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The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by $X^{p}LX...
This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein distances. While the Alpha-Procrustes framework has unified many classical metrics i...
This work proposes a novel block-diagonal Riemannian metric derived from the pullback of the Frobenius inner product and develops a Riemannian gradient descent algorithm that uses a tuning-free Gaussian step size and scales linearly in the number of observed entries per iteration.
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