Topological autocorrelation in multiscale clusterings via 2-parameter persistent homology

Date

Jul 14, 2025

Time

1:00 PM - 2:00 PM

Speaker

Juni Schindler

Affiliation

Imperial College London

Language

en

Main Topic

Biologie

Host

Heather Harrington

Description

In many areas of data science, networks have an intrinsic multiscale structure, whereby meaningful descriptions exist at different levels of coarseness (or scales). In such cases, it is desirable to go beyond clustering into a single partition to find a (not necessarily hierarchical) sequence of partitions that captures aspects of the data at multiple levels of resolution. A natural problem is then to analyse and characterise such sequences of coarsening multiscale clusterings. To enhance the interpretability for multiscale clusterings, we use multi-parameter persistent homology (MPH) and introduce a 2-parameter filtration of abstract simplicial complexes, termed Multiscale Clustering Bifiltration (MCbiF). The MCbiF captures the “topological autocorrelation” of the history-dependent, non-stationary sequence of non-hierarchical, coarsening partitions, and leads to rich algebraic invariants like the 0- and 1-dimensional Hilbert functions. We illustrate the MCbiF with an application to ensembles of graphs sampled from stochastic block models with different planted partition structure and find that our method both captures the hierarchy of the models and recovers the ground-truth scales as “conflict-resolving” partitions. To our knowledge, MCbiF is the first application of multiparameter persistence to analyse multiscale networks. By disentangling the “aggregation history” in multiscale clusterings, MCbiF provides enhanced sensitivity and robustness to characterise the higher-order interactions in non-hierarchical sequences of partitions.

Last modified: Jul 14, 2025, 7:36:30 AM