灰主成分分析研究及其应用
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摘要
针对主成分分析方法对于具有时间序列数据的处理存在的不足,根据灰系统中数据具有时间序列的特性,将灰色系统思想与经典主成分分析相结合,提出一种新的模型,即灰主成分分析。时间序列分析不仅可以从数量上揭示某一现象的发展变化规律,还可从动态的角度刻画某一现象与其他现象之间的内在数量关系及其变化规律。灰色系统理论通过序列的生成和开发,致力于现实规律的探讨,而数理统计则致力于统计历史规律的研究。将两种方法的优点结合到一起,用于解决时间序列问题,并利用面向对象程序设计的方法进行了系统实现。将该方法应用到我国国债风险指标的综合评价中,突出了新的时间序列数据对整个数据的影响性,分析结果能够为决策者提供有价值的决策依据。实验结果表明,采用灰主成分分析的效果更优越,能较真实地反映出时间对于样本数据的影响。
In order to make up the deficiency that it can not solve the time series data,we propose a new method.Time series analysis can reflect the development of change order from the data,and also can depict the interior data relation and the change orderliness from a phenomenon to a phenomenon.Because the grey system data have time series characteristics,we combine the grey system method with the Principal Component Analysis,forming a new model,i.e.Grey principal component analysis.Grey system theory is devoted to the discussion of real order,while the mathematical statistics is devoted to counting the research of the historical orders.Therefore we combine the two methods to solve the time series.We use object-oriented programming method to implement the system,and based on correlation to make analysis separately.Finally,we apply this method to the synthesis appraisal of our national debt's risk,the result is remarkable,the new time data can affect the whole data of the system,and the result can help the manager make a decision.There is certain reference value to the research for the future in the time series'problem that this paper puts forward.
In order to make up the deficiency that it can not solve the time series data,we propose a new method.Time series analysis can reflect the development of change order from the data,and also can depict the interior data relation and the change orderliness from a phenomenon to a phenomenon.Because the grey system data have time series characteristics,we combine the grey system method with the Principal Component Analysis,forming a new model,i.e.Grey principal component analysis.Grey system theory is devoted to the discussion of real order,while the mathematical statistics is devoted to counting the research of the historical orders.Therefore we combine the two methods to solve the time series.We use object-oriented programming method to implement the system,and based on correlation to make analysis separately.Finally,we apply this method to the synthesis appraisal of our national debt's risk,the result is remarkable,the new time data can affect the whole data of the system,and the result can help the manager make a decision.There is certain reference value to the research for the future in the time series'problem that this paper puts forward.
引文
[1]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,1999.ZHANG Yao-ting,FANG Kai-tai.Multivariate Statistical Analysis's Theory[M].Beijing:Science Press,1999.
[2]RICHARD A,JOHNSON,DEAN W WICHERN.实用多元统计分析[M].第4版.陆璇,译.北京:清华大学出版社,2001.RICHARD A.JOHNSON,DEAN W WICHERN.Applied Multivariate Statistical Analysis[M].4rth ed.Beijing:TsinghuaUniversity Press,2001.
[3]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002.DENG Ju-long.Elements on Grey Theory[M].Wuhan:Huazhong University of Science and Technology Press,2002.
[4]林和平,刘丁慧,鲍乃源.灰色相关分析及其应用研究[J].吉林大学学报:信息科学版,2007,25(1):84-90LIN He-ping,LIU Ding-hui,BAO Nai-yuan.Grey Relation Analysis and Its Application[J].Journal of Jilin University:In-formation Science Edition,2007,25(1):84-90.
[5]WANG W P,DENG J L.Foundamantal Study of Relational Analysis in Grey System[J].Proceeding ISUMA(93)MD,1993,25(28),63-64.
[6]王炜.主成分分析在地震预测中的应用研究[J].中国地震,2005,21(3):409-416.WANG Wei.The Primary Component Analysis Method and Its Application in Earthquake Prediction[J].Earthquake Researchin China,2005,21(3):409-416.
[7]钱道翠.关于主成分分析的进一步探讨[J].嘉兴学院学报,2002,14(3):66-68.QIAN Dao-cui.The Study about Principal Component Analysis[J].Journal of Jiaxing College,2002,14(3):66-68.
[8]田波平,王勇,郭文明.主成分分析在中国上市公司综合评价中的作用[J].数学实践与认识,2004,34(4):74-80.TIAN Bo-ping,WANG Yong,GUO Wen-ming.Role of Principal Component Analysis in the Valuation of Chinese Listed Com-panies on Stock Market[J].Mathematics in Practice and Theory,2004,34(4):74-80.
[9]HEUNG-YEUNG SHUM,KATSUSHI IKEUCHI,RAJ REDDY.Principal Component Analysis with Missing Data and Its Ap-plication to Polyhedral Object Modeling[J].IEEE Transactions on Pattern Analysis and Machine Intelligence:IEEE Com-puter Society,1995,17(9):854-867.
[10]马亚静.关于我国国债风险问题的探讨[J].经济师,2005,3(2):66-67.MA Ya-jing.The Discussion of Our Country National Debt Risk[J].China Economist,2005,3(2):66-67.
[11]曾鹏.多变量时间序列的主成分分析及估计[J].南京邮电学院学报,1996,16(4):112-116.ZENG Peng.The Main Component Analysis and Estimation of Multi-Variable Time Series[J].Journal of Nanjing Institute ofPosts and Telecommunications,1996,16(4):112-116.
[12]宋涛,唐德善.基于灰色数列预测和主成分分析的国债风险仿真模型[J].统计与决策,2006,4(3):55-58.SONG Tao,TANG De-shan.Based on Grey Series Predit and Principal Component Analysis on National Debt Risk's Model[J].Statistics and Decision,2006,4(3):55-58.
[13]乔峰,姚俭.时序全局主成分分析在经济发展动态描绘中的应用[J].数理统计与管理,2003,22(2):1-5.QIAO Feng,YAO Jian.The Application of Time Series Analysis and All-Around PCA in the Economic Dynamic Description[J].Application of Statistics and Management,2003,22(2):1-5.
[14]ZHOU Z X,DENG J L.Stability Analysis of Grey Discrete Time Systems[J].IEEE,Tranc A C,1989,7(2):173-174.
[15]HYUNJIN YOON,KIYOUNG YANG,CYRUS SHAHABI.Feature Subset Selection and Feature Ranking for MultivariateTime Series[J].IEEE Transactions on Knowledge and Data Engineerin:IEEE Computer Society,2005,17(9):1186-1198.
[2]RICHARD A,JOHNSON,DEAN W WICHERN.实用多元统计分析[M].第4版.陆璇,译.北京:清华大学出版社,2001.RICHARD A.JOHNSON,DEAN W WICHERN.Applied Multivariate Statistical Analysis[M].4rth ed.Beijing:TsinghuaUniversity Press,2001.
[3]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002.DENG Ju-long.Elements on Grey Theory[M].Wuhan:Huazhong University of Science and Technology Press,2002.
[4]林和平,刘丁慧,鲍乃源.灰色相关分析及其应用研究[J].吉林大学学报:信息科学版,2007,25(1):84-90LIN He-ping,LIU Ding-hui,BAO Nai-yuan.Grey Relation Analysis and Its Application[J].Journal of Jilin University:In-formation Science Edition,2007,25(1):84-90.
[5]WANG W P,DENG J L.Foundamantal Study of Relational Analysis in Grey System[J].Proceeding ISUMA(93)MD,1993,25(28),63-64.
[6]王炜.主成分分析在地震预测中的应用研究[J].中国地震,2005,21(3):409-416.WANG Wei.The Primary Component Analysis Method and Its Application in Earthquake Prediction[J].Earthquake Researchin China,2005,21(3):409-416.
[7]钱道翠.关于主成分分析的进一步探讨[J].嘉兴学院学报,2002,14(3):66-68.QIAN Dao-cui.The Study about Principal Component Analysis[J].Journal of Jiaxing College,2002,14(3):66-68.
[8]田波平,王勇,郭文明.主成分分析在中国上市公司综合评价中的作用[J].数学实践与认识,2004,34(4):74-80.TIAN Bo-ping,WANG Yong,GUO Wen-ming.Role of Principal Component Analysis in the Valuation of Chinese Listed Com-panies on Stock Market[J].Mathematics in Practice and Theory,2004,34(4):74-80.
[9]HEUNG-YEUNG SHUM,KATSUSHI IKEUCHI,RAJ REDDY.Principal Component Analysis with Missing Data and Its Ap-plication to Polyhedral Object Modeling[J].IEEE Transactions on Pattern Analysis and Machine Intelligence:IEEE Com-puter Society,1995,17(9):854-867.
[10]马亚静.关于我国国债风险问题的探讨[J].经济师,2005,3(2):66-67.MA Ya-jing.The Discussion of Our Country National Debt Risk[J].China Economist,2005,3(2):66-67.
[11]曾鹏.多变量时间序列的主成分分析及估计[J].南京邮电学院学报,1996,16(4):112-116.ZENG Peng.The Main Component Analysis and Estimation of Multi-Variable Time Series[J].Journal of Nanjing Institute ofPosts and Telecommunications,1996,16(4):112-116.
[12]宋涛,唐德善.基于灰色数列预测和主成分分析的国债风险仿真模型[J].统计与决策,2006,4(3):55-58.SONG Tao,TANG De-shan.Based on Grey Series Predit and Principal Component Analysis on National Debt Risk's Model[J].Statistics and Decision,2006,4(3):55-58.
[13]乔峰,姚俭.时序全局主成分分析在经济发展动态描绘中的应用[J].数理统计与管理,2003,22(2):1-5.QIAO Feng,YAO Jian.The Application of Time Series Analysis and All-Around PCA in the Economic Dynamic Description[J].Application of Statistics and Management,2003,22(2):1-5.
[14]ZHOU Z X,DENG J L.Stability Analysis of Grey Discrete Time Systems[J].IEEE,Tranc A C,1989,7(2):173-174.
[15]HYUNJIN YOON,KIYOUNG YANG,CYRUS SHAHABI.Feature Subset Selection and Feature Ranking for MultivariateTime Series[J].IEEE Transactions on Knowledge and Data Engineerin:IEEE Computer Society,2005,17(9):1186-1198.
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