Exact Multi-Parameter Persistent Homology of Time-Series Data

Explore the application of multi-parameter persistent homology in time-series data analysis and classification through this 48-minute lecture. Delve into the development of a multi-parameter filtration method based on Fourier decomposition and understand the exact formula for one-dimensional reduction of multi-parameter persistent homology. Learn how the Liouville torus, inspired by complete integrable Hamiltonian systems, is utilized instead of the traditional sliding window embedding method. Discover how this approach significantly reduces computational complexity while maintaining comparable performance in supervised learning experiments. Gain insights into finding diverse topological inferences by exploring different rays in the filtration space, offering a novel perspective on time-series data analysis using topological data analysis (TDA) techniques.