Diagonality Measures of Hermitian Positive-Definite Matrices with Application to the Approximate Joint Diagonalization Problem [PDF]
arXiv.org, 2016 In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part.
Alyani, Khaled +2 more
core +4 more sources
Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices
Entropy, 2016 The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective ...
Hatem Hajri +4 more
doaj +2 more sources
Tensor Sparse Coding for Positive Definite Matrices [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014 In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data.
Ravishankar, Sivalingam +3 more
openaire +4 more sources
Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices. [PDF]
Int Stat Rev, 2016 Schwartzman A.
europepmc +2 more sources
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization, 2019 openaire +2 more sources
Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals [PDF]
International Conference on Machine Learning, 2023 When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals.
Clément Bonet +6 more
semanticscholar +1 more source
Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization [PDF]
SIAM Journal on Matrix Analysis and Applications, 2021 We address the problem of computing the smallest symplectic eigenvalues and the corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theorem.
N. T. Son, P. Absil, Bin Gao, T. Stykel
semanticscholar +1 more source
Probabilistic Learning Vector Quantization on Manifold of Symmetric Positive Definite Matrices [PDF]
Neural Networks, 2021 In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices,
Fengzhen Tang +4 more
semanticscholar +1 more source
IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2017 Xiaofeng Xie +4 more
semanticscholar +3 more sources
On the Bures–Wasserstein distance between positive definite matrices [PDF]
Expositiones mathematicae, 2017 The metric $d(A,B)=\left[ \tr\, A+\tr\, B-2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2}$ on the manifold of $n\times n$ positive definite matrices arises in various optimisation problems, in quantum information and in the theory of optimal transport.
R. Bhatia, Tanvi Jain, Y. Lim
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