Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Intro
Matchings between diagrams
Bottleneck distance distance
The main contenders
Coordinates have separate meanings
An example with height functions
An example with point clouds
Recall: Sublevel sets of functions on simplicial complexes
Local Stability for functions on simplicial complexes
Interleaving distance
The p-norm of a persistence module
Morphisms between persistence diagrams
Example with persistence modules of a single interval
Constructing a span from a matching
Spans for the bottleneck distance - matching the diagonal
Mean as minimiser of sum of distances squared
Candidates for the Mean
Candidates for the Median
Median of a selection - q=p=1
A case for change - replace
Lipschitz stability corollaries
Taught by
Applied Algebraic Topology Network