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?
An important research subject is to reveal the correlation of two meteorologica l fields while analyzing in the meteorological data. In this field, two kin ds of different analytical methods exist at present: one is canonica l correlation analysis, abbreviated as CCA; the other is singular value decompos ition, abbreviated as SVD. CCA and SVD is compared using theory ana lysis, method comparison and example calculation. Four principal results have be en achieved as follows. Firstly, to the same data X and Y , after carrying on relevant ana lysis with CCA and SVD method separately, the results are total different. The r esults indicate that SVD cannot distill correlativity of two variable fields eff ectively, but CCA can distill them as effectively as possible. Correlation of CC A combination variable fields can embody more correlativity of original variable fields than that of SVD, and using CCA eigenvector fields to express their corr elation distribution are significant than using that of SVD. The example calcula tion also shows that maximal correlations obtained from the two methods have pro minent difference and the value of correlation coefficient of CCA is obviously b igger than that of SVD. Secondly, it is more significant to study the correlatio ns of source variable fields through studying the correlation of combination var iable fields using CCA than that of using SVD. The combination variable fields o btained from CCA are independent and orthogonal but not for SVD. Thirdly, it is obvious that CCA is more fully and truly embody the correlativity of original va riable fields than that of SVD for CCA takes into account that the self change o f each variable fields when studying original variable fields but not for SVD. F inally, it is deserved to study more about the results obtained from SVD in resp ect that the correlation between x and y is significant if CCA is adopted.
出处
《气象学报》
CAS
CSCD
北大核心
2004年第1期71-76,共6页
Acta Meteorologica Sinica
基金
云南省重点基金项目 ( 2 0 0 3D0 0 1 42 )
国家科委基金项目( 40 0 6 50 0 1 )共同资助
