Extracting Persistence Features with Hierarchical Stabilisation

Explore the complexities of multi-parameter persistence in this 43-minute conference talk by Martina Scolamiero. Delve into the hierarchical stabilisation framework for producing stable invariants in persistence modules. Understand the fundamental role of metrics in comparing persistence modules and focus on the stable rank invariant. Examine the challenges of computing stable rank in multi-parameter cases and its practical applications in one-parameter persistence. Learn how varying metrics can enhance classification accuracy in both artificial and real-world datasets. Gain insights from the collaborative work of the TDA group at KTH in extracting persistence features and understanding complex correlation patterns in multi-measurement datasets.