Principal geodesic analysis for the study of nonlinear statistics of shape

By P. T. Fletcher, Conglin Lu, S. Pizer, Sarang C. Joshi. IEEE Transactions on Medical Imaging, 2004

917 citations recorded by the source corpus.

Subfields: Food Science, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/11647c4d6867daaa90e67850f36d2cd8e614acdc

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Citations in the corpus

Riemannian geometry for the statistical analysis of diffusion tensor data (2007, methodology): “In our previous work [14] we introduced principal geodesic analysis (PGA) as an analog of principal component analysis for studying the statistical variability of Lie group data.”
From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices (2014, methodology): “While some manifold-based dimensionality reduction techniques have been proposed [4,22], as illustrated in Fig.”
INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS (2007, methodology): “(2003), Fletcher et al. (2004) as well as Fuchs and Scherzer (2007).”
Principal component analysis for functional data on Riemannian manifolds and spheres (2017, methodology): “Specifically, versions of principal component analysis methods that adapt to the Riemannian or spherical geometry, such as principal geodesic analysis (Fletcher et al. 2004) or nested spheres (Huckemann and Eltzner 2016), have substantially advanced the study of data on manifolds.”
Spherical and Hyperbolic Embeddings of Data (2014, methodology): “found use in the statistical analysis of data on manifolds, for example, in Principal Geodesic Analysis [13] and in the analysis of diffusion tensor data [23].”
Coding Kendall's Shape Trajectories for 3D Action Recognition (2018, methodology): “Thus, we propose to perform principal geodesic analysis (PGA), first proposed by [12], to generate the most representative atoms of the cluster.”
Elastic functional coding of human actions: From vector-fields to latent variables (2015, background): “Principal Geodesic Analysis (PGA)[6]: Performs PCA on the tangent space of static points on a manifold.”
Population Shape Regression from Random Design Data (2007, methodology): “try of shapes in flat Euclidean vector spaces limits our ability to represent natural variability in populations [9, 11, 24].”
The Optimal Template Effect in Hippocampus Studies of Diseased Populations (2009, methodology): “The overall SyGN approach is similar to that given by Fletcher et al. (2004) for computing intrinsic means for the statistics of medial shapes.”
Review of statistical shape spaces for 3D data with comparative analysis for human faces (2012, positive): “To capture the structure of this high-dimensional manifold, Fletcher et al. [43] generalized PCA to this setting.”
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups (2013, neutral): “Actually, the proposed algorithm was computing a bi-invariant mean as we will see below instead of a Karcher mean! The confusion was later corrected in [26] with the proper use of Riemannian logarithms.”
Riemannian Approaches in Brain-Computer Interfaces: A Review (2017, neutral): “3 and already noticed in [31], is the fact that Euclidean geometry”
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].”
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].”
Latent Space Non-Linear Statistics (2018, methodology): “For this reason, we here focus on a subset of selected methods to exemplify the use of nonlinear statistics tools in the latent space setting: Principal component analysis on manifolds with the principal geodesic analysis (PGA, [6]) and inference of maximum likelihood means from intrinsic diffusion ”
Barycentric subspace analysis on manifolds (2016, methodology): “Thus it generalizes the Principal Geodesic Analysis (PGA) of Fletcher et al. (2004); Sommer, Lauze and Nielsen (2013) when starting with a zeroth dimensional space (the Fréchet mean) and the Geodesic PCA (GPCA) of Huckemann and Ziezold (2006); Huckemann, Hotz and Munk (2010) when starting directly…”