The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Case study: application of fused sliced average variance estimation to near-infrared spectroscopy of biscuit dough data

Fused sliced average variance estimation의 실증분석: 비스킷 반죽의 근적외분광분석법 분석 자료로의 적용

  • Um, Hye Yeon (Department of Statistics, Ewha Womans University) ;
  • Won, Sungmin (Department of Statistics, Ewha Womans University) ;
  • An, Hyoin (Department of Statistics, Ewha Womans University) ;
  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University)
  • 엄혜연 (이화여자대학교 통계학과) ;
  • 원성민 (이화여자대학교 통계학과) ;
  • 안효인 (이화여자대학교 통계학과) ;
  • 유재근 (이화여자대학교 통계학과)
  • Received : 2018.11.22
  • Accepted : 2018.11.24
  • Published : 2018.12.31
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Abstract

The so-called sliced average variance estimation (SAVE) is a popular methodology in sufficient dimension reduction literature. SAVE is sensitive to the number of slices in practice. To overcome this, a fused SAVE (FSAVE) is recently proposed by combining the kernel matrices obtained from various numbers of slices. In the paper, we consider practical applications of FSAVE to large p-small n data. For this, near-infrared spectroscopy of biscuit dough data is analyzed. In this case study, the usefulness of FSAVE in high-dimensional data analysis is confirmed by showing that the result by FASVE is superior to existing analysis results.

충분차원축소의 대표적 방법론 중 하나인 sliced average variance estimation (SAVE)은 슬라이스라고 불리우는 반응변수의 범주화의 총 수에 민감하다고 알려져 있다. 이러한 점을 극복하기 위한 방법으로 최근에 다양한 수의 슬라이스로부터 얻어진 SAVE의 정보를 결합하는 fused SAVE (FSAVE)가 개발되었다. 본 논문에서는 소위 large p-small n 자료라고 불리우는 자료의 수가 변수의 수보다 적은 자료에서 FASVE가 어떻게 실제적으로 사용될 수 있을지에 대해 실증적 분석을 하고자 한다. 이를 위해 근적외분광분석을 통해 얻어진 비스킷 자료를 이용할 것이고, 이러한 자료분석에서 FASVE에 의한 차원축소에 의해 분석된 결과가 기존의 방법론에 비해 우수함을 보고자 한다.

Keywords

Table 3.1. Dimension estimation in cookie data

GCGHDE_2018_v31n6_835_t0001.png 이미지

Table 3.2. MSEs from FSAVE, partial least squares and principal component regression

GCGHDE_2018_v31n6_835_t0002.png 이미지

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