  Robust topological information commonly comes in the form of a set of
persistence diagrams, finite measures that are in nature uneasy to affix to
generic machine learning frameworks. We introduce a fast, learnt, unsupervised
vectorization method for measures in Euclidean spaces and use it for reflecting
underlying changes in topological behaviour in machine learning contexts. The
algorithm is simple and efficiently discriminates important space regions where
meaningful differences to the mean measure arise. It is proven to be able to
separate clusters of persistence diagrams. We showcase the strength and
robustness of our approach on a number of applications, from emulous and modern
graph collections where the method reaches state-of-the-art performance to a
geometric synthetic dynamical orbits problem. The proposed methodology comes
with a single high level tuning parameter: the total measure encoding budget.
We provide a completely open access software.
