• Corpus ID: 235266078

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

@article{Han2021OnRO,
  title={On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry},
  author={Andi Han and Bamdev Mishra and Pratik Jawanpuria and Junbin Gao},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.00286}
}
In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an observation that the BW metric has a linear dependence on SPD matrices in contrast to the quadratic dependence of the AI metric. We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill… 
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