Department of Applied Mathematics, Sejong University, Seoul, 143-747, Korea.
Behav Res Methods. 2012 Dec;44(4):1239-43. doi: 10.3758/s13428-012-0193-1.
Principal component analysis identifies uncorrelated components from correlated variables, and a few of these uncorrelated components usually account for most of the information in the input variables. Researchers interpret each component as a separate entity representing a latent trait or profile in a population. However, the components are guaranteed to be independent and uncorrelated only when the multivariate normality of the variables is assumed. If the normality assumption does not hold, components are guaranteed to be uncorrelated, but not independent. If the independence assumption is violated, each component cannot be uniquely interpreted because of contamination by other components. Therefore, in the present study, we introduced independent component analysis, whose components are uncorrelated and independent even when the multivariate normality assumption is violated, and each component carries unique information.
主成分分析从相关变量中识别出不相关的成分,其中少数几个不相关的成分通常可以解释输入变量中的大部分信息。研究人员将每个成分解释为代表人群中潜在特征或特征的单独实体。然而,只有当变量的多元正态性假设成立时,才能保证这些成分是独立的且不相关的。如果正态性假设不成立,则可以保证成分是不相关的,但不是独立的。如果独立性假设被违反,由于其他成分的污染,每个成分都不能被唯一地解释。因此,在本研究中,我们引入了独立成分分析,即使多元正态性假设被违反,其成分也是不相关和独立的,并且每个成分都携带独特的信息。
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