Abstract
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.
Highlights
The actively functioning transportation of various particles through intracellular movements is a vital process for cells of living organisms (Porter and Day (2016))
The uninformative prior cardinality produces very low variance in the posterior cardinality estimation. For this case we present a comparison between the cardinality statistics given by using i.i.d. cluster point process characterization of the persistence diagrams (PDs) presented and a Poisson point process framework presented in Maroulas et al (2020) that estimates the number of homological features by integrating the estimated posterior intensity
In this work we focus on developing Bayesian model for PDs only
Summary
The actively functioning transportation of various particles through intracellular movements is a vital process for cells of living organisms (Porter and Day (2016)). We develop a fully data-driven Bayesian topological learning method, which could aid researchers by providing a pathway to predict cytoskeleton structural properties by classifying simulated actin filament networks to identify the effect of the number of cross-linking proteins on the network. The direct benefits of this closed form solution of the posterior distribution are two-fold: (i) it demonstrates the computational tractability of the proposed Bayesian model and (ii) it provides a means to develop a robust classification scheme through Bayes’ factors Another computational benefit of these closed forms is the quantification of the intensity of the unexpected PP by means of an exponential density. (ii) it provides a more computationally automatic approach as we only need to modify one parameter This Bayesian paradigm provides a method for the classification of actin filament networks in plant cells that captures their distinguishing topological features. We delegate all of the proofs, as well as some definitions, lemmas, and notations required for the proofs to the supplementary materials (Maroulas et al, 2021)
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