AKHØJ , Morten

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...

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank $k$ tangent subbundle on $\mathbb{R}^d$, $k