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

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

Applied Algebraic Topology Network via YouTube Direct link

Intro

1 of 24

1 of 24

Intro

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

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

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