基于成分数据处理的主成分分析研究

Principal Component Analysis Research Based on Component Data Processing

由于成分数据的定和限制,传统的主成分分析在成分数据的应用上会产生一定的不适性,从而得出不可靠的推断。为了解决主成分分析在成分数据中的局限性,将成分数据进行适当的处理变换显得十分重要。以数学建模赛题中的古代玻璃文物化学成分数据为例,对成分数据进行加性、中心化和等距3种不同的对数比变换,基于KMO检验和Bartlett球形度检验只有加性对数比转换后的数据更适合做主成分分析,且获得的结果更加准确。此研究过程为成分数据的主成分分析提供了有效的借鉴思路和方法。

Due to the limitation of component data,traditional principal component analysis will produce certain discomfort in the application of component data,resulting in unreliable inferences.In order to solve the limitations of principal component analysis in component data,it is important to properly process and transform the component data.Taking the chemical compositional data of ancient glass relics in the mathematical modeling contest as an example,three different log-ratio transformations of additive,centralized and isometric were carried out on the compositional data.Based on KMO test and Bartlett spherical test,only the additive log-ratio transformed data was more suitable for principal compositional analysis,and the results obtained were more accurate.This research process provides effective reference ideas and methods for principal component analysis of component data.