Generative hypergraph clustering: From blockmodels to modularity

Chodrow, Philip S.; Veldt, Nate; Benson, Austin R.

doi:10.1126/sciadv.abh1303

Cited by 103 publications

(130 citation statements)

References 68 publications

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“…In the enronemail hypergraph, vertices correspond to emails at Enron and a hyperedge consists of the sender and all the recipients of an email. The hypergraph contact-highschool is based on close-proximity human interactions [40], obtained from sensor data worn by students at a high school, wherein vertices represent students and each hyperedge is a group of students that were in close proximity of one another.…”

Section: Hypergraph Datasetsmentioning

confidence: 99%

A Poset-Based Approach to Curvature of Hypergraphs

2022

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In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a two-dimensional simplicial complex associated with a hypergraph, such that the vertices of the simplicial complex represent the vertices and hyperedges of the original hypergraph. We then define the Forman–Ricci curvature of the vertices and the hyperedges as the scalar curvature of the associated vertices in the simplicial complex. Remarkably, Forman–Ricci curvature has a simple combinatorial expression and it can effectively capture the variation in symmetry or asymmetry over a hypergraph. Finally, we perform an empirical study involving computation and analysis of the Forman–Ricci curvature of hyperedges in several real-world hypergraphs. We find that Forman–Ricci curvature shows a moderate to high absolute correlation with standard hypergraph measures such as eigenvector centrality and cardinality. Our results suggest that the notion of Forman–Ricci curvature extended to hypergraphs in this work can be used to gain novel insights on the organization of higher-order interactions in real-world hypernetworks.

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Section: Hypergraph Datasetsmentioning

confidence: 99%

A Poset-Based Approach to Curvature of Hypergraphs

2022

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“…The only heuristic computations which may be difficult to reproduce are the network layouts, which we sought to make as reproducible as possible by avoiding random seeds, and the Louvain-based modularity clustering [Blondel et al, 2008], for which we used the HyperModularity code [Chodrow et al, 2021] without the randomization techniques. Towards those ends, we provide the clustering we found as the final/temporal-modularity-clusters.json file.…”

Section: Full List Of Derived Datasets and Associated Filesmentioning

confidence: 99%

fauci-email: a json digest of Anthony Fauci's released emails

Benson¹,

Veldt²,

Gleich³

2021

Preprint

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A collection of over 3000 pages of emails sent by Anthony Fauci and his staff were released in an effort to understand the United States government response to the COVID-19 pandemic. We describe how this email data was translated into a resource consisting of json files that make many future studies easy. Findings from our processed data include (i) successful organizational partitions using the simple mincut techniques in Zachary's karate club methodology, (ii) a natural example where the normalized cut and minimum conductance set are extremely different, and (iii) organizational groups identified by optimal modularity clusters that illustrate a working hierarchy. These example uses suggest the data will be useful for future research and pedagogical uses in terms of human and system behavioral interactions. We explain a number of ways to turn email information into a network, a hypergraph, a temporal sequence, and a tensor for subsequent analysis as well as a few examples of such analysis.

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“…These penalties satisfy the normalizing condition that f e (A) = 1 when |A| = 1, though if desired they could be scaled by a constant. Scaling the clique penalty |A||e\A| by (|e| − 1) −1 has several other additional desirable properties that have led to its use in numerous other hypergraph clustering frameworks [46,27,10].…”

Section: C2 Hypergraph Localized Clustering Experimentsmentioning

confidence: 99%

Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components

Veldt¹,

Benson²,

Kleinberg³

2021

Preprint

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Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where components in the sum are cardinality-based, meaning they depend only on the size of the input set. This variant is one of the most widely applied in practice, encompassing, e.g., common energy functions arising in image segmentation and recent generalized hypergraph cut functions. We develop the first approximation algorithms for this problem, where the approximations can be quickly computed via reduction to a sparse graph cut problem, with graph sparsity controlled by the desired approximation factor. Our method relies on a new connection between sparse graph reduction techniques and piecewise linear approximations to concave functions. Our sparse reduction technique leads to significant improvements in theoretical runtimes, as well as substantial practical gains in problems ranging from benchmark image segmentation tasks to hypergraph clustering problems. * This paper is an adaptation (for NeurIPS 2021) of an earlier manuscript titled Augmented Sparsifiers for Generalized Hypergraph Cuts [8], with a new emphasis and exposition, and updated proofs for several results.

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Generative hypergraph clustering: From blockmodels to modularity

Cited by 103 publications

References 68 publications

A Poset-Based Approach to Curvature of Hypergraphs

A Poset-Based Approach to Curvature of Hypergraphs

fauci-email: a json digest of Anthony Fauci's released emails

Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components

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