Persistence Bag-of-Words for Topological Data Analysis

Bartosz Zielinski, Michal Lipinski, Mateusz Juda, Matthias Zeppelzauer, Pawel Dlotko

Abstract: Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.