Stochastic Convergence of Persistence Landscapes and Silhouettes

Understand

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram.

• It is difficult to apply statistical theory directly to a random sample of diagrams.
• Instead, we can summarize the persistent homology with the persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function.
• We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap.