模糊分类新方法及应用
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摘要
模糊集理论是一种重要的处理不精确,不确定信息的智能计算方法.它扩展了过去经典集合论中对精确数字和精确关系的要求,将模糊性和不明确性引入到精确的数据关系中,从而为传统的机器学习算法(例如,粗糙集,神经网络,聚类算法等)研究和处理的更多的信息提供了更加灵活,宽泛的条件.模糊粗糙集(与粗糙集相结合)和模糊神经网络(与神经网络相结合)就是两种颇受关注的基于模糊理论的算法.
粗糙集理论也是一种处理不完备,不完整数据的数学工具.与模糊集理论相比,它更强调数据间的不可分辨性.但是由于定义的原因,使得粗糙集只能处理离散的数据集.通过使用模糊等价关系和模糊逻辑算子代替精确等价关系和经典逻辑算子,模糊粗糙集可以有效的分析离散数据或者连续数据(或是二者的混合数据)之间的关系.在本文中,从算法发展和运算机制的两个角度研究了两种基于模糊粗糙集理论的近邻分类算法：模糊粗糙近邻算法和不确定量化近邻算法.从算法上,文中提出了一种基于核函数的模糊粗糙集,并得到相应的两种基于核函数的模糊粗糙近邻算法.实验给出了该算法在乳癌风险评估方面的表现.与一些常用分类算法相比,基于核函数的模糊近邻算法都得到了更好更稳定的结果.另一方面,从理论上,文中分析了模糊粗糙近邻算法和不明确量化近邻算法的运算机制,指出他们的分类结果分别是由与待分类样本有最大相似度和与待分类样本的最大的相似度和决定.根据这一结论提出了两种分别与模糊粗糙近邻算法和不明确量化近邻算法等价的基于模糊相似关系的近邻算法.进一步的,文中提出了一种高度灵活的通用的基于模糊相似关系的近邻分类结构.并从理论上和实验上都证明了,这种分类结构的两种特例分别与模糊粗糙近邻算法和不明确量化近邻算法在分类结果上等价.
模糊神经网络作为模糊系统和神经网络相结合的一种人工智能系统,主要有两种形式,一种是将模糊理论引入神经网络,实现结构上的模糊化.这样一来神经网络处理信息的范围和能力就得到了拓宽和提高.另一方面,使用神经网络的结构处理模糊信息.利用神经网络的训练方法,模糊规则和模糊化方法可以从结构上和方法上进行自动提取和优化.本文中采用进化极端学习机算法训练零阶TSK模糊推理系统,得到了一种进化模糊极端学习机算法.并同样使用乳癌诊断数据集对算法进行评估.这一算法也取得了比较好的实验结果.另外对一种具有模糊化性质的局部耦合前向神经网络进行了研究.一种改进的梯度学习算法被用来训练这一网络以提高学习效率,同时给出了使用这种改进的梯度学习算法的误差函数的单调性集算法的弱收敛和强收敛性定理.
Fuzzy set theory (FST) plays an important role in dealing with imprecise, and uncertain information. It relaxes the precise number and exact relation constraints of classical set theory, by introducing fuzziness to the relation between the data. Fuzzy sets provide a wider and more flexible framework for dealing with data than traditional machine learning methods (e.g. neural networks, clustering methods, etc). FST is a mature research area, and has also been widely applied in the areas of mechanical control, pattern recognition, and decision support systems. Fuzzy-rough sets (a hybridisation of rough and fuzzy sets) and fuzzy neural networks (a hybridi-sation of neural networks and fuzzy sets) have enjoyed much attention as two fuzzy set theory based approaches.
Rough set theory was also proposed as a mathematical tool for dealing with imperfect and incomplete knowledge. Compared with FST, rough set theory is more concerned with a dif-ferent type of uncertainty:indiscernibility. However,due to its definition, rough sets can only operate effectively with datasets containing discrete values. By employing a fuzzy equivalence relation and fuzzy logical operators instead of a crisp equivalence relation and classical logical operators,respectively, fuzzy-rough sets provide a means by which the relationship between dis-crete data or real-valued data (or a mixture of both) can be effectively analysed. In this thesis, fuzzy-rough nearest-neighbour classification algorithms are studied from both methodological and theoretical perspectives. From theoretical development, a kernel-based fuzzy-rough set tech-nique and associated nearest-neighbour algorithms are proposed. Real-world medical datasets for the task of mammographic risk assessment are employed in order to evaluate such classi-fication approaches. The experimental results demonstrate that such kernel-based fuzzy-rough nearest-neighbour approaches offer improved and more robust performances over other classi-fiers. Theoretically, the underlying mechanism of fuzzy-rough nearest-neighbour (FRNN) and vaguely quantified nearest-neighbour (VQNN) algorithms are explored. The research shows that the resulting classification of FRNN and VQNN depends only upon the highest similarity and greatest summation of the similarities of each class, respectively. This fact is exploited in or-der to formulate two novel fuzzy similarity-based parallel methods. Furthermore, a generalised fuzzy similarity-based nearest-neighbour framework is presented. The theoretical proof and em-pirical evaluation demonstrate that FRNN and VQNN can be considered as the special cases of the proposed new framework.
As the combination of fuzzy systems with neural networks, fuzzy neural networks have two main categories:1) The fuzzified structure of neural networks are implemented via introducing the fuzzy sets to neural networks. In so doing, the range and the ability of processing information for neural networks can be widened and improved.2) The fuzzy information is handled under the framework of neural networks. By using the training algorithms for neural networks, the fuzzy rules and the fuzzification approaches can be automatically extracted and optimised from both constructive and methodological perspectives. In this thesis, the hybridisation of the zero-order TSK fuzzy system with the evolutionary extreme learning machine approach leads an evolutionary fuzzy extreme learning machine. This technique is also applied to the task of mammographic risk analysis. The experimental results demonstrate that the evolutionary fuzzy extreme learning machine offers improved classification accuracy, both at the overall image level and at the level of individual risk types. Also, a local coupled feed-forward neural network is also used as the property for fuzzification for this work. In order to enhance the lcarning efficiency, a modified gradient-based learning method is employed to train such neural networks. The monotonicity of the error functions and the weak and strong convergence results for this algorithm are also proven.
粗糙集理论也是一种处理不完备,不完整数据的数学工具.与模糊集理论相比,它更强调数据间的不可分辨性.但是由于定义的原因,使得粗糙集只能处理离散的数据集.通过使用模糊等价关系和模糊逻辑算子代替精确等价关系和经典逻辑算子,模糊粗糙集可以有效的分析离散数据或者连续数据(或是二者的混合数据)之间的关系.在本文中,从算法发展和运算机制的两个角度研究了两种基于模糊粗糙集理论的近邻分类算法：模糊粗糙近邻算法和不确定量化近邻算法.从算法上,文中提出了一种基于核函数的模糊粗糙集,并得到相应的两种基于核函数的模糊粗糙近邻算法.实验给出了该算法在乳癌风险评估方面的表现.与一些常用分类算法相比,基于核函数的模糊近邻算法都得到了更好更稳定的结果.另一方面,从理论上,文中分析了模糊粗糙近邻算法和不明确量化近邻算法的运算机制,指出他们的分类结果分别是由与待分类样本有最大相似度和与待分类样本的最大的相似度和决定.根据这一结论提出了两种分别与模糊粗糙近邻算法和不明确量化近邻算法等价的基于模糊相似关系的近邻算法.进一步的,文中提出了一种高度灵活的通用的基于模糊相似关系的近邻分类结构.并从理论上和实验上都证明了,这种分类结构的两种特例分别与模糊粗糙近邻算法和不明确量化近邻算法在分类结果上等价.
模糊神经网络作为模糊系统和神经网络相结合的一种人工智能系统,主要有两种形式,一种是将模糊理论引入神经网络,实现结构上的模糊化.这样一来神经网络处理信息的范围和能力就得到了拓宽和提高.另一方面,使用神经网络的结构处理模糊信息.利用神经网络的训练方法,模糊规则和模糊化方法可以从结构上和方法上进行自动提取和优化.本文中采用进化极端学习机算法训练零阶TSK模糊推理系统,得到了一种进化模糊极端学习机算法.并同样使用乳癌诊断数据集对算法进行评估.这一算法也取得了比较好的实验结果.另外对一种具有模糊化性质的局部耦合前向神经网络进行了研究.一种改进的梯度学习算法被用来训练这一网络以提高学习效率,同时给出了使用这种改进的梯度学习算法的误差函数的单调性集算法的弱收敛和强收敛性定理.
Fuzzy set theory (FST) plays an important role in dealing with imprecise, and uncertain information. It relaxes the precise number and exact relation constraints of classical set theory, by introducing fuzziness to the relation between the data. Fuzzy sets provide a wider and more flexible framework for dealing with data than traditional machine learning methods (e.g. neural networks, clustering methods, etc). FST is a mature research area, and has also been widely applied in the areas of mechanical control, pattern recognition, and decision support systems. Fuzzy-rough sets (a hybridisation of rough and fuzzy sets) and fuzzy neural networks (a hybridi-sation of neural networks and fuzzy sets) have enjoyed much attention as two fuzzy set theory based approaches.
Rough set theory was also proposed as a mathematical tool for dealing with imperfect and incomplete knowledge. Compared with FST, rough set theory is more concerned with a dif-ferent type of uncertainty:indiscernibility. However,due to its definition, rough sets can only operate effectively with datasets containing discrete values. By employing a fuzzy equivalence relation and fuzzy logical operators instead of a crisp equivalence relation and classical logical operators,respectively, fuzzy-rough sets provide a means by which the relationship between dis-crete data or real-valued data (or a mixture of both) can be effectively analysed. In this thesis, fuzzy-rough nearest-neighbour classification algorithms are studied from both methodological and theoretical perspectives. From theoretical development, a kernel-based fuzzy-rough set tech-nique and associated nearest-neighbour algorithms are proposed. Real-world medical datasets for the task of mammographic risk assessment are employed in order to evaluate such classi-fication approaches. The experimental results demonstrate that such kernel-based fuzzy-rough nearest-neighbour approaches offer improved and more robust performances over other classi-fiers. Theoretically, the underlying mechanism of fuzzy-rough nearest-neighbour (FRNN) and vaguely quantified nearest-neighbour (VQNN) algorithms are explored. The research shows that the resulting classification of FRNN and VQNN depends only upon the highest similarity and greatest summation of the similarities of each class, respectively. This fact is exploited in or-der to formulate two novel fuzzy similarity-based parallel methods. Furthermore, a generalised fuzzy similarity-based nearest-neighbour framework is presented. The theoretical proof and em-pirical evaluation demonstrate that FRNN and VQNN can be considered as the special cases of the proposed new framework.
As the combination of fuzzy systems with neural networks, fuzzy neural networks have two main categories:1) The fuzzified structure of neural networks are implemented via introducing the fuzzy sets to neural networks. In so doing, the range and the ability of processing information for neural networks can be widened and improved.2) The fuzzy information is handled under the framework of neural networks. By using the training algorithms for neural networks, the fuzzy rules and the fuzzification approaches can be automatically extracted and optimised from both constructive and methodological perspectives. In this thesis, the hybridisation of the zero-order TSK fuzzy system with the evolutionary extreme learning machine approach leads an evolutionary fuzzy extreme learning machine. This technique is also applied to the task of mammographic risk analysis. The experimental results demonstrate that the evolutionary fuzzy extreme learning machine offers improved classification accuracy, both at the overall image level and at the level of individual risk types. Also, a local coupled feed-forward neural network is also used as the property for fuzzification for this work. In order to enhance the lcarning efficiency, a modified gradient-based learning method is employed to train such neural networks. The monotonicity of the error functions and the weak and strong convergence results for this algorithm are also proven.
引文
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[2]ZADEH L A. Fuzzy sets[J]. Information and Control,1965,8:338-353.
[3]DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General Systems, 1990,17(2-3):191-209.
[4]DAs M, CHAKRABORTY M K, GHOSHAL T K. Fuzzy tolerance relation, fuzzy tolerance space and basis[J]. Fuzzy Sets and Systems,1998,97:361-369.
[5]YAO Y Y. A comparative study of fuzzy sets and rough sets[J]. Information Sciences,1998,109(l-4):227-242.
[6]YEUNG D S, CHEN D, TSANG E C C, et al. On the generalization of fuzzy rough sets[J]. IEEE Transactions on Fuzzy Systems,2005,13(3):343-361.
[7]BELIAKOV G, PRADERA A, CALVO T. Aggregation Functions:A Guide for Practitioners[M]. Berlin: Springer,2007.
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