# Generalized Bures-Wasserstein Geometry for Positive Definite Matrices

@inproceedings{Han2021GeneralizedBG, title={Generalized Bures-Wasserstein Geometry for Positive Definite Matrices}, author={Andi Han and Bamdev Mishra and Pratik Jawanpuria and Junbin Gao}, year={2021} }

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices. We explore the generalization of the BW geometry in three different ways: 1) by generalizing the Lyapunov operator in the metric, 2) by generalizing the orthogonal Procrustes distance, and 3) by generalizing the Wasserstein distance between the Gaussians. We show that they all lead to the same geometry. The proposed generalization is parameterized by a symmetric…

## One Citation

On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry

- Computer Science, MathematicsArXiv
- 2021

This study comparatively analyzes the Bures-Wasserstein geometry with the popular Affine-Invariant geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold to show that the BW metric is a more suitable and robust choice for several RiemANNian optimization problems over ill-conditioned SPD matrices.

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This study comparatively analyzes the Bures-Wasserstein geometry with the popular Affine-Invariant geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold to show that the BW metric is a more suitable and robust choice for several RiemANNian optimization problems over ill-conditioned SPD matrices.

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