Results 11 to 20 of about 294,893 (309)
A Canonical Form for Positive Definite Matrices [PDF]
Open Book Series, 2020 We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.
Haensch, Anna +3 more
core +6 more sources
Bayesian Nonparametric Clustering for Positive Definite Matrices [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016 Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are ...
Anoop, Cherian +2 more
semanticscholar +5 more sources
POSITIVE-DEFINITE MATRICES OVER FINITE FIELDS [PDF]
Rocky Mountain Journal of Mathematics, 2022 The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes. In the classical setting, positive-definite matrices enjoy a multitude of equivalent definitions and properties.
Cooper, Joshua +2 more
openaire +4 more sources
Ordering positive definite matrices [PDF]
Information Geometry, 2018 We introduce new partial orders on the set Sn+$$S^+_n$$ of positive definite matrices of dimension n derived from the affine-invariant geometry of Sn+$$S^+_n$$. The orders are induced by affine-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous geometry of Sn+$$S^+_n$$ defined by ...
Cyrus Mostajeran, Rodolphe Sepulchre
semanticscholar +6 more sources
Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
Mathematics, 2016 We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X )
Jean-Paul Chehab, Marcos Raydan
doaj +5 more sources
Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation. [PDF]
J Stat Comput Simul, 2018 We present geodesic Lagrangian Monte Carlo, an extension of Hamiltonian Monte Carlo for sampling from posterior distributions defined on general Riemannian manifolds.
Holbrook A +3 more
europepmc +3 more sources
Intrinsic data depth for Hermitian positive definite matrices [PDF]
Journal of Computational And Graphical Statistics, 2018 Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian positive ...
Chau, Joris +2 more
core +2 more sources
Approximate joint diagonalization and geometric mean of symmetric positive definite matrices. [PDF]
PLoS ONE, 2014 We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint ...
Marco Congedo +3 more
doaj +2 more sources
NeuroImage, 2021 Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure ...
Kisung You, Hae-Jeong Park
doaj +2 more sources
Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition [PDF]
SIAM Journal on Matrix Analysis and Applications, 2019 We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space, the collection
Zhenhua Lin
semanticscholar +3 more sources