Actin cytoskeleton networks generate local topological signatures due to the natural variations in the number, size, and shape of holes of the networks. Persistent homology is a method that explores these topological properties of data and summarizes them as persistence diagrams. In this work, we analyze and classify simulated actin filament networks by transforming them into persistence diagrams whose variability is quantified via a Bayesian framework on the space of persistence diagrams. The proposed generalized Bayesian framework adopts an independent and identically distributed cluster point process characterization of persistence diagrams and relies on a substitution likelihood argument. This framework provides the flexibility to estimate the posterior cardinality distribution of points in a persistence diagram and their posterior spatial distribution simultaneously. We present a closed form of the posteriors under the assumption of a Gaussian mixture and binomial for prior intensity and cardinality respectively. Using this posterior calculation, finally, we implement a Bayes factor algorithm to classify simulated actin filament networks and benchmark it against several state-of-the-art classification methods.
We thank the associate editor and two anonymous reviewers for their comments, which helped us to improve our manuscript. We also thank the Abel Research Group for providing the simulated filament network data. The work has been partially supported by the ARO W911NF-21-1-0094, NSF MCB-1715794 and DMS-1821241, and ARL Co-operative Agreement # W911NF-19-2-0328. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes not withstanding any copyright notation herein.
"Bayesian Topological Learning for Classifying the Structure of Biological Networks." Bayesian Anal. Advance Publication 1 - 26, 2021. https://doi.org/10.1214/21-BA1270