Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization
نویسندگان
چکیده
Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization
منابع مشابه
Riemannian Metric Learning for Symmetric Positive Definite Matrices
Over the past few years, symmetric positive definite matrices (SPD) have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the two most widely-used measures are affine-invariant distance and log-Euclidean distance. This is because these two measures are true geodesic distances induced...
متن کاملA Riemannian quasi-Newton method for computing the Karcher mean of symmetric positive definite matrices
This paper tackles the problem of computing the Karcher mean of a collection of symmetric positive-definite matrices. We present a concrete limited-memory Riemannian BFGS method to handle this computational task. We also provide methods to produce efficient numerical representations of geometric objects on the manifold of symmetric positive-definite matrices that are required for Riemannian opt...
متن کاملA Trace Bound for Positive Definite Connected Integer Symmetric Matrices
Let A be a connected integer symmetric matrix, i.e., A = (aij) ∈ Mn(Z) for some n, A = AT , and the underlying graph (vertices corresponding to rows, with vertex i joined to vertex j if aij 6= 0) is connected. We show that if all the eigenvalues of A are strictly positive, then tr(A) ≥ 2n− 1. There are two striking corollaries. First, the analogue of the Schur-SiegelSmyth trace problem is solve...
متن کاملWasserstein Riemannian Geometry of Positive-definite Matrices∗
The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we derive an explicit form of the Riemannian metrics on positive-definite matrices and compute its tensor form with respect to the trace scalar product. The tensor is a matrix, which is the solution of a Lyapunov equation. W...
متن کاملRiemannian Sparse Coding for Positive Definite Matrices
Inspired by the great success of sparse coding for vector valued data, our goal is to represent symmetric positive definite (SPD) data matrices as sparse linear combinations of atoms from a dictionary, where each atom itself is an SPD matrix. Since SPD matrices follow a non-Euclidean (in fact a Riemannian) geometry, existing sparse coding techniques for Euclidean data cannot be directly extende...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2021
ISSN: ['1095-7162', '0895-4798']
DOI: https://doi.org/10.1137/21m1390621