ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning

Abstract

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.

References in corpus (9)

• Scikit-learn: Machine Learning in Python
• Persistence weighted Gaussian kernel for topological data analysis
• Deep Learning with Topological Signatures
• Sliced Wasserstein Kernel for Persistence Diagrams
• PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
• Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams
• RetGK: Graph Kernels based on Return Probabilities of Random Walks
• Approximating Continuous Functions on Persistence Diagrams Using Template Functions
• Optimal quantization of the mean measure and applications to statistical learning

Cited by in corpus (2)

• giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration
• Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence