English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper proposes an original Riemmanian geometry for low-rank structuredelliptical models, i.e., when samples are elliptically distributed with acovariance matrix that has a low-rank plus identity structure. The consideredgeometry is the one induced by the product of the Stiefel manifold and themanifold of Hermitian positive definite matrices, quotiented by the unitarygroup. One of the main contribution is to consider an original Riemannianmetric, leading to new representations of tangent spaces and geodesics. Fromthis geometry, we derive a new Riemannian optimization framework for robustcovariance estimation, which is leveraged to minimize the popular Tyler's costfunction on the considered quotient manifold. We also obtain a new divergencefunction, which is exploited to define a geometrical error measure on thequotient, and the corresponding intrinsic Cram\'er-Rao lower bound is derived.Thanks to the structure of the chosen parametrization, we further consider thesubspace estimation error on the Grassmann manifold and provide its intrinsicCram\'er-Rao lower bound. Our theoretical results are illustrated on somenumerical experiments, showing the interest of the proposed optimizationframework and that performance bounds can be reached.

A Riemannian Framework for Low-Rank Structured Elliptical Models