symmetric positive-definite matrices
Kernel density estimation on spaces of Gaussian distributions and symmetric positive definite matrices
... of symmetric positive definite matrices under the affine-invariant met- ric and the space of univariate Gaussian distributions is isometric to the hyperbolic ...
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Random projections on manifolds of Symmetric Positive Definite matrices for image classification
... To address the above issue, two lines of research have been proposed: (1) embedding manifolds into tangent spaces [21, 24, 27, 35, 36]; (2) embedding into Reproduc- ing Kernel Hilbert Spaces (RKHS), induced by kernel ...
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Motor Imagery Classification Based on Bilinear Sub-Manifold Learning of Symmetric Positive-Definite Matrices
... the symmetric positive-definite (SPD) covariance matrices of electroencephalogram (EEG) signals carry important discriminative ...SPD matrices endowed with Riemannian distance is a ...
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Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection
... the constraints. It is well known that the Bregman projection into the intersection of convex re- gions can be solved by sequential projections to each region (Bregman, 1967; Censor and Lent, 1981). In the original ...
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Multisplitting Iterative Methods with General Weighting Matrices for Solving Symmetric Positive Linear Complementarity Problem
... weighting matrices of the multisplitting parallel methods for solving the symmetric positive definite linear complementarity problem, which is a powerful alternative for solving the large ...
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Integrals of Four Variables with Statistical Distribution associated with hyper geometric Function of Matrix Argument
... In this paper, we have evaluated forty integrals associated with hypergeometric function of four variables of matrix argument with their statistical distribution. All the matrices involved are real positive ...
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Translucent Voices: Creating Sound Pedagogy And Safe Spaces For Transgender Singers In The Choral Rehearsal
... a positive definite matrix allows us to classify matrices that behave in a similar way to the positive real ...of positive definite matrices is vast and yet, up to this ...
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Properties of Matrix Variate Beta Type 3 Distribution
... gamma matrices. An m × m random symmetric positive definite matrix Y is said to have a matrix variate gamma distribution with parameters Ψ > 0, and κ > m − 1/2, denoted by Y ∼ Gam, κ, Ψ, ...
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Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals
... Abstract. Although Selberg-type single positive definite symmetric matrices gamma and beta integrals have been evaluated by several authors, see e.g., Askey and Richards [1], Gupta and Kabe ...
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Threshold Extension of Gallium Arsenide/Aluminum Gallium Arsenide Terahertz Detectors and Switching in Heterostructures
... real, symmetric matrices is an inner product space with < A, B >= ...is positive semidefinite if and only if tr(P Q) ≥ 0 for every Q ≥ ...is positive definite if and only if tr(P ...
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Sum of squared logarithms an inequality relating positive definite matrices and their matrix logarithm
... The structure of the inequality in dimensions n = and n = and extensive numerical sampling strongly suggest that the inequality holds for all n ∈ N if the n corresponding conditions are satisfied. More precisely, in ...
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A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator
... For symmetric positive definite (spd) matrices, this question has been examined extensively ...indefinite matrices there seems to be no way to ensure that using a two-level method with ...
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Selberg-type squared matrices gamma and beta integrals
... single positive definite symmetric matrices, gamma and beta integrals are evaluated by several authors; see ...of positive signature symmetric matrices, skew ...
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Generalized Wishart processes for interpolation over diffusion tensor fields
... of symmetric positive definite random matrices indexed by an arbitrary dependent variable [15], ...advantages: positive definite matrices, robustness to noise, smooth ...
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Rank modifications of semi-definite matrices with applications to secant updates
... for symmetric positive denite matrices followed by a general rank-restoration theorem for rectangular matri- ces and a symmetric rank-restoration theorem directly applicable to the BFGS ...
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On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications
... given positive definite matrix is a problem which has been extensively studied from an algorithmic point of view and which can be implemented in a very efficient way — see, ...of symmetric ...
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The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning
... covariance matrices. Since nonsingular covariance matrices lie on a Riemannian manifold, a kernel function is used to explicitly embed the Riemannian structure into a Eu- clidean ...
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Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
... In this paper, a new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for ...
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Darboux transformation and perturbation of linear functionals
... L + Cδ(x) [12,13] in the context of the spectral analysis of fourth-order linear differential equations with polynomial coefficients. They were interested in the poly- nomial solutions of such differential equations, the ...
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k Kernel Symmetric Matrices
... Remark 3.2. In particular, when κi i for each i 1 to n, the associated permutation matrix K reduces to the identity matrix and Definition 3.1 reduces to NA NA T , that is, A is Kernel symmetric. If A is ...
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