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Conference Papers (Preprint) Year : 2022

Tangent phylogenetic PCA


Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, due to shared evolutionary history. The method works on Euclidean data, but in evolutionary biology there is a need for applying it to data on manifolds, particularly shapes. We provide a generalization of p-PCA to data lying on Riemannian manifolds, called Tangent p-PCA. Tangent p-PCA thus makes it possible to perform dimension reduction on a data set of shapes, taking into account both the non-linear structure of the shape space as well as phylogenetic covariance. We show simulation results on the sphere, demonstrating well-behaved error distributions and fast convergence of estimators. Furthermore, we apply the method to a data set of mammal jaws, represented as points on a landmark manifold equipped with the LDDMM metric.
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hal-03842847 , version 1 (07-11-2022)





Morten Akhøj, Xavier Pennec, Stefan Sommer. Tangent phylogenetic PCA. Scandinavian Conference on Image Analysis 2023, Apr 2023, Levi Ski Resort (Lapland), Finland. ⟨hal-03842847⟩
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