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.
CITATION STYLE
Akhøj, M., Pennec, X., & Sommer, S. (2023). Tangent Phylogenetic PCA. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13886 LNCS, pp. 77–90). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-31438-4_6
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