Papers › Quotient geometry of bounded or fixed rank correlation matrices
Quotient geometry of bounded or fixed rank correlation matrices
Hengchao Chen
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper studies the quotient geometry of bounded or fixed-rank correlation matrices. We establish a bijection between the set of bounded-rank correlation matrices and a quotient set of a spherical product manifold by an orthogonal group. We show that it forms an orbit space, whose stratification is determined by the rank of the matrices, and the principal stratum has a compatible Riemannian quotient manifold structure. We show that any minimizing geodesic in the orbit space has constant rank on the interior of the segment. We also develop efficient Riemannian optimization algorithms for computing the distance and weighted the Frechet mean in the orbit space. Moreover, we examine geometric properties of the quotient manifold, including horizontal and vertical spaces, Riemannian metric, injectivity radius, exponential and logarithmic map, curvature, gradient and Hessian. Finally, we apply our approach to a functional connectivity study using the Autism Brain Imaging Data Exchange.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections