The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Separating Signals and Noises Using Mixture Model and Multiple Testing

혼합모델 및 다중 가설 검정을 이용한 신호와 잡음의 분류

  • Park, Hae-Sang (Department of Industrial and Management Engineering POSTECH) ;
  • Yoo, Si-Won (Customer Satisfaction Improvement Team, NHN) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH)
  • 박해상 (포항공과대학교 산업경영공학과) ;
  • 유시원 (NHN 고객만족추진팀) ;
  • 전치혁 (포항공과대학교 산업경영공학과)
  • Published : 2009.08.31
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Abstract

A problem of separating signals from noises is considered, when they are randomly mixed in the observation. It is assumed that the noise follows a Gaussian distribution and the signal follows a Gamma distribution, thus the underlying distribution of an observation will be a mixture of Gaussian and Gamma distributions. The parameters of the mixture model will be estimated from the EM algorithm. Then the signals and noises will be classified by a fixed threshold approach based on multiple testing using positive false discovery rate and Bayes error. The proposed method is applied to a real optical emission spectroscopy data for the quantitative analysis of inclusions. A simulation is carried out to compare the performance with the existing method using 3 sigma rule.

본 논문은 신호와 잡음이 혼합된 관측치로부터 신호 관측치를 분류하는 문제를 다룬다. 잡음은 가우시안 분포를 따르고 신호는 감마 분포를 따른다고 가정할 때 관측치의 분포는 가우시안과 감마의 혼합 분포를 따르게 된다. EM 알고리즘을 통해 혼합 모델의 모수를 추정하고 신호 및 잡음을 분류하는 것을 다중 가설 검정으로 간주하여 베이즈 오류를 바탕으로 분류를 위한 경계치를 설정한다. 제안하는 방법을 분광 데이터에 근거하여 철강 제품에서 개재물 유무를 검출하는 문제에 적용하였고 별도의 시뮬레이션 데이터를 통해 성능의 우수성을 보였다.

Keywords

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