arXiv subjects

Juni Schindler

Publications and source records attributed to Juni Schindler.

8 recordsLinked to original sources

arXiv2026

MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.

math.AT↗

arXiv2025

Community as a Vague Operator: Epistemological Questions for a Critical Heuristics of Community Detection Algorithms

In this article, we aim to analyse the nature and epistemic consequences of what figures in network science as patterns of nodes and edges called 'communities'. Tracing these patterns as multi-faceted and ambivalent, we propose to describe the concept of community as a 'vague operator', a variant of Susan Leigh Star's notion of the boundary object, and propose that the ability to construct different modes of description that are both vague in some registers and hyper-precise in others, is core both to digital politics and the analysis of 'communities'. Engaging with these formations in terms drawn from mathematics and software studies enables a wider mapping of their formation. Disentangling different lineages in network science then allows us to contextualise the founding account of 'community' popularised by Michelle Girvan and Mark Newman in 2002. After studying one particular community detection algorithm, the widely-used 'Louvain algorithm', we comment on controversies arising with some of their more ambiguous applications. We argue that 'community' can act as a real abstraction with the power to reshape social relations such as producing echo chambers in social networking sites. To rework the epistemological terms of community detection and propose a reconsideration of vague operators, we draw on debates and propositions within the literature of network science to imagine a 'critical heuristics' that embraces partiality, epistemic humbleness, reflexivity and artificiality.

cs.SI↗

arXiv2025

Multiscale mobility patterns and the restriction of human movement

From the perspective of human mobility, the COVID-19 pandemic constituted a natural experiment of enormous reach in space and time. Here, we analyse the inherent multiple scales of human mobility using Facebook Movement Maps collected before and during the first UK lockdown. First, we obtain the pre-lockdown UK mobility graph, and employ multiscale community detection to extract, in an unsupervised manner, a set of robust partitions into flow communities at different levels of coarseness. The partitions so obtained capture intrinsic mobility scales with better coverage than NUTS regions, which suffer from mismatches between human mobility and administrative divisions. Furthermore, the flow communities in the fine scale partition match well the UK Travel to Work Areas (TTWAs) but also capture mobility patterns beyond commuting to work. We also examine the evolution of mobility under lockdown, and show that mobility first reverted towards fine scale flow communities already found in the pre-lockdown data, and then expanded back towards coarser flow communities as restrictions were lifted. The improved coverage induced by lockdown is well captured by a linear decay shock model, which allows us to quantify regional differences both in the strength of the effect and the recovery time from the lockdown shock.

physics.soc-ph↗

arXiv2025

PyGenStability: Multiscale community detection with generalized Markov Stability

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualisation tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithms. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed and signed graphs, and to include other user-defined quality functions.

cs.SI↗

arXiv2025

LGDE: Local Graph-based Dictionary Expansion

We present Local Graph-based Dictionary Expansion (LGDE), a method for data-driven discovery of the semantic neighbourhood of words using tools from manifold learning and network science. At the heart of LGDE lies the creation of a word similarity graph from the geometry of word embeddings followed by local community detection based on graph diffusion. The diffusion in the local graph manifold allows the exploration of the complex nonlinear geometry of word embeddings to capture word similarities based on paths of semantic association, over and above direct pairwise similarities. Exploiting such semantic neighbourhoods enables the expansion of dictionaries of pre-selected keywords, an important step for tasks in information retrieval, such as database queries and online data collection. We validate LGDE on two user-generated English-language corpora and show that LGDE enriches the list of keywords with improved performance relative to methods based on direct word similarities or co-occurrences. We further demonstrate our method through a real-world use case from communication science, where LGDE is evaluated quantitatively on the expansion of a conspiracy-related dictionary from online data collected and analysed by domain experts. Our empirical results and expert user assessment indicate that LGDE expands the seed dictionary with more useful keywords due to the manifold-learning-based similarity network.

cs.CL↗

arXiv2025

Convergence of Markov chain transition probabilities

Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $μ$. There are several sufficient conditions in the literature which guarantee convergence of all or $μ$-almost all transition probabilities to $μ$ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively $μ$-almost all transition probabilities. In addition, we discuss so-called generalized couplings.

math.PR↗

arXiv2025

Situated Bayes -- Feminist and Pluriversal Perspectives on Bayesian Knowledge

This is the introduction and lead article to the Situated Bayes special issue of Computational Culture. The article introduces Bayes' Theorem and aspects of its contemporary uses, for instance in machine learning. A mathematical discussion is developed alongside a consideration of Bayes Theorem in relation to critical theories of knowledge, specifically the discussion of situated knowledge in feminist theories of science, pluriversal knowledge in decolonial theory, and critical approaches to mathematics. We discuss whether there are possible resonances between Bayesian mapping of multiple functions and the idea of the subjective on the one hand and these theoretical propositions on the other and propose further lines of enquiry for future research. In closing the introduction, the contributions to the special issue are briefly described.

cs.CY↗

arXiv2025

Analysing Multiscale Clusterings with Persistent Homology

In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare the (not necessarily hierarchical) sequences of partitions that underpin such multiscale descriptions. Here, we use tools from topological data analysis and introduce the Multiscale Clustering Filtration (MCF), a well-defined and stable filtration of abstract simplicial complexes that encodes arbitrary cluster assignments in a sequence of partitions across scales of increasing coarseness. We show that the zero-dimensional persistent homology of the MCF measures the degree of hierarchy of this sequence, and the higher-dimensional persistent homology tracks the emergence and resolution of conflicts between cluster assignments across the sequence of partitions. To broaden the theoretical foundations of the MCF, we provide an equivalent construction via a nerve complex filtration, and we show that, in the hierarchical case, the MCF reduces to a Vietoris-Rips filtration of an ultrametric space. Using synthetic data, we then illustrate how the persistence diagram of the MCF provides a feature map that can serve to characterise and classify multiscale clusterings.

math.AT↗