Comparing Graph Clusterings: Set Partition Measures vs. Graph-Aware Measures

Poulin, Valérie; Théberge, François

doi:10.1109/tpami.2020.3009862

Cited by 2 publications

(1 citation statement)

References 35 publications

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“…For example, graph neural networks are proposed to learn both global topological structure and the local connectivity structure within a network [30]. Other algorithms, such as support vector machines, principal component analysis, or entropic models are also commonly used to perform statistical inference of network structure [31,32].…”

Section: Related Workmentioning

confidence: 99%

Statistical structural inference from edge weights using a mixture of gamma distributions

Wang,

Hancock

2023

Journal of Complex Networks

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The inference of reliable and meaningful connectivity information from weights representing the affinity between nodes in a graph is an outstanding problem in network science. Usually, this is achieved by simply thresholding the edge weights to distinguish true links from false ones and to obtain a sparse set of connections. Tools developed in statistical mechanics have provided particularly effective ways to locate the optimal threshold so as to preserve the statistical properties of the network structure. Thermodynamic analogies together with statistical mechanical ensembles have been proven to be useful in analysing edge-weighted networks. To extend this work, in this article, we use a statistical mechanical model to describe the probability distribution for edge weights. This models the distribution of edge weights using a mixture of Gamma distributions. Using a two-component Gamma mixture model with components describing the edge and non-edge weight distributions, we use the Expectation–Maximization algorithm to estimate the corresponding Gamma distribution parameters and mixing proportions. This gives the optimal threshold to convert weighted networks to sets of binary-valued connections. Numerical analysis shows that it provides a new way to describe the edge weight probability. Furthermore, using a physical analogy in which the weights are the energies of molecules in a solid, the probability density function for nodes is identical to the degree distribution resulting from a uniform weight on edges. This provides an alternative way to study the degree distribution with the nodal probability function in unweighted networks. We observe a phase transition in the low-temperature region, corresponding to a structural transition caused by applying the threshold. Experimental results on real-world weighted and unweighted networks reveal an improved performance for inferring binary edge connections from edge weights.

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Section: Related Workmentioning

confidence: 99%

Statistical structural inference from edge weights using a mixture of gamma distributions

Wang,

Hancock

2023

Journal of Complex Networks

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Facilitating Compromise in Redistricting with Transfer Distance Midpoints

Dobbs,

King,

Ludden

et al. 2024

INFORMS Journal on Optimization

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States in the United States redraw their electoral district boundaries every 10 years. This redistricting process can be contentious and has long-lasting consequences for political representation. To reduce bias in the redistricting process, some states require bipartisan commissions; however, bipartisan commissions can still involve partisan tension if the political parties cannot compromise. We propose an optimization framework to facilitate compromise between two redistricting stakeholders. This framework seeks a midpoint between two stakeholder plans with respect to a distance metric. A midpoint can help the stakeholders visualize a potential compromise that incorporates district structure common to both of their proposed plans. First, we consider multiple distance metrics and evaluate whether midpoints with respect to these metrics are achievable and align with redistricting requirements. Then we formulate a mixed-integer linear program to find a midpoint (or any fractional point) between two given plans with respect to the transfer distance. This formulation incorporates district structure from both given plans by fixing variables; consequently, it is possible to solve some realistically sized instances exactly in reasonable amounts of time. We present experiments on grid instances and Missouri’s congressional redistricting instance to demonstrate how this method can quickly generate compromise options that align with redistricting requirements. Funding: This material is based on work supported by the National Science Foundation Graduate Research Fellowship Program [Grant DGE-1746047]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2023.0029 .

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Comparing Graph Clusterings: Set Partition Measures vs. Graph-Aware Measures

Cited by 2 publications

References 35 publications

Statistical structural inference from edge weights using a mixture of gamma distributions

Statistical structural inference from edge weights using a mixture of gamma distributions

Facilitating Compromise in Redistricting with Transfer Distance Midpoints

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