Persistence Bag-of-Words for Topological Data Analysis

Persistence Bag-of-Words for Topological Data Analysis

Bartosz Zieliński, Michał Lipiński, Mateusz Juda, Matthias Zeppelzauer, Paweł Dłotko

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 4489-4495. https://doi.org/10.24963/ijcai.2019/624

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.
Keywords:
Machine Learning: Classification
Computer Vision: Recognition: Detection, Categorization, Indexing, Matching, Retrieval, Semantic Interpretation
Computer Vision: Statistical Methods and Machine Learning
Machine Learning: Dimensionality Reduction and Manifold Learning