The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A summary on the distance metric between two subspaces

두 부공간의 거리측도에 대한 요약

  • Kipoong Kim (Department of Statistics, Seoul National University) ;
  • Choongrak Kim (Department of Statistics, Pusan National University)
  • Received : 2023.05.23
  • Accepted : 2023.05.30
  • Published : 2023.06.30
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Abstract

In this paper, we introduced distance metric between two subspaces. For this, several matrix norms such as the spectral norm and the Frobenius norm are introduced. Further, the distance between two matrices based on the projection and principal angles are introduced. Finally, its application to the matrix perturbation theory with the famous Davis-Kahan theorem (1970) is illlustrated.

본 논문에서는 두 부공간의 거리측도에 대해 소개하였다. 이를 위해 여러 가지 행렬의 노름을 소개하고 주어진 노름하에서 여러 가지 행렬간의 거리측도를 소개하였으며 이들간의 관계를 설명하였다. 이를 이용하여 행렬의 교란이론에 적용하고 교란이론의 핵심적 결과인 Davis-Kahan (1970) 정리를 소개하였다. 두 부공간의 거리측도는 통계학의 다양한 분야 뿐만 아니라 후방탐색, 안면인식 등 인공지능의 중요한 분야에 많이 활용되고 있다.

Keywords

Acknowledgement

본 연구는 부산대학교 2년 과제 연구비에 의하여 수행되었음.

References

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