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Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?
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- 1 Intro
- 2 Matchings between diagrams
- 3 Bottleneck distance distance
- 4 The main contenders
- 5 Coordinates have separate meanings
- 6 An example with height functions
- 7 An example with point clouds
- 8 Recall: Sublevel sets of functions on simplicial complexes
- 9 Local Stability for functions on simplicial complexes
- 10 Interleaving distance
- 11 The p-norm of a persistence module
- 12 Morphisms between persistence diagrams
- 13 Example with persistence modules of a single interval
- 14 Constructing a span from a matching
- 15 Spans for the bottleneck distance - matching the diagonal
- 16 Mean as minimiser of sum of distances squared
- 17 Candidates for the Mean
- 18 Candidates for the Median
- 19 Median of a selection - q=p=1
- 20 A case for change - replace
- 21 Lipschitz stability corollaries
