Luis Scoccola - Density-Sensitive and Robust Vietoris-Rips Filtrations

Explore density-sensitive and robust Vietoris-Rips filtrations in this 54-minute conference talk by Luis Scoccola for the Applied Algebraic Topology Network. Delve into the limitations of traditional Vietoris-Rips (VR) filtrations, including their inability to distinguish datasets with similar metrics but different density structures, and their lack of robustness against outliers. Examine alternative filtrations designed to address these issues, such as function-Rips, degree-Rips, and subdivision-Rips. Learn about the applications and open questions in this field, covering topics like introduction, goals, definitions, distances, properties, and special results. Gain insights into advanced concepts in topological data analysis and participate in a discussion and Q&A session to deepen your understanding of these innovative filtration techniques.