Learning Persistent Community Structures in Dynamic Networks via
  Topological Data Analysis
Dexu Kong Anping Zhang Yang Li
Dynamic community detection methods often lack effective mechanisms to ensure
temporal consistency, hindering the analysis of network evolution. In this
paper, we propose a novel deep graph clustering framework with temporal
consistency regularization on inter-community structures, inspired by the
concept of minimal network topological changes within short intervals.
Specifically, to address the representation collapse problem, we first
introduce MFC, a matrix factorization-based deep graph clustering algorithm
that preserves node embedding. Based on static clustering results, we construct
probabilistic community networks and compute their persistence homology, a
robust topological measure, to assess structural similarity between them.
Moreover, a novel neural network regularization TopoReg is introduced to ensure
the preservation of topological similarity between inter-community structures
over time intervals. Our approach enhances temporal consistency and clustering
accuracy on real-world datasets with both fixed and varying numbers of
communities. It is also a pioneer application of TDA in temporally persistent
community detection, offering an insightful contribution to field of network
analysis. Code and data are available at the public git repository:
https://github.com/kundtx/MFC_TopoReg