INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS

By Stephan F. Huckemann, Thomas Hotzand, Axel Munk, Georgia Augusta. 2007

177 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d295bd407d82fc3054d2c47ec08f0620d63c8e09

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Citations in the corpus

Fréchet means and Procrustes analysis in Wasserstein space (2017, methodology): “The Procrustes maps can also be used in order to produce a Principal Component Analysis, capturing the main modes of deformation-based variation (Bigot et al. [13], Panaretos & Zemel [61]; Huckemann, Munk & Hotz [42], Wang et al. [75]).”
Geodesic Finite Mixture Models (2014, methodology): “For example, there exists several PCA generalizations to non-linear data such as the Principal Geodesic Analysis [10, 32] and the Geodesic PCA [13].”
Representation Tradeoffs for Hyperbolic Embeddings (2018, methodology): “Our algorithm essentially provides new recovery results for convergence for Principal Geodesic Analysis (PGA) in hyperbolic space [12, 17].”
Statistical Aspects of Wasserstein Distances (2018, background): “Existence, uniqueness, computation, laws of large numbers and central limit theorems for Fr´echet means with respect to general metrics have been studied extensively, under the umbrella of non-Euclidean statistics (e.g., Huckemann et al., 2010; Kendall & Le, 2011).”
Principal component analysis for functional data on Riemannian manifolds and spheres (2017, background): “…on manifolds have also been well developed over the years, such as data on spheres (Fisher et al. 1987), Kendall’s shape spaces (Kendall et al. 2009; Huckemann et al. 2010), and data on other classical Riemannian manifolds (Cornea et al. 2017); for a comprehensive overview of nonparametric methods…”