典型相关分析及其应用实例.docVIP

摘 要 典型相关分析是多元统计分析的一个重要研究课题.它是研究两组变量之间相关的一种统计分析方法，能够有效地揭示两组变量之间的相互线性依赖关系.它借助主成分分析降维的思想，用少数几对综合变量来反映两组变量间的线性相关性质.目前它已经在众多领域的相关分析和预测分析中得到广泛应用. 本文首先描述了典型相关分析的统计思想，定义了总体典型相关变量及典型相关系数，并简要概述了它们的求解思路，然后深入对样本典型相关分析的几种算法做了比较全面的论述.根据典型相关分析的推理，归纳总结了它的一些重要性质并给出了证明，接着推导了典型相关系数的显著性检验.最后通过理论与实例分析两个层面论证了典型相关分析的应用于实际生活中的可行性与优越性.【关键词】 典型相关分析，样本典型相关，性质，实际应用 ABSTRACT The Canonical Correlation Analysis is an important studying topic of theMultivariate Statistical Analysis. It is the statistical analysis method which studies thecorrelation between two sets of variables. It can work to reveal the mutual linedependence relation availably between two sets of variables. With the help of thethought about the Principal Components we can use a few comprehensive variablesto reflect the linear relationship between two sets of variables. Nowadays It hasalready been used widely in the correlation analysis and forecasted analysis. This text describes the statistical thought of the Canonical Correlation Analysisfirstly and then defines the total canonical correlation variables and canonicalcorrelation coefficient and sum up their solution method briefly. After it I go deepinto discuss some algorithm of the sample canonical correlation analysis thoroughly.According to the reasoning of the Canonical Correlation Analysis sum up some of itsimportant properties and give the identification following it I infer the significancetesting about the canonical correlation coefficient. According to the analysis from thetheories and the application we can achieve the possibility and the superiority fromcanonical correlation analysis in the real life.【Key words】Canonical Correlation Analysis，Sample canonical correlation， Character，Practical applications 目 录前 言...............................................................1第1章 典型相关分析的数学描述......................................2第2章 典型变量与典型相关系数......................................3 2.1 总体典型相关 ................................................3 2.2 样本典型相关 ................