Persistence Diagrams Courses and Certifications

Applied Algebraic Topology Network

Ulrich Bauer - Persistence Diagrams as Diagrams

Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

On the Metric Distortion of Embedding Persistence Diagrams into RKHS

Explores embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces, analyzing metric properties and stability guarantees for machine learning applications in Topological Data Analysis.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?

Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Massimo Ferri - Selection of Points in Persistence Diagrams

Explore point selection in persistence diagrams, including Kurlin's criterion and the Ziqqurat method, for noise reduction and improved data analysis in topological data analysis.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers

Explore how generalized persistence diagrams encode bigraded Betti numbers in 2-parameter persistence modules, with implications for RIVET software and interval decomposable modules.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Comparing Neural Networks via Generalized Persistence

Exploring generalized persistence to compare neural network architectures, analyzing data representations at each layer and providing insights into network behavior and performance.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Möbius Inversion and Persistence in Algebraic Topology

Explore the connection between Möbius inversion and persistence theory, understanding how combinatorial derivatives relate to multiparameter persistence and rank functions in algebraic topology.

• YouTube
• 10 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Liz Munch - Featurization of Persistence Diagrams Using Template Functions for ML Tasks

Explore topological data analysis and persistence diagrams for machine learning, focusing on featurization techniques using template functions to map complex data into Euclidean space.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

A Canonical Framework for Summarizing Persistence Diagrams

Explore a canonical framework for summarizing persistence diagrams in topological data analysis, including theoretical foundations, applications, and future developments.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Edit Distance and Persistence Diagrams Over Lattices

Functorial pipeline for persistent homology: from filtered simplicial complexes to persistence diagrams. Addresses multiparameter persistent homology and functoriality of persistence diagrams.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances

Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Studying the Space of Persistence Diagrams Using Optimal Partial Transport II

Exploring persistence diagrams through optimal transport theory, bridging topological data analysis with measure spaces to characterize convergence and prove new results in random settings.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Studying the Space of Persistence Diagrams Using Optimal Partial Transport - Part I

Exploring persistence diagrams through optimal partial transport, bridging topological data analysis with measure theory. Novel approach enables new insights into convergence, continuity, and random settings in TDA.

• YouTube
• 26 minutes
• On-Demand
• Free Video