We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in an Euclidean space. This work is motivated by applications in bioinformatics where researchers aim to automatically homogenize large datasets to compare and analyze characteristics within a same cell population. Inconveniently, the information acquired is most certainly noisy due to mis-alignment caused by technical variations of the environment. To overcome this problem, we propose to register multiple point clouds by using the notion of regularized Wasserstein barycenters of a set of probability measures. We propose data-driven choices for the regularization parameters involved in our approach using the Goldenshluger-Lepski's principle, and an application to the analysis of flow cytometry data is finally proposed.
Enseignant-chercheurs en statistique - Campus bordelais