  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 these 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 the posterior spatial
distribution simultaneously. We present a closed form of the posteriors under
the assumption of Gaussian mixtures and binomials for prior intensity and
cardinality respectively. Using this posterior calculation, we implement a
Bayes factor algorithm to classify the actin filament networks and benchmark it
against several state-of-the-art classification methods.
