混合数据知识发现的粗糙计算模型和算法
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摘要
机器学习和知识发现是人工智能最重要的研究方向,而复杂环境下信息的不确定性和不一致性是知识发现面临的主要困难。粗糙集理论模拟了人类认知推理中粒化和近似的特点,是刻画分类数据的不一致性程度的有效数学工具,已经成功应用于符号数据知识发现,但是还没有系统研究广泛存在的符号、数值和模糊变量共存的复杂分类问题。本文提出在人类的思维中存在6种决策的一致性假设。基于粗糙计算方法论中粒化和近似的思想,本文分别建立了这些一致性假设的数学模型,并给出了一般形式。具体从以下几个方面进行了探索:
第一,提出了度量空间多粒度分类学习的邻域粗糙计算模型和算法。度量空间中点的δ邻域形成了论域的一种粒化结构,基于邻域粒化建立了度量空间的邻域粗糙集模型,形成了度量空间分类分类一致性的粗糙计算模型。邻域的大小可视为分析分类的粒度,改变邻域的大小可形成混合数据分类一致性的多粒度分析工具。基于邻域粗糙集模型设计了边界样本选择算法和混合数据属性约简算法。
第二,提出了混合数据分类分析的核模糊粗糙计算模型和算法。当前模糊粗糙集的研究主要集中于模糊近似算子的构造,忽略了对模糊粒化结构的分析。研究发现一大类核函数计算的核矩阵都满足模糊等价关系的性质,从而可引入这些核函数为模糊粗糙计算建立模糊粒化结构。本文提出了基于核函数粒化的核模糊粗糙集模型,建立了分类模糊一致性分析的数学模型。设计了基于核近似的混合属性重要度评价指标,探讨了模糊依赖度函数和特征评价算法ReliefF之间的关联,提出了抗噪声的属性约简算法和大样本集的样本加权重采样方法。
第三,提出了混合数据描述的有序决策问题的模糊偏好粗糙分析模型。有序分类学习是一大类分类学习任务,在多标准决策分析中具有重要的地位。本文引入多标准决策分析中广泛使用的模糊偏好关系,并将其与广义的模糊粗糙集模型结合起来,从而建立了混合数据排序一致性分析的模糊粗糙计算模型。
第四,给出了一系列粗糙计算模型的一般形式,统一了Pawlak粗糙集、邻域粗糙集、核粒化粗糙集和模糊偏好粗糙集,从而建立了粗糙数据分析的统一视角。并且基于一般模型,提出了各种近似空间的不确定性的统一度量模型。分析表明多种近似空间的不确定性程度都可以采用这一信息函数进行刻画。由此,本文给出了混合数据描述的一般分类问题和有序决策问题的一般信息度量理论。
第五,本文分析了各种粗糙集属性评价指标的参数和样本稳定性。研究表明,信息熵和模糊信息熵是非常稳定的属性评价指标,少量样本的扰动不会对属性约简产生影响,而邻域依赖度和邻域一致性是不稳定的评价函数,评价结果易受样本扰动影响。
第六,设计了混合数据约简的算法平台,测试了各种算法在真实分类中的性能,并提出采用选择性集成方法利用多个约简的互补信息。某些决策系统可以得到一组约简,每个约简都保持了原始数据分类的一致性,提供了分类数据的一种理解视角。基于选择性多分类器集成的研究成果,本文提出有选择地集成部分约简训练的分类器构造多分类器系统,并且设计了前向贪心选择和后剪枝的分类器选择策略,试验表明该方法能够获得相对紧凑并且分类能力很强的多分类器系统。
本文的研究建立了符号和数值数据共存的混合决策系统的粗糙计算模型。基于邻域粗糙集模型和核粒化的模糊粗糙集模型,本文建立了混合数据一般分类问题的统一计算模型。接下来又基于模糊偏好粗糙模型建立了混合数据有序分类问题的粗糙计算模型。最后,本文基于广义的粗糙模型统一了一般分类问题和有序分类问题的粗糙计算模型,并为各种粗糙计算模型提出了统一的信息度量理论,从而形成了一大类决策问题的粗糙计算理论。
Machine learning and knowledge discovery is one of the most important issues to be addressed in artificial intelligence. And uncertainty and inconsistency are the key problems in knowledge discovery from complex data. Rough set theory, which simulates the capability of granulation and approximation in human cognition, has proven to be an effective mathematical tool to characterize incosistency in classification data. This theory has been applied in knowledge discovery from symbolic data. However, most of data sets in real-world applications are numerical, fuzzy or their mixture. Not much work has been devoted to discussing knowledge discovery from heterogeneous data with rough sets so far. It is proposed that there are six types of consistency in human’s reasoning in this work. The mathematical models of these types consistency are built based on granulation and approximation in rough sets. Moreover, uniform model and algorithm are developed for knowledge discovery from heterogeneous data are developed. The main contributions of the work are listed as follows.
First, Neighborhood rough set model and algorithms in general metric spaces are constructed. The objects described with numerical attributes can be considered as points in metric spaces. The neighborhoods of these points form a structure of granulation of the universe. Based on neighborhood granulation, a rough set model is developed for classification analysis in metric spaces. Neighborhood rough sets construct a framework for analyzing consistency of classification with numerical or symbolic features. If the size of neighborhood is looked as the granularity in data analysis, a multi-granularity data analysis tool is developed by varying the size of neighborhood. Algorithms for sample and feature reduction are constructed based on the neighborhood model.
Second, a kernelized fuzzy rough model is developed for rough computation with heterogeneous data. The current researches on fuzzy rough sets are focused on construction of fuzzy rough approximation operators. Howerver little attention is paid to fuzzy granulation. It is found that a class of kernel functions can be used to compute the fuzzy T-equivalence relations between samples. Then these kernel functions can be used to build fuzzy granular structures for fuzzy rough sets. Based on this observation, a kernelized fuzzy rough set model is proposed for analyzing consistency in the fuzzy case. The connections between fuzzy dependency and ReliefF are shown. We introduce the idea in ReliefF to reduce the influence of noise in fuzzy rough sets based attribute reduction and we construct a generalized classification certainty measure.
Third, a rough set model for fuzzy preference analysis is developed. Ordered classification is one class of learning tasks in decision modeling and multi-criterion analysis. Fuzzy preference relations, which are widely in multi-criterion analysis, are introduced and combined with general fuzzy rough set model, thus a fuzzy preference rough set model is proposed and algorithms for dependency analysis and attribute reduction are developed.
Fourth, a general fuzzy rough set model is discussed to give a uniform definition of lower and upper approximations for all kinds of rough sets. Therefore, a uniform viewpoint for thereotical analysis and algorithm design is introduced. Moreover, based on the general model, we design a uniform information measure for Pawlak rough sets, neighborhood rough set, fuzzy rough sets and fuzzy preference rough sets.
Fifth, the stability of attribute evlaution functions and attribute reduction algorithms proposed in this work is evaluated. It is found that Shannon entropy and fuzzy entropy are more robust than dependency and consistency, while neighborhood consistency and neighborhood dependency are the most instable.
Sixth, a system is developed for rough set based knowledge discovery from heterogeneous data. Systematically comparative experiments are conducted. The results validate the effectiveness of the proposed techniques. Moreover, a multiple classifier system is designed by selectively combining a set of classifiers trained with rough set based reducts. In most cases, a set of reducts, rather than one reduct can be obtained from a decision system. Each reduct is a viewpoint to analyze the classification task. The information in different reducts is distinct and complement. Based on the theoretical results of classifier ensemble, a selective ensemble algorithm is developed based on a strategy of forward greedy selection and post-pruning. The experiments show the proposed algorithm can get a compact and effective classification system.
This work develops a uniform rough set model for symbolic and numerical data analysis. Based on neighborhood rough sets and kernelized fuzzy rough sets, we develop a uniform model for classification learning from heterogeneous data. Then fuzzy preference rough sets show a uniform model for fuzzy preference learning with heterogeneous data. Finally, we construct a general rough set model and an information measure model for classification and preference learning.
第一,提出了度量空间多粒度分类学习的邻域粗糙计算模型和算法。度量空间中点的δ邻域形成了论域的一种粒化结构,基于邻域粒化建立了度量空间的邻域粗糙集模型,形成了度量空间分类分类一致性的粗糙计算模型。邻域的大小可视为分析分类的粒度,改变邻域的大小可形成混合数据分类一致性的多粒度分析工具。基于邻域粗糙集模型设计了边界样本选择算法和混合数据属性约简算法。
第二,提出了混合数据分类分析的核模糊粗糙计算模型和算法。当前模糊粗糙集的研究主要集中于模糊近似算子的构造,忽略了对模糊粒化结构的分析。研究发现一大类核函数计算的核矩阵都满足模糊等价关系的性质,从而可引入这些核函数为模糊粗糙计算建立模糊粒化结构。本文提出了基于核函数粒化的核模糊粗糙集模型,建立了分类模糊一致性分析的数学模型。设计了基于核近似的混合属性重要度评价指标,探讨了模糊依赖度函数和特征评价算法ReliefF之间的关联,提出了抗噪声的属性约简算法和大样本集的样本加权重采样方法。
第三,提出了混合数据描述的有序决策问题的模糊偏好粗糙分析模型。有序分类学习是一大类分类学习任务,在多标准决策分析中具有重要的地位。本文引入多标准决策分析中广泛使用的模糊偏好关系,并将其与广义的模糊粗糙集模型结合起来,从而建立了混合数据排序一致性分析的模糊粗糙计算模型。
第四,给出了一系列粗糙计算模型的一般形式,统一了Pawlak粗糙集、邻域粗糙集、核粒化粗糙集和模糊偏好粗糙集,从而建立了粗糙数据分析的统一视角。并且基于一般模型,提出了各种近似空间的不确定性的统一度量模型。分析表明多种近似空间的不确定性程度都可以采用这一信息函数进行刻画。由此,本文给出了混合数据描述的一般分类问题和有序决策问题的一般信息度量理论。
第五,本文分析了各种粗糙集属性评价指标的参数和样本稳定性。研究表明,信息熵和模糊信息熵是非常稳定的属性评价指标,少量样本的扰动不会对属性约简产生影响,而邻域依赖度和邻域一致性是不稳定的评价函数,评价结果易受样本扰动影响。
第六,设计了混合数据约简的算法平台,测试了各种算法在真实分类中的性能,并提出采用选择性集成方法利用多个约简的互补信息。某些决策系统可以得到一组约简,每个约简都保持了原始数据分类的一致性,提供了分类数据的一种理解视角。基于选择性多分类器集成的研究成果,本文提出有选择地集成部分约简训练的分类器构造多分类器系统,并且设计了前向贪心选择和后剪枝的分类器选择策略,试验表明该方法能够获得相对紧凑并且分类能力很强的多分类器系统。
本文的研究建立了符号和数值数据共存的混合决策系统的粗糙计算模型。基于邻域粗糙集模型和核粒化的模糊粗糙集模型,本文建立了混合数据一般分类问题的统一计算模型。接下来又基于模糊偏好粗糙模型建立了混合数据有序分类问题的粗糙计算模型。最后,本文基于广义的粗糙模型统一了一般分类问题和有序分类问题的粗糙计算模型,并为各种粗糙计算模型提出了统一的信息度量理论,从而形成了一大类决策问题的粗糙计算理论。
Machine learning and knowledge discovery is one of the most important issues to be addressed in artificial intelligence. And uncertainty and inconsistency are the key problems in knowledge discovery from complex data. Rough set theory, which simulates the capability of granulation and approximation in human cognition, has proven to be an effective mathematical tool to characterize incosistency in classification data. This theory has been applied in knowledge discovery from symbolic data. However, most of data sets in real-world applications are numerical, fuzzy or their mixture. Not much work has been devoted to discussing knowledge discovery from heterogeneous data with rough sets so far. It is proposed that there are six types of consistency in human’s reasoning in this work. The mathematical models of these types consistency are built based on granulation and approximation in rough sets. Moreover, uniform model and algorithm are developed for knowledge discovery from heterogeneous data are developed. The main contributions of the work are listed as follows.
First, Neighborhood rough set model and algorithms in general metric spaces are constructed. The objects described with numerical attributes can be considered as points in metric spaces. The neighborhoods of these points form a structure of granulation of the universe. Based on neighborhood granulation, a rough set model is developed for classification analysis in metric spaces. Neighborhood rough sets construct a framework for analyzing consistency of classification with numerical or symbolic features. If the size of neighborhood is looked as the granularity in data analysis, a multi-granularity data analysis tool is developed by varying the size of neighborhood. Algorithms for sample and feature reduction are constructed based on the neighborhood model.
Second, a kernelized fuzzy rough model is developed for rough computation with heterogeneous data. The current researches on fuzzy rough sets are focused on construction of fuzzy rough approximation operators. Howerver little attention is paid to fuzzy granulation. It is found that a class of kernel functions can be used to compute the fuzzy T-equivalence relations between samples. Then these kernel functions can be used to build fuzzy granular structures for fuzzy rough sets. Based on this observation, a kernelized fuzzy rough set model is proposed for analyzing consistency in the fuzzy case. The connections between fuzzy dependency and ReliefF are shown. We introduce the idea in ReliefF to reduce the influence of noise in fuzzy rough sets based attribute reduction and we construct a generalized classification certainty measure.
Third, a rough set model for fuzzy preference analysis is developed. Ordered classification is one class of learning tasks in decision modeling and multi-criterion analysis. Fuzzy preference relations, which are widely in multi-criterion analysis, are introduced and combined with general fuzzy rough set model, thus a fuzzy preference rough set model is proposed and algorithms for dependency analysis and attribute reduction are developed.
Fourth, a general fuzzy rough set model is discussed to give a uniform definition of lower and upper approximations for all kinds of rough sets. Therefore, a uniform viewpoint for thereotical analysis and algorithm design is introduced. Moreover, based on the general model, we design a uniform information measure for Pawlak rough sets, neighborhood rough set, fuzzy rough sets and fuzzy preference rough sets.
Fifth, the stability of attribute evlaution functions and attribute reduction algorithms proposed in this work is evaluated. It is found that Shannon entropy and fuzzy entropy are more robust than dependency and consistency, while neighborhood consistency and neighborhood dependency are the most instable.
Sixth, a system is developed for rough set based knowledge discovery from heterogeneous data. Systematically comparative experiments are conducted. The results validate the effectiveness of the proposed techniques. Moreover, a multiple classifier system is designed by selectively combining a set of classifiers trained with rough set based reducts. In most cases, a set of reducts, rather than one reduct can be obtained from a decision system. Each reduct is a viewpoint to analyze the classification task. The information in different reducts is distinct and complement. Based on the theoretical results of classifier ensemble, a selective ensemble algorithm is developed based on a strategy of forward greedy selection and post-pruning. The experiments show the proposed algorithm can get a compact and effective classification system.
This work develops a uniform rough set model for symbolic and numerical data analysis. Based on neighborhood rough sets and kernelized fuzzy rough sets, we develop a uniform model for classification learning from heterogeneous data. Then fuzzy preference rough sets show a uniform model for fuzzy preference learning with heterogeneous data. Finally, we construct a general rough set model and an information measure model for classification and preference learning.
引文
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