Explore the mathematical concepts of persistence diagrams and their associated metrics in this 28-minute lecture. Delve into the universality of persistence diagrams and gain a deeper understanding of bottleneck and Wasserstein distances. Learn how these tools are applied in topological data analysis and their significance in capturing the shape and structure of data. Discover the theoretical foundations and practical applications of these concepts as presented by Alex Elchesen from the Applied Algebraic Topology Network.
Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Alex Elchesen (1/14/21): Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances
Taught by
Applied Algebraic Topology Network
Related Courses
-
Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?
-
Ulrich Bauer - Persistence Diagrams as Diagrams
-
Amit Patel - Generalized Persistence Diagrams
-
Comparative Stability of Two Zigzag Bottleneck Distances
-
Michael Lesnick - Algebraic Stability of Zigzag Persistence Modules
-
Metric Geometry of Spaces of Persistence Diagrams
