ATOL: Automatic Topologically-Oriented Learning

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

1 DATASHAPE - Understanding the Shape of Data
2 Fujitsu Laboratories Ltd.

There are abundant cases for using Topological Data Analysis (TDA) in a learning context, but robust topological information commonly comes in the form of a set of persistence diagrams, objects that by nature are uneasy to affix to a generic machine learning framework. We introduce a vectorisation method for diagrams that allows to collect information from topological descriptors into a format fit for machine learning tools. Based on a few observations, the method is learned and tailored to discriminate the various important plane regions a diagram is set into. With this tool one can automatically augment any sort of machine learning problem with access to a TDA method, enhance performances, construct features reflecting underlying changes in topological behaviour. The proposed methodology comes with only high level tuning parameters such as the encoding budget for topological features. We provide an open-access, ready-to-use implementation and notebook. We showcase the strengths and versatility of our approach on a number of applications. From emulous and modern graph collections to a highly topological synthetic dynamical orbits data, we prove that the method matches or beats the state-of-the-art in encoding persistence diagrams to solve hard problems. We then apply our method in the context of an industrial, difficult time-series regression problem and show the approach to be relevant.

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

Martin Royer, Frédéric Chazal, Yuichi Ike, Yuhei Umeda. ATOL: Automatic Topologically-Oriented Learning. 2019. ⟨hal-02296513v1⟩