Persistent homology method to detect block structures in weighted networks

08/03/2021
by   Wooseok Jung, et al.
0

Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for weighted networks, but it is not always optimal. We introduce a novel topological method to study the block structure of weighted networks by comparing their persistence diagrams. We found persistence diagrams of networks with different block structures show distinct features, sufficient to distinguish. Moreover, the overall characteristics are preserved even with more stochastic examples or modified hyperparameters. Finally, when random graphs whose latent block structure is unknown are tested, results from persistence diagram analysis are consistent with their weighted stochastic block model. Although this topological method cannot completely replace the original WSBM method for some reasons, it is worth to be investigated further.

READ FULL TEXT

page 1

page 7

research
03/22/2018

Persistence Weighted Gaussian Kernel for Probability Distributions on the Space of Persistence Diagrams

A persistence diagram characterizes robust geometric and topological fea...
research
09/17/2020

A Fast and Robust Method for Global Topological Functional Optimization

Topological statistics, in the form of persistence diagrams, are a class...
research
04/03/2022

Bayesian estimation of topological features of persistence diagrams

Persistent homology is a common technique in topological data analysis p...
research
10/11/2017

A Note on Community Trees in Networks

We introduce the concept of community trees that summarizes topological ...
research
09/24/2020

Bayesian Topological Learning for Classifying the Structure of Biological Networks

Actin cytoskeleton networks generate local topological signatures due to...
research
05/24/2013

Adapting the Stochastic Block Model to Edge-Weighted Networks

We generalize the stochastic block model to the important case in which ...
research
03/07/2018

Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams

We introduce a nonparametric way to estimate the global probability dens...

Please sign up or login with your details

Forgot password? Click here to reset