稳健模糊粗糙集模型研究
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摘要
在数据分析中,模糊粗糙集理论为处理不确定性提供了一种强大的数学工具。近年来,该理论引起了粒计算、机器学习和不确定性推理的广泛关注,然而经典的模糊粗糙集模型对数据噪声敏感的缺陷使得该理论在实际应用中受到了严重的限制。至今设计稳健的模糊粗糙集模型仍然是一个研究热点。本文分别从数据噪声的两类处理方式出发设计稳健的模糊粗糙集模型,具体的研究工作如下:
分析了现有的粗糙集模型的稳健性及局限性。为了揭示粗糙集理论对数据噪声的敏感性,本文分析了Pawlak粗糙集、邻域粗糙集、模糊粗糙集、变精度粗糙集、邻域一致度、??-精度模糊粗糙集、模糊变精度粗糙集、变精度模糊粗糙集和模糊量化粗糙集的稳健性及局限性,并用实验对理论分析结果进行了验证。
研究了一种基于软最小超球的模糊粗糙集模型。软最小超球问题是新颖检测的常用方法,本文将这个问题与模糊粗糙集模型结合建立了一种稳健模糊粗糙集模型,分析模型的性质,并用实验验证该模型的稳健性。本文利用基于软最小超球的模糊粗糙集模型的稳健性设计了一个稳健的模糊粗糙策树模型,并用实验对该模型的稳健性进行验证。
研究了一种基于稳健统计量的模糊粗糙集模型。经典的模糊粗糙集是建立在最小值和最大值的基础之上的,这是导致该模型不稳健的直接原因。本文将稳健统计量的概念与模糊粗糙集结合设计了一种稳健的模糊粗糙集模型。该模型改进了经典模糊粗糙集模型上、下近似隶属度的计算方式,使得即使数据噪声存在隶属度的值也不会产生明显偏差。此外,本文用基于稳健统计量的模糊粗糙集模型的下近似设计了一个稳健的分类模型,并用实验验证了分类模型的稳健性。
研究了一种稳健的模糊粗糙集模型――软模糊粗糙集。该模型是在软间隔支持向量机的启示下提出的,它将上、下近似隶属度与被忽略的样本数紧密地结合在一起,在增加样本的下近似隶属度或减小样本的上近似隶属度的同时限制了被忽略的样本数。为了验证软模糊粗糙集模型的有效性和稳健性,本文以软模糊粗糙集模型的依赖度函数作为特征评价指标设计了一个特征选择算法,并用数据集在选择的特征子集上的分类精度作为评价验证算法和软模糊粗糙集模型的稳健性。
从抗噪方式和参数设置方式两方面将稳健模糊粗糙集模型进行了对比分析,并将这些模型应用于太阳耀斑预报中。本文以稳健模糊粗糙集的下近似隶属度作为案例选择和案例推理的理论依据,设计了一个基于案例的太阳耀斑预报模型,对预报模型的有效性进行了实验验证。
Fuzzy rough set theory is claimed to be a powerful mathematical tool for dealingwith uncertainty in data analysis. It has attracted much attention from domains of granularcomputing, machine learning and uncertainty reasoning in the past decade. However, theclassical fuzzy rough set model is sensitive to noise, which makes the theory limited inapplication. Now much work is still focusing on the research of robust fuzzy rough setmodels. It is significant to design robust fuzzy rough set models. In this work, we designrobust fuzzy rough set models in the two ways to handling noisy data. Our work is shownas follows:
The robustness and limitation of existent rough sets are analyzed. In order to showthe sensitivity of rough set theory to noise, the robustness and limitation of rough setmodels are analyzed, such as Pawlak’s rough sets, neighborhood rough sets, fuzzy roughsets, variable precision rough sets, neighborhood consistency, ??-precision fuzzy roughsets, fuzzy variable precision rough sets, variable precision fuzzy rough sets and vaguelyquantified rough sets. And analyzed results are tested with experiments.
A soft minimum enclosing ball-based fuzzy rough set model is designed. Soft mini-mum enclosing ball is a state-of-the-art method in novelty detection. It is introduced intofuzzy rough sets to form a robust model, the robustness of which is tested with experi-ments. Moreover, with the proposed model a robust fuzzy rough decision tree model ispresented and tested by experiments.
A robust statistics-based fuzzy rough set model is introduced. The classical fuzzyrough set model is defined with minimum and maximum, which results in its sensitivityto noise. In this work, three robust statistics are introduced into fuzzy rough sets to designa robust model. The new model is robust to noise by changing the computational ways oflower and upper approximations. Besides, a robust classification model is designed withthe lower approximation of the robust statistics-based fuzzy rough sets, and is tested withexperiments.
A robust fuzzy rough set model named soft fuzzy rough sets is introduced. It isinspired by soft margin support vector machines. The new model makes trade-off betweenmemberships and numbers of overlooked samples. It enlarges the lower approximations or reduces the upper approximations as well as restricting numbers of samples neglected.In order to test the validity and robustness of soft fuzzy rough sets, a feature selectionalgorithm is designed by taking soft fuzzy dependency as feature evaluation measure andclassification accuracies of data sets on selected features as the evaluation measure of thealgorithm and soft fuzzy rough sets.
Robust fuzzy rough set models are compared and applied in solar ?are prediction.A case-based prediction model is present. It takes the lower approximation membershipsof robust fuzzy rough sets as theoretical sustainment of case selection and case reasoning.The robustness of the prediction model is tested with experiments.
分析了现有的粗糙集模型的稳健性及局限性。为了揭示粗糙集理论对数据噪声的敏感性,本文分析了Pawlak粗糙集、邻域粗糙集、模糊粗糙集、变精度粗糙集、邻域一致度、??-精度模糊粗糙集、模糊变精度粗糙集、变精度模糊粗糙集和模糊量化粗糙集的稳健性及局限性,并用实验对理论分析结果进行了验证。
研究了一种基于软最小超球的模糊粗糙集模型。软最小超球问题是新颖检测的常用方法,本文将这个问题与模糊粗糙集模型结合建立了一种稳健模糊粗糙集模型,分析模型的性质,并用实验验证该模型的稳健性。本文利用基于软最小超球的模糊粗糙集模型的稳健性设计了一个稳健的模糊粗糙策树模型,并用实验对该模型的稳健性进行验证。
研究了一种基于稳健统计量的模糊粗糙集模型。经典的模糊粗糙集是建立在最小值和最大值的基础之上的,这是导致该模型不稳健的直接原因。本文将稳健统计量的概念与模糊粗糙集结合设计了一种稳健的模糊粗糙集模型。该模型改进了经典模糊粗糙集模型上、下近似隶属度的计算方式,使得即使数据噪声存在隶属度的值也不会产生明显偏差。此外,本文用基于稳健统计量的模糊粗糙集模型的下近似设计了一个稳健的分类模型,并用实验验证了分类模型的稳健性。
研究了一种稳健的模糊粗糙集模型――软模糊粗糙集。该模型是在软间隔支持向量机的启示下提出的,它将上、下近似隶属度与被忽略的样本数紧密地结合在一起,在增加样本的下近似隶属度或减小样本的上近似隶属度的同时限制了被忽略的样本数。为了验证软模糊粗糙集模型的有效性和稳健性,本文以软模糊粗糙集模型的依赖度函数作为特征评价指标设计了一个特征选择算法,并用数据集在选择的特征子集上的分类精度作为评价验证算法和软模糊粗糙集模型的稳健性。
从抗噪方式和参数设置方式两方面将稳健模糊粗糙集模型进行了对比分析,并将这些模型应用于太阳耀斑预报中。本文以稳健模糊粗糙集的下近似隶属度作为案例选择和案例推理的理论依据,设计了一个基于案例的太阳耀斑预报模型,对预报模型的有效性进行了实验验证。
Fuzzy rough set theory is claimed to be a powerful mathematical tool for dealingwith uncertainty in data analysis. It has attracted much attention from domains of granularcomputing, machine learning and uncertainty reasoning in the past decade. However, theclassical fuzzy rough set model is sensitive to noise, which makes the theory limited inapplication. Now much work is still focusing on the research of robust fuzzy rough setmodels. It is significant to design robust fuzzy rough set models. In this work, we designrobust fuzzy rough set models in the two ways to handling noisy data. Our work is shownas follows:
The robustness and limitation of existent rough sets are analyzed. In order to showthe sensitivity of rough set theory to noise, the robustness and limitation of rough setmodels are analyzed, such as Pawlak’s rough sets, neighborhood rough sets, fuzzy roughsets, variable precision rough sets, neighborhood consistency, ??-precision fuzzy roughsets, fuzzy variable precision rough sets, variable precision fuzzy rough sets and vaguelyquantified rough sets. And analyzed results are tested with experiments.
A soft minimum enclosing ball-based fuzzy rough set model is designed. Soft mini-mum enclosing ball is a state-of-the-art method in novelty detection. It is introduced intofuzzy rough sets to form a robust model, the robustness of which is tested with experi-ments. Moreover, with the proposed model a robust fuzzy rough decision tree model ispresented and tested by experiments.
A robust statistics-based fuzzy rough set model is introduced. The classical fuzzyrough set model is defined with minimum and maximum, which results in its sensitivityto noise. In this work, three robust statistics are introduced into fuzzy rough sets to designa robust model. The new model is robust to noise by changing the computational ways oflower and upper approximations. Besides, a robust classification model is designed withthe lower approximation of the robust statistics-based fuzzy rough sets, and is tested withexperiments.
A robust fuzzy rough set model named soft fuzzy rough sets is introduced. It isinspired by soft margin support vector machines. The new model makes trade-off betweenmemberships and numbers of overlooked samples. It enlarges the lower approximations or reduces the upper approximations as well as restricting numbers of samples neglected.In order to test the validity and robustness of soft fuzzy rough sets, a feature selectionalgorithm is designed by taking soft fuzzy dependency as feature evaluation measure andclassification accuracies of data sets on selected features as the evaluation measure of thealgorithm and soft fuzzy rough sets.
Robust fuzzy rough set models are compared and applied in solar ?are prediction.A case-based prediction model is present. It takes the lower approximation membershipsof robust fuzzy rough sets as theoretical sustainment of case selection and case reasoning.The robustness of the prediction model is tested with experiments.
引文
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