Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

From MaRDI portal
Publication:985028

DOI10.1214/09-AOAS249zbMath1196.62063arXiv0910.1656OpenAlexW2112759033WikidataQ58419247 ScholiaQ58419247MaRDI QIDQ985028

Alexey Koloydenko, Diwei Zhou, Ian L. Dryden

Publication date: 20 July 2010

Published in: The Annals of Applied Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1656



Related Items

Diffusion tensor regularization with metric double integrals, Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats, Nonparametric matrix regression function estimation over symmetric positive definite matrices, Manifold valued data analysis of samples of networks, with applications in corpus linguistics, Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models, Uniform convergence of local Fréchet regression with applications to locating extrema and time warping for metric space valued trajectories, Intrinsic Riemannian functional data analysis for sparse longitudinal observations, Randomized Wasserstein Barycenter Computation: Resampling with Statistical Guarantees, Kriging Riemannian Data via Random Domain Decompositions, Entropy-regularized 2-Wasserstein distance between Gaussian measures, Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices, Overview of object oriented data analysis, Concurrent object regression, Geometry-aware principal component analysis for symmetric positive definite matrices, Exploiting the categorical reliability difference for binary classification, Information geometry for phylogenetic trees, Averages of unlabeled networks: geometric characterization and asymptotic behavior, Estimating summary statistics in the spike-train space, The geometry of mixed-Euclidean metrics on symmetric positive definite matrices, Optimal shrinkage of eigenvalues in the spiked covariance model, Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and diffusion tensor image analysis, Entropic regularization of Wasserstein distance between infinite-dimensional Gaussian measures and Gaussian processes, Penalized model-based clustering of complex functional data, Geostatistical modeling of positive‐definite matrices: An application to diffusion tensor imaging, From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings, Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices, Group-wise shrinkage estimation in penalized model-based clustering, Modal clustering of matrix-variate data, Preliminary Multiple-Test Estimation, With Applications to k-Sample Covariance Estimation, \(O(n)\)-invariant Riemannian metrics on SPD matrices, Limit theorems for Fréchet mean sets, Characterization of invariant inner products, An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices, Hoffmann-Jørgensen inequalities for random walks on the cone of positive definite matrices, Geometry-preserving Lie group integrators for differential equations on the manifold of symmetric positive definite matrices, Anisotropy preserving DTI processing, Two-sample and change-point inference for non-Euclidean valued time series, Intrinsic and extrinsic deep learning on manifolds, Representation and reconstruction of covariance operators in linear inverse problems, Estimation of the mean for spatially dependent data belonging to a Riemannian manifold, Varying coefficient model for modeling diffusion tensors along white matter tracts, Regression for non-Euclidean data using distance matrices, Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics, Geometric mean of partial positive definite matrices with missing entries, Statistical Analysis of Trajectories of Multi-Modality Data, O2S2 for the Geodata Deluge, Riemannian Distances between Covariance Operators and Gaussian Processes, Geometric Matrix Midranges, Fibre-generated point processes and fields of orientations, Integral transform methods in goodness-of-fit testing. II: The Wishart distributions, How to asses, visualize and compare the anisotropy of linear structures reconstructed from optical sections -- a study based on histopathological quantification of human brain microvessels, A smeary central limit theorem for manifolds with application to high-dimensional spheres, Intrinsic Riemannian functional data analysis, Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition, Kriging prediction for manifold-valued random fields, Model-free two-sample test for network-valued data, Rate-invariant analysis of covariance trajectories, Transporting deformations of face emotions in the shape spaces: a comparison of different approaches, Pairwise rigid registration based on Riemannian geometry and Lie structures of orientation tensors, Beyond covariance: SICE and kernel based visual feature representation, Principal Flows, Intrinsic Data Depth for Hermitian Positive Definite Matrices, Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces, Nonparametric analysis of non-Euclidean data on shapes and images, Gaussian asymptotic limits for the \({\alpha}\)-transformation in the analysis of compositional data, Procrustes metrics on covariance operators and optimal transportation of Gaussian processes, Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics, Total variation regularized Fréchet regression for metric-space valued data, A Spatial Modeling Approach for Linguistic Object Data: Analyzing Dialect Sound Variations Across Great Britain, Discussion: Object-Oriented Data Analysis, Power Metrics, and Graph Laplacians, Quantum entropic regularization of matrix-valued optimal transport, Functional random effects modeling of brain shape and connectivity, The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics, Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices, Scaling-Rotation Distance and Interpolation of Symmetric Positive-Definite Matrices, Robustness of lognormal confidence regions for means of symmetric positive definite matrices when applied to mixtures of lognormal distributions, Spectral statistics for the difference of two Wishart matrices, Quantum Jensen-Shannon divergences between infinite-dimensional positive definite operators


Uses Software


Cites Work