A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric
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[1] Pierre-Antoine Absil,et al. Optimization on the Orthogonal Group for Independent Component Analysis , 2007, ICA.
[2] Boris Kolev,et al. Lie Groups and Mechanics: An Introduction , 2004, math-ph/0402052.
[3] Robert E. Mahony,et al. The Geometry of the Newton Method on Non-Compact Lie Groups , 2002, J. Glob. Optim..
[4] J. Marsden,et al. Mechanical SystemsMechanical systems : Symmetries and Reduction , 2012 .
[5] Jerrold E. Marsden,et al. Lagrangian Reduction, the Euler{Poincar e Equations, and Semidirect Products , 1999, chao-dyn/9906004.
[6] Ronen Talmon,et al. Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation , 2018, IEEE Transactions on Signal Processing.
[7] Axel Barrau,et al. The Invariant Extended Kalman Filter as a Stable Observer , 2014, IEEE Transactions on Automatic Control.
[8] François-Xavier Vialard,et al. Invariant Higher-Order Variational Problems II , 2011, J. Nonlinear Sci..
[9] J. Milnor. Curvatures of left invariant metrics on lie groups , 1976 .
[10] E. Celledoni. Lie group methods , 2009 .
[11] Hans-Christian Hege,et al. Geodesic Analysis in Kendall’s Shape Space with Epidemiological Applications , 2019, Journal of Mathematical Imaging and Vision.
[12] Xavier Pennec,et al. Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds , 2020, Foundations of Computational Mathematics.
[13] Pierre-Antoine Absil,et al. Gradient-optimization on the orthogonal group for Independent Component Analysis , 2007 .
[14] Xavier Pennec,et al. geomstats: a Python Package for Riemannian Geometry in Machine Learning , 2018, ArXiv.
[15] V. Arsigny,et al. Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups , 2013 .
[16] Søren Hauberg,et al. Unscented Kalman Filtering on Riemannian Manifolds , 2013, Journal of Mathematical Imaging and Vision.
[17] Xavier Pennec,et al. Efficient Parallel Transport of Deformations in Time Series of Images: From Schild’s to Pole Ladder , 2013, Journal of Mathematical Imaging and Vision.
[18] V. Arnold. Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits , 1966 .
[19] Katie E. Severn,et al. Smoothing splines on Riemannian manifolds, with applications to 3D shape space , 2018, Journal of the Royal Statistical Society: Series B (Statistical Methodology).
[20] Matthieu Cord,et al. Riemannian batch normalization for SPD neural networks , 2019, NeurIPS.
[21] François Gay-Balmaz,et al. Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics , 2020, Entropy.
[22] J. Gallier,et al. Differential Geometry and Lie Groups , 2020, Geometry and Computing.