ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning
This work addresses the challenge of using topological data in machine learning for researchers and practitioners in fields like graph analysis and dynamical systems, representing a novel method for a known bottleneck.
The authors tackled the problem of integrating topological information from persistence diagrams into machine learning frameworks by introducing ATOL, a fast, unsupervised vectorization method that efficiently identifies important regions for differences in measures. The method achieved state-of-the-art performance on graph collections and demonstrated robustness in applications like a synthetic dynamical orbits problem.
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.