Bayesian Topological Learning for Classifying the Structure of Biological Networks

09/24/2020
by   Vasileios Maroulas, et al.
59

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.

READ FULL TEXT

page 12

page 14

page 15

01/07/2019

Bayesian Inference for Persistent Homology

Persistence diagrams offer a way to summarize topological and geometric ...
12/04/2018

A Stable Cardinality Distance for Topological Classification

This work incorporates topological and geometric features via persistenc...
04/03/2022

Bayesian estimation of topological features of persistence diagrams

Persistent homology is a common technique in topological data analysis p...
01/10/2019

Understanding the Topology and the Geometry of the Persistence Diagram Space via Optimal Partial Transport

We consider a generalization of persistence diagrams, namely Radon measu...
08/03/2021

Persistent homology method to detect block structures in weighted networks

Unravelling the block structure of a network is critical for studying ma...
08/03/2022

A Convolutional Persistence Transform

We consider a new topological feauturization of d-dimensional images, ob...
03/31/2022

Topological Optimization with Big Steps

Using persistent homology to guide optimization has emerged as a novel a...