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math.FA2021★ 1 cited
Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry
Andi Han, Bamdev Mishra, Pratik Jawanpuria +1
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning. Consequently, understanding the Riemannian geometry of SPD matrices has attracte…
cs.LG2021
A Discussion On the Validity of Manifold Learning
Dai Shi, Andi Han, Yi Guo +1
Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroi…
math.OC2021★ 8 cited
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
Andi Han, Bamdev Mishra, Pratik Jawanpuria +1
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 de…