Studies And Applications Of Grouped Principal Component Analysis And Kernel Principal Component Analysis

Multivariate statistical analysis is an important branch of statistics, which hasbeen widely applied in scientific researches and real life. However, the directapplication of principal component analysis, one of the key multivariate statisticalmethods, can result in a conclusion incompatible with reality and even a significantbias. Thus, it is of great importance to improve the principal component analysis. Andthe thesis, which aims to improve traditional principal component analysis, is mainlyunfolded from two aspects namely grouped principal component analysis and kernelprincipal component analysis.Firstly, on the basis of related references, mathematic form of grouped principalcomponent analysis is described in detail. Based on the improved grouped principalcomponent analysis, which improved the component score coefficient of factors, theeconomic development of Jiangsu Province in2010is analyzed, which has provedthat the result is closer to reality than that of the traditional principal componentsanalysis. And the same conclusion can be drawn as well from the further researchconcerning the economic development of Jiangsu Province between2009and2012.Secondly, improved kernel principal component model has an obvious advantageover other analysis methods in dealing with nonlinear data by using Matlab to debug asuitable kernel parameters and thus offering a simple algorithm afterwards to analyzethe living standard of residents of Jiangsu Province in2010. And the same conclusioncan be drawn as well from the further research concerning the living standard ofresidents of Jiangsu Province between2009and2012.Finally, as the conclusive part of the whole thesis, has layed out some unsolvedproblems and prospects for further researches.