ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning

Understand

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.