Timezone: »

 
Poster
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
Andi Han · Bamdev Mishra · Pratik Kumar Jawanpuria · Junbin Gao

Wed Dec 08 12:30 AM -- 02:00 AM (PST) @
in Poster Session 3 »

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-conditioned SPD matrices. We show that the BW geometry has a non-negative curvature, which further improves convergence rates of algorithms over the non-positively curved AI geometry. Finally, we verify that several popular cost functions, which are known to be geodesic convex under the AI geometry, are also geodesic convex under the BW geometry. Extensive experiments on various applications support our findings.

Keywords: Optimization

Author Information

Andi Han (University of Sydney)
Bamdev Mishra (Microsoft)
Pratik Kumar Jawanpuria (Microsoft)
Junbin Gao (University of Sydney)

More from the Same Authors