Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces

By Stephan F. Huckemann, H. Ziezold. Advances in Applied Probability, 2006

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Dimension reduction in multivariate extreme value analysis (2015, methodology): “394 E. Chautru Other algorithms could have been used to project the data on manifolds of smaller dimension, see for instance Fletcher et al. (2004); Huckemann and Ziezold (2006); Jung et al. (2011).”
Barycentric subspace analysis on manifolds (2016, methodology): “In Statistics, directional data occupy a place of choice (Dryden, 2005; Huckemann and Ziezold, 2006).”
INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS (2007, methodology): “One main feature of non-Euclidean geometry is the fact that in general, due to curvature, the IM will differ from the PM, cf., Huckemann and Ziezold (2006) for a detailed discussion.”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, methodology): “We phrase our general CLT in terms of sufficiently well behaved generalized Fréchet means, e.g. geodesic principal components (Huckemann and Ziezold (2006); Huckemann et al. (2010)) or principal nested spheres (Jung et al. (2012, 2011)).”
Fréchet means and Procrustes analysis in Wasserstein space (2017, methodology): “he template and registration maps are the two ingredients of Procrustes analysis (Gower [38]; Dryden & Mardia [30]) and non-Euclidean PCA (Huckemann, Munk & Hotz [42]; Huckemann & Ziezold [43]). Obviously, the methods and algorithms for estimating a mean and carrying out a registration/P”