
TL;DR
This paper introduces a novel autoregressive hypergraph model for dynamic, non-uniform hypergraphs, providing theoretical guarantees, efficient inference, community detection, and change-point estimation, with demonstrated effectiveness on real-world datasets.
Contribution
It presents the first dynamic hypergraph model with provable guarantees, including a spectral clustering method for community detection and a change-point estimator, advancing the analysis of evolving complex relational data.
Findings
Effective community detection via spectral clustering.
Accurate change-point detection in hypergraph time series.
Validated methods on real-world datasets with meaningful insights.
Abstract
Traditional graph representations are insufficient for modelling real-world phenomena involving multi-entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve the intrinsic nature of such complex relationships, existing models often overlook temporal evolution in relational data. To address this, we introduce a first-order autoregressive (i.e. AR(1)) model for dynamic non-uniform hypergraphs. This is the first dynamic hypergraph model with provable theoretical guarantees, explicitly defining the temporal evolution of hyperedge presence through transition probabilities that govern persistence and change dynamics. This framework provides closed-form expressions for key probabilistic properties and facilitates straightforward maximum-likelihood inference with uniform error bounds and asymptotic normality,…
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Taxonomy
TopicsComplex Network Analysis Techniques · Bioinformatics and Genomic Networks · Advanced Graph Neural Networks
