On the Expectation of a Persistence Diagram by the Persistence Weighted Kernel

Understand

In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram.

• Statistical research for persistence diagrams have been actively developed, and the persistence weighted kernel shows several advantages over other statistical methods for persistence diagrams.
• If data is drawn from some probability distribution, the corresponding persistence diagram have randomness.
• Then, the expectation of the persistence diagram by the persistence weighted kernel is well-defined.