CCA与SVD分析方法比较研究

THE STUDY ON CCA AND SVD ANALYTICAL METHODS

中文关键词:  CCA  SVD  特征向量  组合变量  相关

英文关键词:CCA  SVD  Eigenvector  Combination variables  Correlation

中文摘要:

      文中从理论分析、方法比较以及实例计算几方面,对目前气象资料处理分析中常用的CCA与SVD分析方法进行了比较,结果表明:(1)对同样的变量组X,Y分别用CCA和SVD方法进行相关分析,得到了完全不同的分析结果,CCA所得到的相关就是原始变量组X,Y之间的相关;SVD所得到的相关是组合变量L,M间的相关而不是原始变量组X,Y之间的相关。理论分析和实例计算都表明,两种方法分析得到的最大相关有非常显著的差别,CCA明显比SVD要大得多,且CCA收敛快而SVD收敛慢。所以SVD不能有效地提取两组变量或两个变量场之间相关关系的主要特征,只有CCA才能最大限度地提取它们之间相关关系的主要特征。(2)CCA所得出的两变量组的变量是独立正交变量,所以通过分析CCA组合变量间的相关来表示原变量组间的相关关系是有意义的。而SVD所得到的两变量组的变量不具有独立性和正交性,信息提供重复,存在共线性,所以通过分析SVD组合变量来表示两变量组的相关关系没有CCA方法有意义。(3)CCA是在考虑了各个变量场自身变化的情况下来分解两个变量场间的相关关系;而SVD是在没有考虑各个变量场自身变化的情况下来分解两个变量场间的协方差关系。很显然,CCA比SVD更全面、更完整和更准确。(4)凡用SVD方法分析得到的结论,由于总可以重新应用CCA方法找到相关更好的不同结果,所以有值得进一步探讨的必要。

英文摘要:

      An important research subjectis to reveal the correlation of two meteorolog ical fields while analyzing in the meteorological data.In this field,two kinds of different analytical methods existat present:one is canonical correlation analysis,abbrev iated as CCA;the other is singular value decomposition,abbreviated as SVD.CCA and SVD is compared using theory analysis,method comparison and example calculation.Four principal results have been achieved as folows.Firstly,to the same data X and Y,after carrying on relevant analysis with CCA and SVD method separately,the results are total different.The results indicate that SVD cannot distill correlativity of two variable fields effectively,but CCA can distill themas effectively as possible.Correlation of CCA combination variable fields can embody more correlativity of original variable fields than that of SVD,and using CCA eigenvect or fields to express their correlation distribution are significant than using that of SVD.The example calculation also shows that maximal correlations obtained from the two methods have prominent difference and the value of correlation coefficient of CCA is obviously bigger than that of SVD.Secondly,it is more significant to study the correlations of source variable fields through studying the correlation of combination variable fields using CCA than that of using SVD.The combination variable fields obtained from CCA are independent and or thogonal but not for SVD.Thirdly,it is obvious that CCA is more fully and truly embody the correlativity of original variable fields than that of SVD for CCA takes into account that the self change of each variable fields when studying original variable fields but not for SVD.Finally,it is deserved to study more about the results obtained from SVD in respect that the correlation between x and y is significant if CCA is adopted.