不一致决策表数据处理方法研究
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摘要
摘要粗糙集是一种处理不确定性信息的数学工具,通过求核属性集、属性约简以及规则提取等步骤,从原始数据集中提取有效的知识。然而,在不一致决策表数据处理过程中,粗糙集处理方法面临着不一致决策表核属性集的不一致问题,不一致决策表的多种处理流程在实际应用中的选择问题,以及最小约简计算的NP难题等问题的困扰。为克服上述问题对处理性能的影响,本文研究相关的解决策略,以提供一套较为系统的不一致决策表数据处理方法。主要研究工作和创新性成果如下：
1,针对不一致决策表中核属性集计算方法多且结论不一致所导致的难以判断全部有效核集的问题,提出基于信息粒划分的核属性集有效性判断方法,并计算所有有效的核属性集。首先,基于经典Pawlak模型分析不一致决策表信息粒的信息类型,并定义信息粒划分的概念描述不一致决策表中的有效信息,在此基础上,证实任一不一致决策表仅存在三类有效的信息粒划分。最后,针对三类信息粒划分提出基于可辨识矩阵的核属性集算法有效性判断方法,并计算所有有效的核属性集。
2,针对不一致决策表多种处理流程共存,造成应用中难以正确选择处理流程的问题,基于信息粒划分构建不一致决策表数据处理框架,并提出一种直观的计算流程选择策略。首先,定义与三类信息粒划分对应的规则类型,建立信息粒划分、可辨识矩阵以及规则类型之间的映射关系,在此基础上,提出基于规则类型的不一致决策表数据计算流程选择策略,建立不一致决策表数据处理框架,确保计算结果中的核属性集、约简以及规则集均包含用户感兴趣的知识。
3,针对启发式算法难以获得最小约简的问题,提出属性排斥矩阵,优化传统启发式属性约简算法的性能。首先,研究最小约简约束下属性之间的排斥特征,提出满足最小约简必要条件的属性排斥矩阵,设计对应的最小约简属性启发策略。在此基础上,分别结合典型加法类与减法类启发式约简算法,提出两种基于属性排斥矩阵的启发式属性约简算法。UCI标准数据集测试表明,属性排斥矩阵包含丰富的最小约简启发信息,能全面提高启发式属性约简算法的性能。
4,提出基于属性关联的启发式最小约简计算算法。首先,在属性排斥特征研究的基础上,进一步分析最小约简集属性之间的吸引特征(与属性排斥特征一起统称为属性关联性质),并定义基于属性关联的属性重要度计算指数。在此基础上,提出基于该重要度的启发式属性约简算法。该算法采取兼顾单个属性的辨识能力以及属性之间关联的约简策略,提高最小约简获得概率。
5,针对现有启发策略难以估计启发有效性的问题,提出了可信度高且可信度可以估计的属性启发策略。首先,基于属性排斥特征,提出对应的启发策略,建立其可信度模型；在此基础上,提出属性互斥特征及其对应的启发策略,并建立对应的可信度模型。最后,以可信度为依据,提出综合的可信度高且可信度可以估计的最小约简启发策略,并给出了具体的算法。UCI标准数据集实验测试表明,可信度模型有效且该策略具有较高的最小约简可信度。
6,针对传统粗糙集数据处理过程面临的最优离散化以及属性约简的NP难题,提出利用规则约简代替属性约简的规则分层约简算法。一方面,提出基于单个属性下近似的分层规则提取方法,研究与分层规则约简相关的聚类策略实现规则约简,直接获得简化分层规则集。另一方面,在规则约简的基础上,基于聚类约束,实现不同离散化区间的相同编码,形成等价决策表,优化了传统粗糙集数据处理方法的计算性能。
Abstract:Rough set theory is a mathematical tool to deal with uncertaint information. It can abstract the effective knowledge from the original data set by three steps, which calculate a core set, a reduct and a rule set, respectively. However, rough set theory sufferes from some improtant problems when it is used in an inconsistent decision table, such as the inconsistency of core sets, the selection strategy on data analysis processes, NP hard problem on minimal reduct, etc. In this paper, we study the related solutions and proposed a systematic data analysis method of inconsistent decision tables. The main works and contributions are listed as follows:
1, There are many core calculation methods for inconsistent decision tables. However, the results of these methods are always inconsistent. An important problem emerges that how many effective core sets are there in inconsistent decision tables. To resolve it, we propose a method based on partition of knowledge granules to judge the effectiveness of the exisiting core calculation methods, and to calculate all the effective core sets. First, information types of the granules are analyzed based on the classical Pawlak model. Next, partitions of knowledge granules are defined to represent the effective information of inconsistent decision tables. On the basis, it is proved that there are only three type of partition of knowledge granule for any inconsistent decision table. Finnaly, a method based on discernibility matrices corresponding to these three partitions are proposed to calculate all the effective core sets.
2, To select a proper data nalysis process in a practical application, an effective data analysis model and the related selection strategy are proposed based on partitions of knowledge granules. First, three types of rules are defined to match the partitions of knowledge granules. The relationship among the defined rules, the three discernibility matrices and the partitions of knowledge granules is then proved, which is also used to form the rule-based strategy for selecting the proper data analysis process of inconsistent decision tables. On the basis, an intelligible data analysis model for inconsistent decision tables is suggested. It can ensure that the knowledge of core set, reduct and rule set are meaningful to users.
3, To calculate a minimal reduct by using a heuristic reduction algorithm, the attribute repulsion matrix is proposed to optimize the classical heuristic reduction algorithms. First, the character of attribute repulsion related to the minimal reducts is analyzed and an attribute repulsion matrix is presented. Some attribute heuristic strategies are then proposed based on the repulsion matrix. On this basis, by combining some classical addition and deletion methods, two heuristic reduction algorithms using the proposed strategies are suggested. The experimental results on some UCI data sets show that the proposed attribute repulsion matrix can completely improve the quality of reduct and is helpful for a heuristic algorithm to calculate the minimal reduct.
4, An attribute-correlation based heuristic reduction method is proposed to calculate a minimal reduct. First, we define the attraction property between the attributes, and show that the attraction property is related with the repulsion property. Based on the correlation, we define the new attribute significance and propose an attribute-correlation based heuristic reduction algorithm which integrates the discernibility ability of single attributes and the correlations among attributes. It is more effective to obtain a minimal reduct.
5, In order to resolve the problem that the confidences of the existing heuristic strategies can not be estimated, some new strategies with the related confidence models are proposed and integrated into a reduction algorithm. Firstly, based on the repulsion property, we propose a related heuristic strategy and design the confidence model. Next, we define the mutex properties and design the related confidence models. According to the defined confidence degrees, we suggest an integrated strategy with high-confidence, which is used in a new reduction algorithm. The experimental results show that the proposed confidence models are effective and the integrated strategy is high-confidecne to obtain a minimal reduct.
6, In view of the NP-hard problem on the optimal discretization and reduction in rough set theory, the hierarchical reduction of rules is proposed by using the rule reduction to replace the attribute reduction. First, a hierarchical rule sets attraction method is proposed based on the low approximation of the single attribute. Then, we analyze the cluster properties of the hierarchical rule sets, which are used to simplify the rule sets. At the same time, based on the rule reduction and cluster properties, an optimal discretization coding way is proposed to code the different discrete intervals to the same value. On the basis, we define the equivalent decision table to simplify the traditional data analysis process based on rough set theory.
1,针对不一致决策表中核属性集计算方法多且结论不一致所导致的难以判断全部有效核集的问题,提出基于信息粒划分的核属性集有效性判断方法,并计算所有有效的核属性集。首先,基于经典Pawlak模型分析不一致决策表信息粒的信息类型,并定义信息粒划分的概念描述不一致决策表中的有效信息,在此基础上,证实任一不一致决策表仅存在三类有效的信息粒划分。最后,针对三类信息粒划分提出基于可辨识矩阵的核属性集算法有效性判断方法,并计算所有有效的核属性集。
2,针对不一致决策表多种处理流程共存,造成应用中难以正确选择处理流程的问题,基于信息粒划分构建不一致决策表数据处理框架,并提出一种直观的计算流程选择策略。首先,定义与三类信息粒划分对应的规则类型,建立信息粒划分、可辨识矩阵以及规则类型之间的映射关系,在此基础上,提出基于规则类型的不一致决策表数据计算流程选择策略,建立不一致决策表数据处理框架,确保计算结果中的核属性集、约简以及规则集均包含用户感兴趣的知识。
3,针对启发式算法难以获得最小约简的问题,提出属性排斥矩阵,优化传统启发式属性约简算法的性能。首先,研究最小约简约束下属性之间的排斥特征,提出满足最小约简必要条件的属性排斥矩阵,设计对应的最小约简属性启发策略。在此基础上,分别结合典型加法类与减法类启发式约简算法,提出两种基于属性排斥矩阵的启发式属性约简算法。UCI标准数据集测试表明,属性排斥矩阵包含丰富的最小约简启发信息,能全面提高启发式属性约简算法的性能。
4,提出基于属性关联的启发式最小约简计算算法。首先,在属性排斥特征研究的基础上,进一步分析最小约简集属性之间的吸引特征(与属性排斥特征一起统称为属性关联性质),并定义基于属性关联的属性重要度计算指数。在此基础上,提出基于该重要度的启发式属性约简算法。该算法采取兼顾单个属性的辨识能力以及属性之间关联的约简策略,提高最小约简获得概率。
5,针对现有启发策略难以估计启发有效性的问题,提出了可信度高且可信度可以估计的属性启发策略。首先,基于属性排斥特征,提出对应的启发策略,建立其可信度模型；在此基础上,提出属性互斥特征及其对应的启发策略,并建立对应的可信度模型。最后,以可信度为依据,提出综合的可信度高且可信度可以估计的最小约简启发策略,并给出了具体的算法。UCI标准数据集实验测试表明,可信度模型有效且该策略具有较高的最小约简可信度。
6,针对传统粗糙集数据处理过程面临的最优离散化以及属性约简的NP难题,提出利用规则约简代替属性约简的规则分层约简算法。一方面,提出基于单个属性下近似的分层规则提取方法,研究与分层规则约简相关的聚类策略实现规则约简,直接获得简化分层规则集。另一方面,在规则约简的基础上,基于聚类约束,实现不同离散化区间的相同编码,形成等价决策表,优化了传统粗糙集数据处理方法的计算性能。
Abstract:Rough set theory is a mathematical tool to deal with uncertaint information. It can abstract the effective knowledge from the original data set by three steps, which calculate a core set, a reduct and a rule set, respectively. However, rough set theory sufferes from some improtant problems when it is used in an inconsistent decision table, such as the inconsistency of core sets, the selection strategy on data analysis processes, NP hard problem on minimal reduct, etc. In this paper, we study the related solutions and proposed a systematic data analysis method of inconsistent decision tables. The main works and contributions are listed as follows:
1, There are many core calculation methods for inconsistent decision tables. However, the results of these methods are always inconsistent. An important problem emerges that how many effective core sets are there in inconsistent decision tables. To resolve it, we propose a method based on partition of knowledge granules to judge the effectiveness of the exisiting core calculation methods, and to calculate all the effective core sets. First, information types of the granules are analyzed based on the classical Pawlak model. Next, partitions of knowledge granules are defined to represent the effective information of inconsistent decision tables. On the basis, it is proved that there are only three type of partition of knowledge granule for any inconsistent decision table. Finnaly, a method based on discernibility matrices corresponding to these three partitions are proposed to calculate all the effective core sets.
2, To select a proper data nalysis process in a practical application, an effective data analysis model and the related selection strategy are proposed based on partitions of knowledge granules. First, three types of rules are defined to match the partitions of knowledge granules. The relationship among the defined rules, the three discernibility matrices and the partitions of knowledge granules is then proved, which is also used to form the rule-based strategy for selecting the proper data analysis process of inconsistent decision tables. On the basis, an intelligible data analysis model for inconsistent decision tables is suggested. It can ensure that the knowledge of core set, reduct and rule set are meaningful to users.
3, To calculate a minimal reduct by using a heuristic reduction algorithm, the attribute repulsion matrix is proposed to optimize the classical heuristic reduction algorithms. First, the character of attribute repulsion related to the minimal reducts is analyzed and an attribute repulsion matrix is presented. Some attribute heuristic strategies are then proposed based on the repulsion matrix. On this basis, by combining some classical addition and deletion methods, two heuristic reduction algorithms using the proposed strategies are suggested. The experimental results on some UCI data sets show that the proposed attribute repulsion matrix can completely improve the quality of reduct and is helpful for a heuristic algorithm to calculate the minimal reduct.
4, An attribute-correlation based heuristic reduction method is proposed to calculate a minimal reduct. First, we define the attraction property between the attributes, and show that the attraction property is related with the repulsion property. Based on the correlation, we define the new attribute significance and propose an attribute-correlation based heuristic reduction algorithm which integrates the discernibility ability of single attributes and the correlations among attributes. It is more effective to obtain a minimal reduct.
5, In order to resolve the problem that the confidences of the existing heuristic strategies can not be estimated, some new strategies with the related confidence models are proposed and integrated into a reduction algorithm. Firstly, based on the repulsion property, we propose a related heuristic strategy and design the confidence model. Next, we define the mutex properties and design the related confidence models. According to the defined confidence degrees, we suggest an integrated strategy with high-confidence, which is used in a new reduction algorithm. The experimental results show that the proposed confidence models are effective and the integrated strategy is high-confidecne to obtain a minimal reduct.
6, In view of the NP-hard problem on the optimal discretization and reduction in rough set theory, the hierarchical reduction of rules is proposed by using the rule reduction to replace the attribute reduction. First, a hierarchical rule sets attraction method is proposed based on the low approximation of the single attribute. Then, we analyze the cluster properties of the hierarchical rule sets, which are used to simplify the rule sets. At the same time, based on the rule reduction and cluster properties, an optimal discretization coding way is proposed to code the different discrete intervals to the same value. On the basis, we define the equivalent decision table to simplify the traditional data analysis process based on rough set theory.
引文
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