Massimo Ferri - Selection of Points in Persistence Diagrams

Explore the concept of point selection in persistence diagrams in this 40-minute lecture by Massimo Ferri. Delve into V. Kurlin's selection criterion of diagonal gaps, designed for creating hierarchical segmentations from point clouds. Examine applications of this criterion on generalized persistence functions. Learn about the Ziqqurat, a 3D construction built on persistence diagrams, and understand its filtering function. Discover how the Ziqqurat filtration leads to a ranking system for diagram points, and observe its effectiveness in noise reduction. The lecture covers introduction, reasons for point selection, noise properties, pooling techniques, diagonal gaps, applications in graphs, and concludes with a Q&A session.