Advances in Geometric Statistics for Manifold Dimension Reduction
From MaRDI portal
Publication:3300543
DOI10.1007/978-3-030-31351-7_11OpenAlexW3014183290MaRDI QIDQ3300543
Publication date: 29 July 2020
Published in: Handbook of Variational Methods for Nonlinear Geometric Data (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/hal-02560938/file/XP_GeomStats_ManifoldReductionPCA.pdf
Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimization over geodesics for exact principal geodesic analysis
- Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
- The Riemannian structure of Euclidean shape spaces: A novel environment for statistics
- A survey of the statistical theory of shape. With discussion and a reply by the author
- Sample-limited \(L_p\) barycentric subspace analysis on constant curvature spaces
- Intrinsic analysis of statistical estimation
- The statistical theory of shape
- Barycentric subspace analysis on manifolds
- Geodesics, parallel transport \& one-parameter subgroups for diffeomorphic image registration
- Backwards principal component analysis and principal nested relations
- How to conjugate C\(^1\)-close group actions
- A Riemannian framework for tensor computing
- Locating Fréchet means with application to shape spaces
- Analysis of principal nested spheres
- Overview of object oriented data analysis
- Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
- Riemannian median and its estimation
- Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
- Riemannian center of mass and mollifier smoothing
- The Geometry of Algorithms with Orthogonality Constraints
- A Panoramic View of Riemannian Geometry
- Means and Averaging in the Group of Rotations
- Estimation of Riemannian Barycentres
- Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups
- Horizontal Dimensionality Reduction and Iterated Frame Bundle Development
- Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces
- On averaging rotations
