ATOL: Measure Vectorisation for Automatic Topologically-Oriented Learning

Martin Royer (1) , Frédéric Chazal (1) , Clément Levrard (2) , Yuichi Ike (3) , Yuhei Umeda (3)

1 DATASHAPE - Understanding the Shape of Data
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 Fujitsu Laboratories Ltd.

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 learnt, unsupervised measure vectorisation method and use it for reflecting underlying changes in topological behaviour in machine learning contexts. Relying on optimal measure quantisation results the method is tailored to efficiently discriminate important plane regions where meaningful differences arise. 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 only high level tuning parameters such as the total measure encoding budget, and we provide a completely open access software.

Mots clés: Measure Vectorisation; Topological Data Analysis; Machine Learning

Domaines: Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Machine Learning [stat.ML]

Martin Royer, Frédéric Chazal, Clément Levrard, Yuichi Ike, Yuhei Umeda. ATOL: Measure Vectorisation for Automatic Topologically-Oriented Learning. 2020. ⟨hal-02296513v2⟩