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References from Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats. Local targets link to admitted publications; unresolved targets remain external evidence.
Super-Efficiency of Automatic Differentiation for Functions Defined as a Minimum
2020 · External reference
10.1007/978-3-642-12598-0_12
10.1007/978-3-642-12598-0_12 · 2010 · External reference
Projection-like Retractions on Matrix Manifolds
10.1137/100802529 · 2012 · External reference
Riemannian Lp Center of Mass: Existence, Uniqueness, and Convexity
10.1090/s0002-9939-2010-10541-5 · 2011 · External reference
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits
10.5802/aif.233 · 1966 · External reference
The Hopf-Rinow Theorem Is False in Infinite Dimensions
10.1112/blms/7.3.261 · 1975 · External reference
Unresolved reference
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10.5281/zenodo.593816
10.5281/zenodo.593816 · 2015 · External reference
Invariant EKF Design for Scan Matching-Aided Localization
10.1109/tcst.2015.2413933 · 2015 · External reference
10.48550/arxiv.1903.02699
10.48550/arxiv.1903.02699 · 2019 · External reference
Riemannian Adaptive Optimization Methods
2019 · External reference
A Grassmann Manifold Handbook: Basic Geometry and Computational Aspects
2020 · External reference
10.1007/978-3-642-18245-7
10.1007/978-3-642-18245-7 · 2003 · External reference
On the Bures-Wasserstein Distance between Positive Definite Matrices
10.1016/j.exmath.2018.01.002 · 2019 · External reference
Large Sample Theory of Intrinsic and Extrinsic Sample Means on Manifolds—II
10.1214/009053605000000093 · 2005 · External reference
10.1017/9781009166164
10.1017/9781009166164 · 2023 · External reference
Sur une classe remarquable d’espaces de Riemann
10.24033/bsmf.1105 · 1926 · External reference
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10.1090/trans2/186
10.1090/trans2/186 · 1998 · External reference
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10.1016/s0924-6509(08)70208-3
10.1016/s0924-6509(08)70208-3 · 1975 · External reference
A Bi-Invariant Statistical Model Parametrized by Mean and Covariance on Rigid Motions
10.3390/e22040432 · 2020 · External reference
10.1007/978-0-387-21540-2
10.1007/978-0-387-21540-2 · 2003 · External reference
A General Theory of Equivariant CNNs on Homogeneous Spaces
2019 · External reference
A Riemannian Structure for Correlation Matrices
10.7153/oam-2019-13-46 · 2019 · External reference
Sampling from a Manifold
10.1214/12-imscoll1006 · 2013 · External reference
Non-Euclidean Statistics for Covariance Matrices, with Applications to Diffusion Tensor Imaging
10.1214/09-aoas249 · 2009 · External reference
10.1002/9781119072492
10.1002/9781119072492 · 2016 · External reference
Unresolved reference
1983 · External reference
Unresolved reference
2019 · External reference
Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape
10.1109/tmi.2004.831793 · 2004 · External reference
Les éléments aléatoires de nature quelconque dans un espace distancié
1948 · External reference
10.1007/978-3-030-46040-2
10.1007/978-3-030-46040-2 · 2020 · External reference
Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition
10.1007/s10208-017-9353-0 · 2018 · External reference
Invariant Higher-Order Variational Problems II
10.1007/s00332-012-9137-2 · 2012 · External reference
Parallel Transport on Kendall Shape Spaces
10.1007/978-3-030-80209-7_12 · 2021 · External reference
A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric
10.1007/978-3-030-80209-7_14 · 2021 · External reference
Directional Statistics with the Spherical Normal Distribution
10.23919/icif.2018.8455242 · 2018 · External reference
Unresolved reference
2019 · External reference
Unresolved reference
1979 · External reference
Intrinsic Shape Analysis: Geodesic Pca for Riemannian Manifolds Modulo Isometric Lie Group Actions
2010 · External reference
Riemannian Center of Mass and Mollifier Smoothing
10.1002/cpa.3160300502 · 1977 · External reference
Unresolved reference
2014 · External reference
Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
10.1112/plms/s3-61.2.371 · 1990 · External reference
10.1093/acprof:oso/9780199232574.003.0010
10.1093/acprof:oso/9780199232574.003.0010 · 2009 · External reference
Smoothing Splines on Riemannian Manifolds, with Applications to 3D Shape Space
10.1111/rssb.12402 · 2021 · External reference
Unresolved reference
1996 · External reference
Unresolved reference
1996 · External reference
10.48550/arxiv.2005.02819
10.48550/arxiv.2005.02819 · 2020 · External reference
Lie Groups and Mechanics: An Introduction
10.2991/jnmp.2004.11.4.5 · 2004 · External reference
Computational Anatomy in Theano
10.1007/978-3-319-67675-3_15 · 2017 · External reference
Differential Geometry and Stochastic Dynamics with Deep Learning Numerics
10.1016/j.amc.2019.03.044 · 2019 · External reference
10.1007/978-3-642-18855-8
10.1007/978-3-642-18855-8 · 2004 · External reference
The Riemannian Structure of Euclidean Shape Spaces: A Novel Environment for Statistics
10.1214/aos/1176349259 · 1993 · External reference
10.1007/978-1-4419-9982-5
10.1007/978-1-4419-9982-5 · 2003 · External reference
10.1007/978-3-319-91755-9
10.1007/978-3-319-91755-9 · 2018 · External reference
Geodesics, Parallel Transport & One-Parameter Subgroups for Diffeomorphic Image Registration
10.1007/s11263-012-0598-4 · 2013 · External reference
10.1007/978-3-030-20351-1_42
10.1007/978-3-030-20351-1_42 · 2019 · External reference
10.1002/9780470316979
10.1002/9780470316979 · 2009 · External reference
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2005 · External reference
10.1201/9781351189675
10.1201/9781351189675 · 2021 · External reference
10.1007/978-0-387-30440-3_326
10.1007/978-0-387-30440-3_326 · 2009 · External reference
Unresolved reference
1965 · External reference
10.48550/arxiv.1810.01811
10.48550/arxiv.1810.01811 · 2018 · External reference
Curvatures of Left Invariant Metrics on Lie Groups
10.1016/s0001-8708(76)80002-3 · 1976 · External reference
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Computing Bi-Invariant Pseudo-Metrics on Lie Groups for Consistent Statistics
10.3390/e17041850 · 2015 · External reference
Introduction to Geometric Learning in Python with Geomstats
10.25080/majora-342d178e-007 · 2020 · External reference
Symmetric Spaces and Lie Triple Systems in Numerical Analysis of Differential Equations
10.1007/s10543-014-0473-5 · 2014 · External reference
The Group of Isometries of a Riemannian Manifold
10.2307/1968928 · 1939 · External reference
Geodesic Analysis in Kendall’s Shape Space with Epidemiological Applications
10.1007/s10851-020-00945-w · 2020 · External reference
Unresolved reference
2017 · External reference
Invariant Affine Connections on Homogeneous Spaces
10.2307/2372398 · 1954 · External reference
The Fundamental Equations of a Submersion
10.1307/mmj/1028999604 · 1966 · External reference
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Unresolved reference
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Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
10.1007/s10851-006-6228-4 · 2006 · External reference
10.1007/978-3-642-30232-9_7
10.1007/978-3-642-30232-9_7 · 2013 · External reference
A Riemannian Framework for Tensor Computing
10.1007/s11263-005-3222-z · 2006 · External reference
10.1016/c2017-0-01561-6
10.1016/c2017-0-01561-6 · 2020 · External reference
10.1007/978-3-662-04433-9
10.1007/978-3-662-04433-9 · 2001 · External reference
Über Die Hypothesen, Welche Der Geometrie Zu Grunde Liegen. (Mitgetheilt Durch r. Dedekind)
1868 · External reference
On the Hypotheses Which Lie at the Bases of Geometry
10.1038/008036a0 · 1873 · External reference
Gaussian Distributions on Riemannian Symmetric Spaces: Statistical Learning With Structured Covariance Matrices
10.1109/tit.2017.2713829 · 2018 · External reference
Infinite Dimentional Lie Groups with Applications to Mathematical Physics
10.7546/jgsp-1-2004-54-120 · 2004 · External reference
Unresolved reference
2021 · External reference
10.1007/978-1-4612-3820-1
10.1007/978-1-4612-3820-1 · 1988 · External reference
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Geodesics and Curvature of the Quotient-Affine Metrics on Full-Rank Correlation Matrices
10.1007/978-3-030-80209-7_11 · 2021 · External reference
O(n)-Invariant Riemannian Metrics on SPD Matrices
10.1016/j.laa.2022.12.009 · 2022 · External reference
Pymanopt: A Python Toolbox for Optimization on Manifolds Using Automatic Differentiation
10.5555/2946645.3007090 · 2016 · External reference
Differentiable Manifolds
10.2307/1968482 · 1936 · External reference
Simulation of the von Mises Fisher Distribution
10.1080/03610919408813161 · 1994 · External reference
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Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation
10.1109/tsp.2019.2894801 · 2019 · External reference
A Matrix-Algebraic Algorithm for the Rie-mannian Logarithm on the Stiefel Manifold under the Canonical Metric
10.1137/16m1074485 · 2017 · External reference
