Bayesian Estimation of Topological Features of Persistence Diagrams

Persistent homology is a common technique in topological data analysis providing geometrical and information about the sample space. All this information, known as features, summarized persistence diagrams, main interest identifying most persisting ones since they correspond to Betti number values. Given randomness inherent sampling process, complex structure of space where diagrams take values, estimation numbers not straightforward. The approach followed work makes use features’ lifetimes provides full Bayesian clustering model, based on random partitions, order estimate numbers. A simulation study also presented.