The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Principal component analysis in the frequency domain: a review and their application to climate data

주파수공간에서의 주성분분석: 리뷰와 기상자료에의 적용

  • Jo, You-Jung (Department of Statistics, Seoul National University) ;
  • Oh, Hee-Seok (Department of Statistics, Seoul National University) ;
  • Lim, Yaeji (Department of Statistics, Pukyong National University)
  • Received : 2017.03.16
  • Accepted : 2017.05.11
  • Published : 2017.06.30
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Abstract

In this paper, we review principal component analysis (PCA) procedures in the frequency domain and apply them to analyze sea surface temperature data. The classical PCA defined in the time domain is a popular dimension reduction technique. Extending the conventional PCA to the frequency domain makes it possible to define PCA in the frequency domain, which is useful for dimension reduction as well as a feature extraction of multiple time series. We focus on two PCA methods in the frequency domain, Hilbert PCA (HPCA) and frequency domain PCA (FDPCA). We review these two PCAs in order for potential readers to easily understand insights as well as perform a numerical study for comparison with conventional PCA. Furthermore, we apply PCA methods in the frequency domain to sea surface temperature data on the tropical Pacific Ocean. Results from numerical experiments demonstrate that PCA in the frequency domain is effective for the analysis of time series data.

본 논문에서는 주파수공간에서의 주성분 분석을 사용하여 기상자료를 분석하고자 한다. 주파수공간에서의 주성분분석은 차원축소를 위해서도 사용되지만, 주요한 패턴을 뽑아내는 데 사용되는 통계적 방법 중 하나이다. 일반적으로 주파수공간에서의 주성분 분석은 두 가지의 방법이 있는데, Hilbert PCA와 frequency domain PCA가 그것이다. 본 논문에서는 기존의 시간공간 주성분 분석과 함께 두 가지 주파수공간 주성분 분석 방법을 비교하였다. 시뮬레이션 자료를 통하여 주파수공간 주성분 분석 방법의 유용성을 보였으며, 열대 태평양 지역의 해수표층 온도값에 주성분 분석 방법들을 적용하여 기상자료 분석에 대한 유용성을 확인하였다.

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References

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