Completed
Persistence diagram space is UGLY
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Classroom Contents
Liz Munch - Featurization of Persistence Diagrams Using Template Functions for ML Tasks
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- 1 Intro
- 2 Shape in data
- 3 Topological Data Analysis (TDA)
- 4 Persistent homology in one slide
- 5 Existing Methods for Stats & ML
- 6 Finite vs infinte diagrams
- 7 A topologist's view of machine learning
- 8 Notation for persistence diagrams
- 9 8-matchings and Bottleneck Distance
- 10 Persistence diagram space is UGLY
- 11 Characterization of relatively compact sets
- 12 Up a creek?
- 13 Coordinate systems
- 14 Birth-Lifetime coordinates
- 15 Combining a function and a diagram to get a number
- 16 Evaluating points
- 17 Template function definition
- 18 Template functions
- 19 what about in practice?
- 20 Example template system 1: Tent functions
- 21 Example template system 2. Chebychev polynomials
- 22 Random diagrams
- 23 Manifold Experiment: Coefficients
- 24 Current and future work: Adaptive partitioning
