Tangent Phylogenetic PCA

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