基于决策分类的分块差别矩阵及其求核算法
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摘要
属性约简是粗糙集理论进行数据挖掘的基本途径,相关算法主要基于核。核的差别矩阵表示及相关求核计算具有重要意义,但已有的差别矩阵及其求核算法还具有时空局限性。对此,依据差别矩阵的稀疏性与大规模性,提出基于决策分类的分块差别矩阵及其求核算法,直接地将决策分类信息融入形式结构与问题求解。首先,基于决策分类来定义分块差别矩阵,设计其计算算法;其次,基于分块差别矩阵,确定核的内涵与算法;最后,进行实例分析与实验验证,说明所建方法的有效性。基于决策分类的分块差别矩阵有效地实施了信息提取与维度降低,相关的求核算法较好地减少了差别矩阵求核算法的时空复杂性。
Attribute reduction is the fundamental approach of rough set theory to implement data mining,and its relevant algorithms are mainly based on the core. For the core,both its representation of the discernibility matrix and its calculation for finding the core exhibit important significance,but the existing discernibility matrix and its core algorithm have time and space limitations. According to the sparsity and large scale of the discernibility matrix,the block discernibility matrix based on the decision classification and its algorithm finding the core are proposed,and thus the decision classification information is directly applied to the form structure and problem solving. At first,the block discernibility matrix is defined by the decision classification,and its calculation algorithm is achieved. Then,based on the block discernibility matrix,the essence and algorithm of the core are provided. Finally,the proposed method's effectiveness is verified by the example and experiment. The block discernibility matrix based on the decision classification effectively implements the information extraction and dimensionality reduction,so its relevant algorithm finding the core well decreases the time and space complexities of the corresponding algorithm based on the discernibility matrix.
Attribute reduction is the fundamental approach of rough set theory to implement data mining,and its relevant algorithms are mainly based on the core. For the core,both its representation of the discernibility matrix and its calculation for finding the core exhibit important significance,but the existing discernibility matrix and its core algorithm have time and space limitations. According to the sparsity and large scale of the discernibility matrix,the block discernibility matrix based on the decision classification and its algorithm finding the core are proposed,and thus the decision classification information is directly applied to the form structure and problem solving. At first,the block discernibility matrix is defined by the decision classification,and its calculation algorithm is achieved. Then,based on the block discernibility matrix,the essence and algorithm of the core are provided. Finally,the proposed method's effectiveness is verified by the example and experiment. The block discernibility matrix based on the decision classification effectively implements the information extraction and dimensionality reduction,so its relevant algorithm finding the core well decreases the time and space complexities of the corresponding algorithm based on the discernibility matrix.
引文
[1]PAWLAK Z.Rough sets:theoretical aspects of reasoning about data[M].Netherlands:Kluwer Academic Publishers,1991.
[2]叶东毅,黄翠微,赵斌.粗糙集属性约简的一个贪心算法[J].系统工程与电子技术,2000,22(09):63-65.YE Dongyi,HUANG Cuiwei,ZHAO Bin.A greedy algorithm for attribute reduction in rough sets[J].Systems Engineering and Electronics,2000,22(9):63-65.
[3]ZHANG Xianyong,MIAO Duoqian.Three-way attribute reducts[J].International Journal of Approximate Reasoning,2017,88:401-434.
[4]程美英,倪志伟,朱旭辉.融合粗糙集和扩散二元萤火虫算法的属性约简方法[J].系统工程与电子技术,2016,38(10):2449-2456.CHENG Meiying,NI Zhiwei,ZHU Xuhui.The properties of combining rough sets and diffused dual firefly algorithms[J].Systems Engineering and Electronics Technology,2016,38(10):2449-2456.
[5]徐怡,程燕.基于属性值变化的动态覆盖系统中近似集增量算法[J].系统工程与电子技术,2017,39(7):1660-1668.XU Yi,CHENG Yan.The approximate set increment algorithm in dynamic coverage system based on property value change[J].Systems Engineering and Electronics Technology,2017,39(7):1660-1668.
[6]丁棉卫,张腾飞,马福民.基于二进制区分矩阵的增量式属性约简算法[J].计算机工程,2017,43(1):201-206.DING Mianwei,ZHANG Tengfei,MA Fumin.The incremental attribute reduction algorithm based on binary discrimination matrix[J].Computer Engineering,2017,43(1):201-206.
[7]胡帅鹏,张清华,姚龙洋.一种基于二进制表示的快速求核算法[J].计算机科学,2016,43(12):79-83.HU Shuaipeng,ZHANG Qinghua,YAO Longyang.A quick calculation method based on binary representation[J].Journal of Computer Science,2016,43(12):79-83.
[8]HU Xiaohua,CERCONE N.Learning in relational databases:a rough set approach[J].Computational Intelligence,1995,11(02):323-337.
[9]徐章艳,杨炳儒,宋威.一个基于差别矩阵的快速求核算法[J].计算机工程与应用,2006,42(6):4-6.XU Zhangyan,YANG Bingru,SONG Wei.A quick accounting method based on differential matrix[J].Computer Engineering and Application,2006,42(6):4-6.
[10]徐章艳,杨炳儒,蔡卫东,等.一个基于正区域的快速求核算法[J].系统工程与电子技术,2006,28(12):1902-1905.XU Zhangyan,YANG Bingru,CAI Weidong,et al.A quick accounting method based on positive region[J].Systems Engineering and Electronics Technology,2006,28(12):1902-1905.
[11]杨传健,马丽生,葛浩.基于水平划分决策表的核属性求解算法[J].计算机工程与应用,2016,52(2):61-64.YANG Chuanjian,MA Lisheng,GE Hao.Algorithm for solving kernel properties of decision table based on horizontal division[J].Computer Engineering and Application,2016,52(2):61-64.
[12]陆光,李想.一种改进的基于差别矩阵的求核属性算法[J].森林工程,2014,30(2):120-124.LU Guang,LI Xiang.An improved attribute the core algorithm based on discernibility matrix[J].Forest Engineering,2014,30(02):120-124.
[13]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法[J].电子学报,2002,30(7):1086-1088.YE Dongyi,CHEN Zhaojiong.A new method of discernibility matrix and its core[J].Journal of Electronics,2002,30(7):1086-1088.
[14]高学东,丁军.基于简化差别矩阵的属性约简算法[J].系统工程理论与实践,2006,26(6):101-107.GAO Xuedong,DING Jun.Attribute reduction algorithm based on simplified discernibility matrix[J].Journal of Systems Engineering Theory and Practice,2006,26(6):101-107.
[15]葛浩,李龙澍,杨传健.基于相对分辨能力的属性约简算法[J].系统工程理论与实践,2015,35(6):1595-1603.GE Hao,LI Longshu,YANG Chuanjian.Based on the relative resolution ability of attribute reduction algorithm[J].System EngineeringTheoryandPractice,2015,35(6):1595-1603.
[16]朱金虎,徐章艳,乔丽娟,等.改进的布尔冲突矩阵的高效属性约简算法[J].计算机工程与应用,2017,53(6):145-149.ZHU Jinhu,XU Zhangyan,QIAO Lijuan,et al.Improved efficient attribute reduction algorithm for Boolean conflict matrix[J].computer Engineering and Applications,2017,53(6):145-149.
[17]杨涛,张贤勇,冯山.基于差别矩阵的属性集求核算法[J].郑州大学学报(理学版),2018,50(1):27-32.YANG Tao,ZHANG Xianyong,FENG Shan.A core algorithm of attribute sets based on the discernibility matrix[J].Journal of Zhengzhou University(Natural Science Edition),2018,50(1):27-32.
[2]叶东毅,黄翠微,赵斌.粗糙集属性约简的一个贪心算法[J].系统工程与电子技术,2000,22(09):63-65.YE Dongyi,HUANG Cuiwei,ZHAO Bin.A greedy algorithm for attribute reduction in rough sets[J].Systems Engineering and Electronics,2000,22(9):63-65.
[3]ZHANG Xianyong,MIAO Duoqian.Three-way attribute reducts[J].International Journal of Approximate Reasoning,2017,88:401-434.
[4]程美英,倪志伟,朱旭辉.融合粗糙集和扩散二元萤火虫算法的属性约简方法[J].系统工程与电子技术,2016,38(10):2449-2456.CHENG Meiying,NI Zhiwei,ZHU Xuhui.The properties of combining rough sets and diffused dual firefly algorithms[J].Systems Engineering and Electronics Technology,2016,38(10):2449-2456.
[5]徐怡,程燕.基于属性值变化的动态覆盖系统中近似集增量算法[J].系统工程与电子技术,2017,39(7):1660-1668.XU Yi,CHENG Yan.The approximate set increment algorithm in dynamic coverage system based on property value change[J].Systems Engineering and Electronics Technology,2017,39(7):1660-1668.
[6]丁棉卫,张腾飞,马福民.基于二进制区分矩阵的增量式属性约简算法[J].计算机工程,2017,43(1):201-206.DING Mianwei,ZHANG Tengfei,MA Fumin.The incremental attribute reduction algorithm based on binary discrimination matrix[J].Computer Engineering,2017,43(1):201-206.
[7]胡帅鹏,张清华,姚龙洋.一种基于二进制表示的快速求核算法[J].计算机科学,2016,43(12):79-83.HU Shuaipeng,ZHANG Qinghua,YAO Longyang.A quick calculation method based on binary representation[J].Journal of Computer Science,2016,43(12):79-83.
[8]HU Xiaohua,CERCONE N.Learning in relational databases:a rough set approach[J].Computational Intelligence,1995,11(02):323-337.
[9]徐章艳,杨炳儒,宋威.一个基于差别矩阵的快速求核算法[J].计算机工程与应用,2006,42(6):4-6.XU Zhangyan,YANG Bingru,SONG Wei.A quick accounting method based on differential matrix[J].Computer Engineering and Application,2006,42(6):4-6.
[10]徐章艳,杨炳儒,蔡卫东,等.一个基于正区域的快速求核算法[J].系统工程与电子技术,2006,28(12):1902-1905.XU Zhangyan,YANG Bingru,CAI Weidong,et al.A quick accounting method based on positive region[J].Systems Engineering and Electronics Technology,2006,28(12):1902-1905.
[11]杨传健,马丽生,葛浩.基于水平划分决策表的核属性求解算法[J].计算机工程与应用,2016,52(2):61-64.YANG Chuanjian,MA Lisheng,GE Hao.Algorithm for solving kernel properties of decision table based on horizontal division[J].Computer Engineering and Application,2016,52(2):61-64.
[12]陆光,李想.一种改进的基于差别矩阵的求核属性算法[J].森林工程,2014,30(2):120-124.LU Guang,LI Xiang.An improved attribute the core algorithm based on discernibility matrix[J].Forest Engineering,2014,30(02):120-124.
[13]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法[J].电子学报,2002,30(7):1086-1088.YE Dongyi,CHEN Zhaojiong.A new method of discernibility matrix and its core[J].Journal of Electronics,2002,30(7):1086-1088.
[14]高学东,丁军.基于简化差别矩阵的属性约简算法[J].系统工程理论与实践,2006,26(6):101-107.GAO Xuedong,DING Jun.Attribute reduction algorithm based on simplified discernibility matrix[J].Journal of Systems Engineering Theory and Practice,2006,26(6):101-107.
[15]葛浩,李龙澍,杨传健.基于相对分辨能力的属性约简算法[J].系统工程理论与实践,2015,35(6):1595-1603.GE Hao,LI Longshu,YANG Chuanjian.Based on the relative resolution ability of attribute reduction algorithm[J].System EngineeringTheoryandPractice,2015,35(6):1595-1603.
[16]朱金虎,徐章艳,乔丽娟,等.改进的布尔冲突矩阵的高效属性约简算法[J].计算机工程与应用,2017,53(6):145-149.ZHU Jinhu,XU Zhangyan,QIAO Lijuan,et al.Improved efficient attribute reduction algorithm for Boolean conflict matrix[J].computer Engineering and Applications,2017,53(6):145-149.
[17]杨涛,张贤勇,冯山.基于差别矩阵的属性集求核算法[J].郑州大学学报(理学版),2018,50(1):27-32.YANG Tao,ZHANG Xianyong,FENG Shan.A core algorithm of attribute sets based on the discernibility matrix[J].Journal of Zhengzhou University(Natural Science Edition),2018,50(1):27-32.