On the Approximation of the Riemannian Barycenter

Simon Mataigne

doi:10.1007/978-3-032-03921-7_2

On the Approximation of the Riemannian Barycenter

2026-01-01

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S

Simon Mataigne *

P

P.-A. Absil

N

Nina Miolane

DOI：10.1007/978-3-032-03921-7_2

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Abstract

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We present a method for computing an approximate Riemannian barycenter of a collection of points lying on a Riemannian manifold. Our approach relies on the use of theoretically proven under- and over-approximations of the Riemannian distance function. We compare it to Riemannian steepest descent on the exact objective function of the Riemannian barycenter and to an approach that approximates the Riemannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.

Keywords:

Riemannian barycenter

Karcher mean

Frechet mean

Riemannian center of mass

Bounds

Stiefel manifold

On the Approximation of the Riemannian Barycenter

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