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.