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Analysing Multiscale Clustering with Persistent Homology

Series: Department Seminar

Speaker: Dominik Schindler, Imperial College London

Date/Time: Jul 26 11:00:00

Location: CSA Conference Room, (Room No. 101, Ground floor)

Abstract:
In data clustering, it's often useful to find a sequence of partitions describing the data at different scales, rather than just a single partition. In this talk, I introduce the Multiscale Clustering Filtration (MCF), which encodes cluster assignments across scales using tools from topological data analysis (TDA). The zero-dimensional persistent homology of the MCF measures the hierarchy in the sequence of partitions, while the higher-dimensional persistent homology tracks conflicts between cluster assignments. I demonstrate the MCF's effectiveness in characterizing multiscale clustering structures through numerical experiments on stochastic block models with different intrinsic structures. Additionally, I present an equivalent construction using a nerve complex filtration, which is computationally advantageous for certain datasets. Finally, I discuss future research directions, including the development of a bootstrapping scheme for MCF and the analysis of minimal cycles to locate conflicts in multiscale clustering.

Speaker Bio:
Dominik Schindler is a PhD candidate in Applied Mathematics at Imperial College London, supervised by Prof. Mauricio Barahona. Drawing from network science, machine learning and topological data analysis, they develop methods for the multiscale analysis of complex graph-based data. Their work has applications in the computational social sciences and as a Research Fellow at the Weizenbaum Institute Berlin, Dominik analyses conspiracy-related online communication. Additionally, they investigate the social and cultural implications of mathematics and machine learning through a feminist and decolonial lens. Dominik is currently exploring critical perspectives on Bayesian learning as a Guest Editor in the Computational Culture journal, together with Prof. Matthew Fuller and Goda KlumbytÄ—. Before the PhD, Dominik attained an MSc in Applied Mathematics from Imperial College and an MA in Digital Media from Goldsmiths, University of London.

Host Faculty: Prof. Vijay Natarajan