Since October 2020, I am doing a PhD on geometric manifold learning under the supervision of Xavier Pennec and Alain Trouvé. More specifically, my thesis focuses on designing intrinsic methods for the analysis of manifold-valued data with a particular interest for shape data and graph data. I leverage Riemannian models and explore non-metric structures such as barycentric subspaces. Additionally, I look for approximations by constant curvature spaces.