day 5

\(\def\Real{\mathbb{R}} \)

Topological inference

From data to simplicial complexes, A: Dowker’s theorem

From data to simplicial complexes, B: Čech and Vietoris-Rips complexes

Approximation results: finite samples from a manifold approximate the manifold well, in case of Čech complexes, thanks to Niyogi-Smale-Weinberger and in case of Vietoris-Rips complexes, thanks to Hausmann-Latschev

 

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