基于误差理论的区间主成分分析及其应用

针对区间数样本,传统的主成分分析需进行拓展。首先讨论了区间样本数据的两种主要来源,即观测误差和符号数据分析。然后将区间数看作一个由中点和半径构成的具有一定误差的数,从误差理论出发,研究基于误差传递公式的区间主成分分析方法,并获得以区间数为表达形式的主成分。最后,结合我国2005年第四季度股票市场的数据进行了实证分析。结果表明,面对海量数据,区间PCA较传统PCA更容易从总体上把握样本的属性。

Principal Component Analysis Based on Error Theory and Its Application

The original principal component analysis(PCA) needs to be extended when the data are intervals.The two main sources of interval sample data are proposed,which are measurement error and symbolic data analysis.An interval number can be seen as a number composed of its center and its radius which denotes the error of the interval number.Based on the error theory,a method of interval PCA is put forward through error transferring formula.The method can give interval principal components.Finally,an empirical study is made on Chinese stock market of the forth quarter in 2005.It implicates that the interval PCA method is more useful than the traditional PCA to gain the overall property of the samples when the data is enormous.