학술행사
- 발표자 임용도 교수(성균관대학교)
- 기간 2022-12-15 ~ 2022-12-15
- 주최 산업수학혁신센터
- 일시: 2022년 12월 15일(목), 14:00-16:00
- 장소: 판교 테크노밸리 산업수학혁신센터 세미나실 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소 /무료주차는 2시간 지원됩니다.
- 발표자: 임용도 교수(성균관대학교)
- 주제: Averages of manifold-valued data
- 초록: Positive definite matrices have become fundamental computational objects in many areas of engineering, computer science, physics, statistics, and applied mathematics. They appear in a diverse variety of settings: covariance matrices in statistics, elements of the search space in semidefinite programming, kernels in machine learning, density matrices in quantum information, data points in radar imaging, diffusion tensors in medical imaging, to cite only a few. A big problem regarding the Cartan-Hadamard-Riemannian (resp. Wasserstein) manifold of positive definite matrices is finding the best averaging of points in such a way that the resulting point is again positive definite and is invariant under the action of inversion and (resp. unitary) congruence transformations. In this talk, we introduce the Cartan and Wasserstein means of positive definite matrices and discuss several open problems.
- 현장강의로만 진행됩니다.
- 일시: 2022년 12월 15일(목), 14:00-16:00
- 장소: 판교 테크노밸리 산업수학혁신센터 세미나실 경기 성남시 수정구 대왕판교로 815, 기업지원허브 231호 국가수리과학연구소 /무료주차는 2시간 지원됩니다.
- 발표자: 임용도 교수(성균관대학교)
- 주제: Averages of manifold-valued data
- 초록: Positive definite matrices have become fundamental computational objects in many areas of engineering, computer science, physics, statistics, and applied mathematics. They appear in a diverse variety of settings: covariance matrices in statistics, elements of the search space in semidefinite programming, kernels in machine learning, density matrices in quantum information, data points in radar imaging, diffusion tensors in medical imaging, to cite only a few. A big problem regarding the Cartan-Hadamard-Riemannian (resp. Wasserstein) manifold of positive definite matrices is finding the best averaging of points in such a way that the resulting point is again positive definite and is invariant under the action of inversion and (resp. unitary) congruence transformations. In this talk, we introduce the Cartan and Wasserstein means of positive definite matrices and discuss several open problems.
- 현장강의로만 진행됩니다.
