Abstract
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and the main interest is in identifying the most persisting ones since they correspond to the Betti number values. Given the randomness inherent in the sampling process, and the complex structure of the space where persistence diagrams take values, estimation of Betti numbers is not straightforward. The approach followed in this work makes use of features’ lifetimes and provides a full Bayesian clustering model, based on random partitions, in order to estimate Betti numbers. A simulation study is also presented.
Funding Statement
The author thankfully acknowledges the support of PAPIIT project number IG100221.
Acknowledgments
The author is very grateful to Professors Victor Pérez-Abreu, Rolando Biscay and Miguel Nakamura for introducing him to this new world of topological data analysis and for all their support during his postdoctoral stay at CIMAT. This acknowledgment also goes to the anonymous referees for their constructive comments that improved the quality of this paper, and to Professor Ramsés H. Mena for his valuable comments and suggestions.
Citation
Asael Fabian Martínez. "Bayesian Estimation of Topological Features of Persistence Diagrams." Bayesian Anal. 19 (1) 1 - 20, March 2024. https://doi.org/10.1214/22-BA1341
Information