11 papers
Halving the size of skew-symmetric eigenvalue problems via the polar decomposition
Daniel Kressner, Simon Mataigne
This paper introduces a novel algorithm for computing eigenvalues and eigenvectors of a dense real skew-symmetric matrix . Its main ingredient is the computation of a polar fact…
A Jacobi-like algorithm for normal matrices by the skew-symmetric part
Simon Mataigne, P. -A. Absil
We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using…
bispectrum: Selective -Bispectra Made Practical
Johan Mathe, Adele Myers, Simon Mataigne +1
Many machine learning tasks are invariant under the action of a group of transformations: signal classification can be invariant under translations, image classification under…
The sketched landing method for large-scale optimization under orthogonality constraints
Florentin Goyens, Simon Mataigne, Pierre-Antoine Absil
We propose the sketched landing method, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a norm…
Shortest Geodesic Loops, Sectional Curvature, and Injectivity Radius of the Stiefel Manifold
Jakob Stoye, Simon Mataigne, P. -A. Absil +1
We determine the length of the shortest nontrivial geodesic loops on the Stiefel manifold endowed with any member of the one-parameter family of Riemannian metrics introduced by Hü…
On the approximation of the Riemannian barycenter
Simon Mataigne, P. -A. Absil, Nina Miolane
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 pro…
The eigenvalue decomposition of normal matrices by the skew-symmetric part
Simon Mataigne, Kyle A. Gallivan
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix through the decomposition of its skew-symmetric part. The method relies on algo…
Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, P. -A. Absil, Nina Miolane
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riem…
The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
Simon Mataigne, Johan Mathe, Sophia Sanborn +2
An important problem in signal processing and deep learning is to achieve \textit{invariance} to nuisance factors not relevant for the task. Since many of these factors are describ…
An efficient algorithm for the Riemannian logarithm on the Stiefel manifold for a family of Riemannian metrics
Simon Mataigne, Ralf Zimmermann, Nina Miolane
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems…
The ultimate upper bound on the injectivity radius of the Stiefel manifold
P. -A. Absil, Simon Mataigne
We exhibit conjugate points on the Stiefel manifold endowed with any member of the family of Riemannian metrics introduced by Hüper et al. (2021). This family contains the well-kno…