究[J].中国机械工程,2000,11(9):1016-1019.
[17]谢延红,宁玉富,刘建军,等.多层不确定综合评价方法及应用[C]//中国青年信息与管理学者大会,2011.
[18]Zhang L,Xu Y,Yeh C H,et al.City sustainability evaluation using multi-criteria decision making with objective weights of interdependent criteria[J].Journal of Cleaner Production,2016,131:491-499.
[19]Boroushaki S.Entropy-based weights for multi-criteria spatial decision-making[J].Yearbook of the Association of Pacific Coast Geographers,2017,79:168-187.
[20]Chen Y,Kilgour D M,Hipel K W.A case-based distance method for screening in multiple-criteria decision aid[J].Omega,2008,36(3):373-383.
[21]Greco S,Mousseau V.Robust ordinal regression for multiple criteria group decision:UTAGMS-GROUP and UTADISGMS-GROUP[J].Decision Support Systems,2012,52(3):549-561.
[22]Ma L C.Screening alternatives graphically by an extended case-based distance approach[J].Omega,2012,40(1):96-103.
[23]Salton G.A vector space model for automatic indexing[J].Communications of the Acm,1974,18(11):613-620.
[24]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社,2002.
[25]胡毓达.实用多目标最优化[M].上海:上海科学技术出版社,1990.