The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Principal Component Analysis of Compositional Data using Box-Cox Contrast Transformation

Box-Cox 대비변환을 이용한 구성비율자료의 주성분분석

  • Published : 2001.03.01
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Abstract

Compositional data found in many practical applications consist of non-negative vectors of proportions with the constraint which the sum of the elements of each vector is unity. It is well-known that the statistical analysis of compositional data suffers from the unit-sum constraint. Moreover, the non-linear pattern frequently displayed by the data does not facilitate the application of the linear multivariate techniques such as principal component analysis. In this paper we develop new type of principal component analysis for compositional data using Box-Cox contrast transformation. Numerical illustrations are provided for comparative purpose.

비율을 나타내는 요소들로 이루어진 구성비율자료는 각 행들의 합이 1이 되는 제약을 가지고 있어 통계적으로 다루기가 쉽지 않다. 더구나 자료의 구조가 선형적인 형태를 보이지 않는 특성을 가지기 때문에 주성분분석과 같은 선형적인 다변량기법들을 구성비율자료에 적용을 할 때 잘못된 해석과 추론이 이루어질 가능성이 있다. 본 논문에서는 구성비율자료의 주성분분석에서 기존의 방법들이 가지는 문제점을 해결하기 위해 Box-Cox 대비변환(Box-Cox contrast transformation)을 이용한 새로운 형태의 분석방법을 제시한다. 그리고 실제자료의 분석과 모의실험을 통해서 Aitchison(1983)이 제시한 방법과 수행능력을 비교하고자 한다.

Keywords

References

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