基于邻域粗糙互信息熵的非单调性属性约简
|
摘要
属性约简是粗糙集理论一项重要的应用,目前已广泛运用于机器学习和数据挖掘等领域,邻域粗糙集是粗糙集理论中处理连续型数据的一种重要方法.针对目前邻域粗糙集模型中属性约简存在的缺陷,构造一种基于邻域粗糙集的邻域粗糙熵模型,并基于此给出邻域粗糙联合熵、邻域粗糙条件熵和邻域粗糙互信息熵等概念.邻域粗糙互信息熵是评估属性集相关性的一种重要的方法,具有非单调性变化的特性,对此,提出一种基于邻域粗糙互信息熵的非单调性属性约简算法.实验分析表明,所提出算法不仅比目前已有的单调性属性约简算法具有更优越的属性约简结果,而且具有更高的约简效率.
Attribute reduction is an important application in rough set theory, and it has been widely used in such areas as machine learning and data mining so far. Neighborhood rough set is a vital method for processing continuous data in rough set theory. For the existed detects of attribute reduction in the current neighborhood rough set model, the model of neighborhood rough entropy based on a neighborhood rough set is defined, meanwhile, the concepts of neighborhood rough combination entropy, neighborhood rough conditional entropy and neighborhood rough mutual information entropy are given, where the neighborhood rough mutual information entropy is an important method for evaluating the correlation of attribute sets, and at the same time, the neighborhood rough mutual information entropy is also proved to has a property of non-monotonic changing, therefore a non-monotonic attribute reduction algorithm based on neighborhood rough mutual information entropy is proposed. The experimental analysis show that the proposed algorithm has not only better results but also higher reduction efficiency than existing monotonic algorithms in attribute reduction.
Attribute reduction is an important application in rough set theory, and it has been widely used in such areas as machine learning and data mining so far. Neighborhood rough set is a vital method for processing continuous data in rough set theory. For the existed detects of attribute reduction in the current neighborhood rough set model, the model of neighborhood rough entropy based on a neighborhood rough set is defined, meanwhile, the concepts of neighborhood rough combination entropy, neighborhood rough conditional entropy and neighborhood rough mutual information entropy are given, where the neighborhood rough mutual information entropy is an important method for evaluating the correlation of attribute sets, and at the same time, the neighborhood rough mutual information entropy is also proved to has a property of non-monotonic changing, therefore a non-monotonic attribute reduction algorithm based on neighborhood rough mutual information entropy is proposed. The experimental analysis show that the proposed algorithm has not only better results but also higher reduction efficiency than existing monotonic algorithms in attribute reduction.
引文
[1]Pawlak Z.Rough sets[J].Int J of Parallel Programming1982,11(5):341-356.
[2]Qian Y H,Liang J Y,Pedrycz W,et al.Positive approximation:An accelerator for attribute reduction in rough set theory[J].Artificial Intelligence,2010174(9/10):597-618.
[3]Hu Q H,Yu D R,Xie Z X.Neighborhood classifiers[J]Expert Systems with Applications,2008,34(2):866-876
[4]Hu Q H,Yu D R,Liu J F,et al.Neighborhood rough set based heterogeneous feature subset selection[J]Information Sciences,2008,178(18):3577-3594.
[5]胡清华,于达仁,谢宗霞.基于邻域粒化和粗糙逼近的数值属性约简[J].软件学报,2008,19(3):640-649.(Hu Q H,Yu D R,Xie Z X.Numerical Attribute Reduction Based on Neighborhood Granulation and Rough Approximation[J].J of Software,2008,19(3)640-649.)
[6]Hu Q H,Zhang L,Chen D G,et al.Gaussian kerne based fuzzy rough sets:Model,uncertainty measures and applications[J].Int J of Approximate Reasoning,201051(4):453-471.
[7]Liu Y,Huang W L,Jiang Y L,et al.Quick attribute reduct algorithm for neighborhood rough set model[J]Information Sciences,2014,271(7):65-81.
[8]Wang C Z,Shao M W,He Q,et al.Feature subse selection based on fuzzy neighborhood rough sets[J]Knowledge-Based Systems,2016,111(1):173-179.
[9]Wang C Z,Hu Q H,Wang X Z,et al.Feature selection based on neighborhood discrimination index[J].IEEETrans on Neural Networks and Learning Systems,201829(7):2986-2999.
[10]Li W W,Huang Z Q,Jia X Y,et al.Neighborhood based decision-theoretic rough set models[J].Int J of Approximate Reasoning,2016,69:1-17.
[11]姚晟,徐风,赵鹏,等.基于邻域量化容差关系粗糙集模型的特征选择算法[J].模式识别与人工智能,2017,30(5):416-428.(Yao S,Xu F,Zhao P,et al.Feature selection algorithm based on neighborhood valued tolerance relation rough set model[J].Pattern Recognition and Artificial Intelligence,2017,30(5):416-428.)
[12]姚晟,徐风,赵鹏,等.基于改进邻域粒的模糊熵特征选择算法[J].南京大学学报:自然科学版,2017,53(4):802-814.(Yao S,Xu F,Zhao P,et al.Fuzzy entropy feature selection algorithm based on improved neighborhood granule[J].J of Nanjing University:Natural Science,2017,52(4):802-814.)
[13]何松华,康婵娟,鲁敏,等.基于邻域组合测度的属性约简方法[J].控制与决策,2016,31(7):1225-1230.(He S H,Kang C J,Lu M,et al.Attribute reduction method based on neighborhood combination measure[J].Control and Decision,2016,31(7):1225-1230.)
[14]段洁,胡清华,张灵均,等.基于邻域粗糙集的多标记分类特征选择算法[J].计算机研究与发展,2015,52(1):56-65.(Duan J,Hu Q H,Zhang L J,et al.Feature selection for multi-Label classification based on neighborhood rough sets[J].J of Computer Research and Development,2015,52(1):56-65.)
[15]Li H X,Zhou X Z,Zhao J B,et al.Non-monotonic attribute reduction in decision-theoretic rough sets[J].Fundamenta Informaticae,2013,126(4):415-432.
[16]Liang J Y,Shi Z Z,Li D Y,et al.Information entropy,rough entropy and knowledge granulation in incomplete information systems[J].Int J of General Systems,2006,35(6):641-654.
[17]Qian Y H,Liang J Y.Combination entropy and combination granulation in incomplete information system[C].The 1st Int Conf on Rough Sets and Knowledge Technology,Chongqing,2006:184-190.
[18]Qian Y H,Liang J Y,Wu W Z,et al.Information granularity in fuzzy binary GrC model[J].IEEE Trans on Fuzzy Systems,2011,19(2):253-264.
[19]徐风,姚晟,纪霞,等.基于模糊邻域粗糙集的信息系统不确定性度量方法[J].南京大学学报:自然科学版,2017,53(5):926-936.(Xu F,Yao S,Ji X,et al.Uncertainty measurement method for information system based on fuzzy neighborhood rough set[J].J of Nanjing University:Natural Science,2017,53(5):926-936.)
[20]Zhang X,Mei C L,Chen D G,et al.Feature selection in mixed data:A method using a novel fuzzy rough set-based information entropy[J].Pattern Recognition,2016,56(1):1-15.
[2]Qian Y H,Liang J Y,Pedrycz W,et al.Positive approximation:An accelerator for attribute reduction in rough set theory[J].Artificial Intelligence,2010174(9/10):597-618.
[3]Hu Q H,Yu D R,Xie Z X.Neighborhood classifiers[J]Expert Systems with Applications,2008,34(2):866-876
[4]Hu Q H,Yu D R,Liu J F,et al.Neighborhood rough set based heterogeneous feature subset selection[J]Information Sciences,2008,178(18):3577-3594.
[5]胡清华,于达仁,谢宗霞.基于邻域粒化和粗糙逼近的数值属性约简[J].软件学报,2008,19(3):640-649.(Hu Q H,Yu D R,Xie Z X.Numerical Attribute Reduction Based on Neighborhood Granulation and Rough Approximation[J].J of Software,2008,19(3)640-649.)
[6]Hu Q H,Zhang L,Chen D G,et al.Gaussian kerne based fuzzy rough sets:Model,uncertainty measures and applications[J].Int J of Approximate Reasoning,201051(4):453-471.
[7]Liu Y,Huang W L,Jiang Y L,et al.Quick attribute reduct algorithm for neighborhood rough set model[J]Information Sciences,2014,271(7):65-81.
[8]Wang C Z,Shao M W,He Q,et al.Feature subse selection based on fuzzy neighborhood rough sets[J]Knowledge-Based Systems,2016,111(1):173-179.
[9]Wang C Z,Hu Q H,Wang X Z,et al.Feature selection based on neighborhood discrimination index[J].IEEETrans on Neural Networks and Learning Systems,201829(7):2986-2999.
[10]Li W W,Huang Z Q,Jia X Y,et al.Neighborhood based decision-theoretic rough set models[J].Int J of Approximate Reasoning,2016,69:1-17.
[11]姚晟,徐风,赵鹏,等.基于邻域量化容差关系粗糙集模型的特征选择算法[J].模式识别与人工智能,2017,30(5):416-428.(Yao S,Xu F,Zhao P,et al.Feature selection algorithm based on neighborhood valued tolerance relation rough set model[J].Pattern Recognition and Artificial Intelligence,2017,30(5):416-428.)
[12]姚晟,徐风,赵鹏,等.基于改进邻域粒的模糊熵特征选择算法[J].南京大学学报:自然科学版,2017,53(4):802-814.(Yao S,Xu F,Zhao P,et al.Fuzzy entropy feature selection algorithm based on improved neighborhood granule[J].J of Nanjing University:Natural Science,2017,52(4):802-814.)
[13]何松华,康婵娟,鲁敏,等.基于邻域组合测度的属性约简方法[J].控制与决策,2016,31(7):1225-1230.(He S H,Kang C J,Lu M,et al.Attribute reduction method based on neighborhood combination measure[J].Control and Decision,2016,31(7):1225-1230.)
[14]段洁,胡清华,张灵均,等.基于邻域粗糙集的多标记分类特征选择算法[J].计算机研究与发展,2015,52(1):56-65.(Duan J,Hu Q H,Zhang L J,et al.Feature selection for multi-Label classification based on neighborhood rough sets[J].J of Computer Research and Development,2015,52(1):56-65.)
[15]Li H X,Zhou X Z,Zhao J B,et al.Non-monotonic attribute reduction in decision-theoretic rough sets[J].Fundamenta Informaticae,2013,126(4):415-432.
[16]Liang J Y,Shi Z Z,Li D Y,et al.Information entropy,rough entropy and knowledge granulation in incomplete information systems[J].Int J of General Systems,2006,35(6):641-654.
[17]Qian Y H,Liang J Y.Combination entropy and combination granulation in incomplete information system[C].The 1st Int Conf on Rough Sets and Knowledge Technology,Chongqing,2006:184-190.
[18]Qian Y H,Liang J Y,Wu W Z,et al.Information granularity in fuzzy binary GrC model[J].IEEE Trans on Fuzzy Systems,2011,19(2):253-264.
[19]徐风,姚晟,纪霞,等.基于模糊邻域粗糙集的信息系统不确定性度量方法[J].南京大学学报:自然科学版,2017,53(5):926-936.(Xu F,Yao S,Ji X,et al.Uncertainty measurement method for information system based on fuzzy neighborhood rough set[J].J of Nanjing University:Natural Science,2017,53(5):926-936.)
[20]Zhang X,Mei C L,Chen D G,et al.Feature selection in mixed data:A method using a novel fuzzy rough set-based information entropy[J].Pattern Recognition,2016,56(1):1-15.