Abstract
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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Acknowledgements
M.A. and X.P. are supported by the European Research Council (ERC) under the EU Horizon 2020 research and innovation program (grantagreement G- Statistics No. 786854). S.S. is partly supported by Novo Nordisk Foundation grant NNF18OC0052000 as well as VILLUM FONDEN research grant 40582 and UCPH Data+ Strategy 2023 funds for interdisciplinary research.
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Akhøj, M., Pennec, X., Sommer, S. (2023). Tangent Phylogenetic PCA. In: Gade, R., Felsberg, M., Kämäräinen, JK. (eds) Image Analysis. SCIA 2023. Lecture Notes in Computer Science, vol 13886. Springer, Cham. https://doi.org/10.1007/978-3-031-31438-4_6
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DOI: https://doi.org/10.1007/978-3-031-31438-4_6
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