DM3L Seminar: Juni Schindler

Exploring Multiscale Clusterings with Markov Stability and Multiparameter Persistent Homology

Talk by Juni Schindler (DM3L)

Date: 11.12.25  Time: 12.00 - 13.15  Room: Y27H12

Many datasets exhibit structure at multiple levels of granularity, but these levels do not always form a strict hierarchy. Such datasets are naturally described as multiscale clusterings, which represent not necessarily hierarchical sequences of partitions across scales. In this talk, I will describe Markov Stability, a graph-based approach that employs a diffusion process to reveal a sequence of partitions ranging from fine to coarse resolution. By varying the diffusion time, the method uncovers robust groupings while allowing the partitions at successive scales to be non-hierarchical. A natural problem that arises is how to analyse and compare these non-hierarchical sequences of partitions. I will address this issue from a topological perspective and present the Multiscale Clustering Bifiltration, a bifiltration of abstract simplicial complexes that encodes the cluster intersection patterns within the sequence of partitions. Its multiparameter persistent homology provides rich feature maps that measure the nestedness and higher-order inconsistencies among cluster assignments across scales. This talk will cover both the underlying theory and concrete applications, illustrating how Markov Stability and the Multiscale Clustering Bifiltration can be utilised to explore and assess multiscale patterns in real-world data.