This work presents a data-driven approach for the localization of an observer on a 2D topological map of the environment. State-of-the-art techniques may yield accurate estimates only when they are tailor-made for a specific data modality that prevents their applicability to broader domains. Here, we establish a model-agnostic framework and formulate the localization problem in the context of parametric manifold learning while leveraging optimal transportation. Our algorithm allows jointly learn…