粗糙集属性协同演化约简关键问题研究
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摘要
粗糙集理论具有能有效定量分析并处理不精确、不一致、不完整信息与知识等特征，已被广泛应用于数据挖掘、模式识别和机器学习等领域。属性约简是粗糙集理论研究的重要内容，其是指在保持决策表中数据分类能力不变的条件下，删除不相关和冗余属性，选择最小属性集，使决策表中知识表示可简化而又不丢失决策表中重要信息。Wong等人已证明找出决策表的最小属性约简是一个典型NP-Hard问题，许多学者对此开展了相关研究，并取得了一定的研究成果，然而至今仍未找到一种通用且高效的解决方法为其求解提供有效途径。
近年来，协同演化算法通过揭示和模拟自然界生态系统中多种群协同进化现象和过程而成为计算智能领域研究热点，它能有效解决许多传统演化算法难以解决的复杂问题，尤其是在NP-Hard问题上凸显其较强优势。本文将协同演化算法引入到粗糙集最小属性约简优化中，对属性协同演化约简中算法收敛性、协同机制、模型优化、演化自适应性、大规模属性约简及其代表性个体选择等关键问题进行了深入系统地研究，致力于完善粗糙集属性演化约简理论方面的工作，构建协同演化框架下属性约简模型和系列算法，并且在属性约简与特征分类、核磁共振成像MRI约简与分割等实际应用问题中展示本文所提相关算法的有效性。具体而言，本文的主要贡献在于：
1.针对传统属性演化约简易早熟收敛和进化种群邻域选择问题，将小生境进化技术引入到粗糙集属性演化约简中，提出了基于小生境圆锥邻域粒子群的属性协同演化约简算法。该算法将具有社会认知行为的粒子种群映射至属性近似空间，进化粒子在属性约简寻优过程中通过圆锥分层空间自主动态构造小生境邻域半径，并利用自适应强化约束罚函数提高粒子种群目标适应度的收敛能力。实验结果表明该算法能充分发挥进化种群在各自小生境邻域内属性协同演化约简作用，较好地避免了属性演化约简早熟收敛，对属性约简性能具有明显的提高。
2.为提高进化种群在粗糙集属性演化约简中的协同优化能力，将协同演化机制进行拓展，构造了基于自适应进化树的属性混合协同演化约简算法。该算法建立了一种基于自适应多层进化树的动态种群协同模型，采用竞争和合作混合的协同演化机制实现各属性子集向量约简寻优经验的协同共享，较好地达到属性演化约简中广度寻优和深度探索的有效平衡。实验结果表明该基于自适应进化树模型的竞争和合作混合协同机制在属性演化约简中的有效性。
3.将量子协同演化引入到粗糙集属性约简模型优化中，提出了基于量子蛙群进化的属性协同演化高效约简算法。该算法用量子态比特进行动态多簇结构蛙群个体编码，提高参与属性演化约简进化个体的多样性；以量子旋转门动态自适应调整机制驱动属性演化约简的搜索过程，在全局搜索和局部求精之间保持属性协同约简均衡；以量子变异和量子纠缠策略避免属性演化约简陷入局部极值，快速向全局最优收敛。该算法并重构了属性量子协同演化约简目标适应度函数，取得了较为满意的最小属性约简集。在此基础上，又提出了一种基于动态交叉协同的量子蛙群属性协同演化约简与分类学习级联算法，进一步提高其在属性约简与决策规则分类学习中的应用性能。实验结果表明该属性量子协同演化约简算法具有极强的全局最小属性约简搜索性能，其属性约简效率和精度较一般算法具有明显提升。
4.为进一步增强新型框架下属性量子协同演化约简的自适应性，基于云模型在非规范知识定性、定量表示及其相互转换过程中优良特征，提出了基于量子云模型的属性协同演化自适应约简算法。该算法利用量子种群基因云对参与属性约简的量子蛙群进行定性控制；基于约简属性熵权逆向云进行量子云旋转门的自适应调整，使其在定性知识指导下能自适应控制属性约简空间的搜索范围；采用量子云变异和云纠缠操作算子使量子蛙群自适应搜索到全局最优属性约简集。该算法利用云模型使属性量子协同演化约简具有更优的自适应性，能较好地处理模糊的和不完整的属性约简问题。
5.为扩大粗糙集属性协同演化约简在大规模实际优化问题中的应用及解决其代表性精英个体选择问题，基于群体协作模式框架下精英角色思想，提出了基于量子种群精英的大规模属性协同演化集成约简算法。该算法首先设计一种量子蛙群多层精英池结构，利用量子精英蛙快速引导整个蛙群进入最优化区域寻优；然后构建大规模属性自适应合作型协同演化约简模型，融合量子种群最优执行经验和分配信任度将大规模属性集分割为自适应规模的属性子集；最后以各蛙群模因组内量子精英蛙优化各自选择的属性子集，有效增强量子种群精英在大规模属性演化约简中的协同求解性能。理论分析和实验结果证明了该算法的可行性和有效性，该算法在核磁共振成像MRI约简和分割中的应用进一步表明其具有较强的适用性。
Rough set theory (RST) was introduced by Professor Pawlak in1982to analyze and deal withsome information and knowledge with imprecision, inconsistency and incompletion. In recent years,it has been widely applied in diversified research areas, such as data mining, pattern recognition,machine learning, and so on. Attribute reduction is one of the most important topics of RST, and it hasbeen recognized as an important feature selection method. Attribute reduction studies how to removeirrelevant and redundant features with minimal information loss, and to select the attribute subsetfrom original attributes in the decision table while retaining the suitably high classificationperformance in representing the original attributes. Finding the minimum reduction set is moredifficult and it has been proven to be a representative NP-hard problem by Wong et al, and manyresearchers have made efforts on the algorithms of attribute reduction and achieved some betterresults. However, there has been no universal and efficient solution for this purpose.
In recent years, the co-evolutionary algorithm has been a growing interest in the field ofcomputational intelligence by revealing and simulating the co-evolutionary phenomenon and process ofmulti-populations in the natural ecosystem. So far it has been proven to be effective in solving manycomplex problems of which are difficult by using the traditional evolutionary algorithms, especially forsome NP-Hard problems. In this thesis, the co-evolutionary algorithm is introduced into theoptimization problem of minimum attribute reduction in RST. Some key problems for attributeco-evolutionary reduction such as convergence, cooperation mechanism, model optimization,evolutionary adaptability, large-scale attribute reduction and its representative individual selection arethoroughly investigated, so that theoretical work of attribute reduction in RST is perfected. A series ofmodels and algorithms about attribute reduction are developed under the co-evolutionary frameworkand applied into some practical applications, such as attribute reduction and feature classification,magnetic resonance images (MRI) reduction and segmentation, and so on. Some experimental resultsdemonstrate the effectiveness of proposed algorithms. In this thesis, some key problems on attributeco-evolutionary reduction in RST are systematically and deeply researched, in which the traditionalalgorithms are improved, and some new models and algorithms are put forward. The related researchresults significantly enhanced the performance of attribute co-evolutionary reduction.
More concretely, the main contributions of this thesis include:
1. For the problems on traditional attribute evolutionary reduction in the premature convergenceand population neighborhood selection, the niche technology is introduced into the attributeevolutionary reduction, and a niche conic neighborhood particle swarm optimization based attribute co-evolutionary reduction algorithm is proposed. Particle swarm with social cognition behavior ismapped into the attribute approximate space for iterative optimization. It can self-adaptively constructthe niche vector of neighborhood by the layered conic space. And the adaptive penalty function isused to strengthen the convergence ability of population fitness, so that the premature convergencecan be avoided well and the minimum attribute reduction set is obtained quickly. Experimental resultsdemonstrated that performance of proposed algorithm is improved much better, by playing the effectof populations’ co-evolutionary reduction within their respective niche neighborhoods as to avoid thepremature convergence.
2. In order to improve the co-evolutionary performance for attribute reduction in RST, a noveland efficient self-adaptive evolutionary tree based attribute mixed co-evolutionary reductionalgorithm is put forward by expanding the essence of co-evolutionary mechanism. It constructs a kindof the dynamic population model with the self-adaptive multilevel evolutionary tree. The mixedco-evolutionary mechanism of competitive and cooperative co-evolution is adopted to select therespective excellent individual in each evolutionary sub-tree, and to carry on their attribute subsetvector to share the co-evolutionary searching experience. The proposed algorithm can better balancebetween exploitation in breadth and exploration in depth. Some experiments are presented to show theeffectiveness of the mixed co-evolutionary mechanism with competitive and cooperativeco-evolution.
3. The quantum-inspired co-evolutionary algorithm is firstly introduced into the research for themodel optimization of attribute reduction in RST, therefore an efficient quantum frog based attributeco-evolutionary reduction algorithm is proposed. In this algorithm, individuals with dynamicmulti-cluster frog structure are represented by multi-state quantum bits, in order to increase thediversity of evolutionary individuals. The self-adaptive adjustment of quantum rotation gate speedsthe search process so that it can keep balance between global search and local refinement during theattribute co-evolutionary reduction. The strategies of quantum mutation and quantum entanglementare applied to accelerate the evolution convergence. The algorithm reconstructs the fitness function ofattribute reduction optimization based on quantum co-evolution, in order to obtain more satisfyingminimum attribute reduction set. And on such basis, the attribute co-evolutionary reduction andclassification learning cascade algorithm based on the quantum frog with adaptive crossovercooperation is proposed so as to further improve the performance of attribute reduction andclassification learning for decision rules. Experimental results indicate it has extremely strong globaloptimization of attribute co-evolutionary reduction and has achieved better high-performance onefficiency and accuracy than traditional algorithms. From the perspective of quantum co-evolution,attribute quantum co-evolutionary reduction algorithm is designed, which will provide a better idea for new framework of attribute evolutionary reduction.
4. In order to further improve the adaptability of attribute quantum co-evolutionary reduction, aquantum cloud model based attribute self-adaptive co-evolution reduction algorithm is presented,according to outstanding characteristics of the cloud model on the process of transforming aqualitative concept to a set of quantitative numerical values. First, quantum population gene cloud isused to encode the evolutionary frog population, and reversible cloud mode based on attribute entropyweight is designed to adjust the quantum revolving gate adaptively, so the scope of search space canbe adaptively controlled under the guidance of qualitative knowledge. Second, both the quantumcloud mutation and quantum cloud entanglement operators are used to make quantum frog populationbe adaptive to get the optimization attribute reduction sets fast. By using of cloud model, the proposedalgorithm can make attribute quantum co-evolutionary reduction with stronger adaptability and canbetter deal with the vague and incomplete attribute reduction.
5. Aiming at the optimization problem of application in large-scale attribute reduction and itsrepresentative elitist individual selection, a novel quantum elitist frog based large-scale attributeco-evolutionary ensemble reduction algorithm is proposed by enlightening the elite role attitude underthe collective collaboration model. First, the algorithm designs the multilevel elitist pool of quantumfrogs, in which quantum elitist frogs can fast guide the evolutionary population into the optimal area.Second, a self-adaptive cooperative co-evolutionary model is constructed to decompose thelarge-scale attribute set into reasonable-scale attribute subsets according to the best historicalperformance experience records and assignment credits. Third, some optimal elitists in differentmemeplexs are selected out to evolve their representing attribute subsets, which can increase thecooperation and efficiency of large-scale attribute reduction. Therefore the global minimum attributereduction set can be gained steadily and efficiently. Theoretical analysis and experimental results arepresented to show the feasibility and effectiveness of the proposed algorithm. Finally this proposedalgorithm is applied into magnetic resonance images (MRI) reduction and segmentation, and theeffective and robust segmentation results further demonstrate it has stronger applicability.
近年来，协同演化算法通过揭示和模拟自然界生态系统中多种群协同进化现象和过程而成为计算智能领域研究热点，它能有效解决许多传统演化算法难以解决的复杂问题，尤其是在NP-Hard问题上凸显其较强优势。本文将协同演化算法引入到粗糙集最小属性约简优化中，对属性协同演化约简中算法收敛性、协同机制、模型优化、演化自适应性、大规模属性约简及其代表性个体选择等关键问题进行了深入系统地研究，致力于完善粗糙集属性演化约简理论方面的工作，构建协同演化框架下属性约简模型和系列算法，并且在属性约简与特征分类、核磁共振成像MRI约简与分割等实际应用问题中展示本文所提相关算法的有效性。具体而言，本文的主要贡献在于：
1.针对传统属性演化约简易早熟收敛和进化种群邻域选择问题，将小生境进化技术引入到粗糙集属性演化约简中，提出了基于小生境圆锥邻域粒子群的属性协同演化约简算法。该算法将具有社会认知行为的粒子种群映射至属性近似空间，进化粒子在属性约简寻优过程中通过圆锥分层空间自主动态构造小生境邻域半径，并利用自适应强化约束罚函数提高粒子种群目标适应度的收敛能力。实验结果表明该算法能充分发挥进化种群在各自小生境邻域内属性协同演化约简作用，较好地避免了属性演化约简早熟收敛，对属性约简性能具有明显的提高。
2.为提高进化种群在粗糙集属性演化约简中的协同优化能力，将协同演化机制进行拓展，构造了基于自适应进化树的属性混合协同演化约简算法。该算法建立了一种基于自适应多层进化树的动态种群协同模型，采用竞争和合作混合的协同演化机制实现各属性子集向量约简寻优经验的协同共享，较好地达到属性演化约简中广度寻优和深度探索的有效平衡。实验结果表明该基于自适应进化树模型的竞争和合作混合协同机制在属性演化约简中的有效性。
3.将量子协同演化引入到粗糙集属性约简模型优化中，提出了基于量子蛙群进化的属性协同演化高效约简算法。该算法用量子态比特进行动态多簇结构蛙群个体编码，提高参与属性演化约简进化个体的多样性；以量子旋转门动态自适应调整机制驱动属性演化约简的搜索过程，在全局搜索和局部求精之间保持属性协同约简均衡；以量子变异和量子纠缠策略避免属性演化约简陷入局部极值，快速向全局最优收敛。该算法并重构了属性量子协同演化约简目标适应度函数，取得了较为满意的最小属性约简集。在此基础上，又提出了一种基于动态交叉协同的量子蛙群属性协同演化约简与分类学习级联算法，进一步提高其在属性约简与决策规则分类学习中的应用性能。实验结果表明该属性量子协同演化约简算法具有极强的全局最小属性约简搜索性能，其属性约简效率和精度较一般算法具有明显提升。
4.为进一步增强新型框架下属性量子协同演化约简的自适应性，基于云模型在非规范知识定性、定量表示及其相互转换过程中优良特征，提出了基于量子云模型的属性协同演化自适应约简算法。该算法利用量子种群基因云对参与属性约简的量子蛙群进行定性控制；基于约简属性熵权逆向云进行量子云旋转门的自适应调整，使其在定性知识指导下能自适应控制属性约简空间的搜索范围；采用量子云变异和云纠缠操作算子使量子蛙群自适应搜索到全局最优属性约简集。该算法利用云模型使属性量子协同演化约简具有更优的自适应性，能较好地处理模糊的和不完整的属性约简问题。
5.为扩大粗糙集属性协同演化约简在大规模实际优化问题中的应用及解决其代表性精英个体选择问题，基于群体协作模式框架下精英角色思想，提出了基于量子种群精英的大规模属性协同演化集成约简算法。该算法首先设计一种量子蛙群多层精英池结构，利用量子精英蛙快速引导整个蛙群进入最优化区域寻优；然后构建大规模属性自适应合作型协同演化约简模型，融合量子种群最优执行经验和分配信任度将大规模属性集分割为自适应规模的属性子集；最后以各蛙群模因组内量子精英蛙优化各自选择的属性子集，有效增强量子种群精英在大规模属性演化约简中的协同求解性能。理论分析和实验结果证明了该算法的可行性和有效性，该算法在核磁共振成像MRI约简和分割中的应用进一步表明其具有较强的适用性。
Rough set theory (RST) was introduced by Professor Pawlak in1982to analyze and deal withsome information and knowledge with imprecision, inconsistency and incompletion. In recent years,it has been widely applied in diversified research areas, such as data mining, pattern recognition,machine learning, and so on. Attribute reduction is one of the most important topics of RST, and it hasbeen recognized as an important feature selection method. Attribute reduction studies how to removeirrelevant and redundant features with minimal information loss, and to select the attribute subsetfrom original attributes in the decision table while retaining the suitably high classificationperformance in representing the original attributes. Finding the minimum reduction set is moredifficult and it has been proven to be a representative NP-hard problem by Wong et al, and manyresearchers have made efforts on the algorithms of attribute reduction and achieved some betterresults. However, there has been no universal and efficient solution for this purpose.
In recent years, the co-evolutionary algorithm has been a growing interest in the field ofcomputational intelligence by revealing and simulating the co-evolutionary phenomenon and process ofmulti-populations in the natural ecosystem. So far it has been proven to be effective in solving manycomplex problems of which are difficult by using the traditional evolutionary algorithms, especially forsome NP-Hard problems. In this thesis, the co-evolutionary algorithm is introduced into theoptimization problem of minimum attribute reduction in RST. Some key problems for attributeco-evolutionary reduction such as convergence, cooperation mechanism, model optimization,evolutionary adaptability, large-scale attribute reduction and its representative individual selection arethoroughly investigated, so that theoretical work of attribute reduction in RST is perfected. A series ofmodels and algorithms about attribute reduction are developed under the co-evolutionary frameworkand applied into some practical applications, such as attribute reduction and feature classification,magnetic resonance images (MRI) reduction and segmentation, and so on. Some experimental resultsdemonstrate the effectiveness of proposed algorithms. In this thesis, some key problems on attributeco-evolutionary reduction in RST are systematically and deeply researched, in which the traditionalalgorithms are improved, and some new models and algorithms are put forward. The related researchresults significantly enhanced the performance of attribute co-evolutionary reduction.
More concretely, the main contributions of this thesis include:
1. For the problems on traditional attribute evolutionary reduction in the premature convergenceand population neighborhood selection, the niche technology is introduced into the attributeevolutionary reduction, and a niche conic neighborhood particle swarm optimization based attribute co-evolutionary reduction algorithm is proposed. Particle swarm with social cognition behavior ismapped into the attribute approximate space for iterative optimization. It can self-adaptively constructthe niche vector of neighborhood by the layered conic space. And the adaptive penalty function isused to strengthen the convergence ability of population fitness, so that the premature convergencecan be avoided well and the minimum attribute reduction set is obtained quickly. Experimental resultsdemonstrated that performance of proposed algorithm is improved much better, by playing the effectof populations’ co-evolutionary reduction within their respective niche neighborhoods as to avoid thepremature convergence.
2. In order to improve the co-evolutionary performance for attribute reduction in RST, a noveland efficient self-adaptive evolutionary tree based attribute mixed co-evolutionary reductionalgorithm is put forward by expanding the essence of co-evolutionary mechanism. It constructs a kindof the dynamic population model with the self-adaptive multilevel evolutionary tree. The mixedco-evolutionary mechanism of competitive and cooperative co-evolution is adopted to select therespective excellent individual in each evolutionary sub-tree, and to carry on their attribute subsetvector to share the co-evolutionary searching experience. The proposed algorithm can better balancebetween exploitation in breadth and exploration in depth. Some experiments are presented to show theeffectiveness of the mixed co-evolutionary mechanism with competitive and cooperativeco-evolution.
3. The quantum-inspired co-evolutionary algorithm is firstly introduced into the research for themodel optimization of attribute reduction in RST, therefore an efficient quantum frog based attributeco-evolutionary reduction algorithm is proposed. In this algorithm, individuals with dynamicmulti-cluster frog structure are represented by multi-state quantum bits, in order to increase thediversity of evolutionary individuals. The self-adaptive adjustment of quantum rotation gate speedsthe search process so that it can keep balance between global search and local refinement during theattribute co-evolutionary reduction. The strategies of quantum mutation and quantum entanglementare applied to accelerate the evolution convergence. The algorithm reconstructs the fitness function ofattribute reduction optimization based on quantum co-evolution, in order to obtain more satisfyingminimum attribute reduction set. And on such basis, the attribute co-evolutionary reduction andclassification learning cascade algorithm based on the quantum frog with adaptive crossovercooperation is proposed so as to further improve the performance of attribute reduction andclassification learning for decision rules. Experimental results indicate it has extremely strong globaloptimization of attribute co-evolutionary reduction and has achieved better high-performance onefficiency and accuracy than traditional algorithms. From the perspective of quantum co-evolution,attribute quantum co-evolutionary reduction algorithm is designed, which will provide a better idea for new framework of attribute evolutionary reduction.
4. In order to further improve the adaptability of attribute quantum co-evolutionary reduction, aquantum cloud model based attribute self-adaptive co-evolution reduction algorithm is presented,according to outstanding characteristics of the cloud model on the process of transforming aqualitative concept to a set of quantitative numerical values. First, quantum population gene cloud isused to encode the evolutionary frog population, and reversible cloud mode based on attribute entropyweight is designed to adjust the quantum revolving gate adaptively, so the scope of search space canbe adaptively controlled under the guidance of qualitative knowledge. Second, both the quantumcloud mutation and quantum cloud entanglement operators are used to make quantum frog populationbe adaptive to get the optimization attribute reduction sets fast. By using of cloud model, the proposedalgorithm can make attribute quantum co-evolutionary reduction with stronger adaptability and canbetter deal with the vague and incomplete attribute reduction.
5. Aiming at the optimization problem of application in large-scale attribute reduction and itsrepresentative elitist individual selection, a novel quantum elitist frog based large-scale attributeco-evolutionary ensemble reduction algorithm is proposed by enlightening the elite role attitude underthe collective collaboration model. First, the algorithm designs the multilevel elitist pool of quantumfrogs, in which quantum elitist frogs can fast guide the evolutionary population into the optimal area.Second, a self-adaptive cooperative co-evolutionary model is constructed to decompose thelarge-scale attribute set into reasonable-scale attribute subsets according to the best historicalperformance experience records and assignment credits. Third, some optimal elitists in differentmemeplexs are selected out to evolve their representing attribute subsets, which can increase thecooperation and efficiency of large-scale attribute reduction. Therefore the global minimum attributereduction set can be gained steadily and efficiently. Theoretical analysis and experimental results arepresented to show the feasibility and effectiveness of the proposed algorithm. Finally this proposedalgorithm is applied into magnetic resonance images (MRI) reduction and segmentation, and theeffective and robust segmentation results further demonstrate it has stronger applicability.
引文
[1]陆汝钤.知识科学与计算科学.北京:清华大学出版社,2003.
[2] T. J. Jech. Set theory. Springer Verlag,2003.
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