Bayesian Topological Learning for Classifying the Structure of Biological Networks

TL;DR

This paper introduces a Bayesian topological learning method that classifies biological actin networks by analyzing their topological features through persistence diagrams and a novel probabilistic framework.

Contribution

It develops a Bayesian framework for classifying biological networks using persistence diagrams, with closed-form posteriors and a new Bayes factor classification algorithm.

Findings

Effective classification of actin networks demonstrated

Outperforms several state-of-the-art methods

Provides a probabilistic understanding of topological features

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 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.