Random spatial network models
for core-periphery structure.
1
Junteng Jia and Austin R. Benson
Our model for spatial core-periphery structure.
2
Pr(edge (u, v) in graph) =
e✓u
+ e✓v
e✓u + e✓v + Kuv<latexit 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✓w is the core score of node w
Kuv is kernel function (distance between u and v)<latexit 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Theory. Given a graph,local maximizers of likelihood are random graph
models with the same expected degree and expected aggregate log-distance.
Problem? Quadratic scaling in
learning & sampling?
Use FMM-like algorithms for
O(n log n) with spatial data.
Core scores {!w} are useful for downstream MLtasks.
3
Cross validation accuracy of fungal networks
classification using different network features.
random degree BC CC EC PR core score
6.7% 38.0% 23.7% 19.0% 20.2% 18.6% 43.5%
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Random spatial network models
for core-periphery structure.
4
Junteng Jia and Austin R. Benson
• Random graph model for core-periphery structure with (possible) spatial data.
• Theory shows learned model parameters give a generalization of Chung-Lu.
• Methods from computational physics yield fast learning.
• Model parameters useful for downstream machine learning tasks.

Random spatial network models for core-periphery structure.

  • 1.
    Random spatial networkmodels for core-periphery structure. 1 Junteng Jia and Austin R. Benson
  • 2.
    Our model forspatial core-periphery structure. 2 Pr(edge (u, v) in graph) = e✓u + e✓v e✓u + e✓v + Kuv<latexit 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✓w is the core score of node w Kuv is kernel function (distance between u and v)<latexit 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Theory. Given a graph,local maximizers of likelihood are random graph models with the same expected degree and expected aggregate log-distance. Problem? Quadratic scaling in learning & sampling? Use FMM-like algorithms for O(n log n) with spatial data.
  • 3.
    Core scores {!w}are useful for downstream MLtasks. 3 Cross validation accuracy of fungal networks classification using different network features. random degree BC CC EC PR core score 6.7% 38.0% 23.7% 19.0% 20.2% 18.6% 43.5% <latexit 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  • 4.
    Random spatial networkmodels for core-periphery structure. 4 Junteng Jia and Austin R. Benson • Random graph model for core-periphery structure with (possible) spatial data. • Theory shows learned model parameters give a generalization of Chung-Lu. • Methods from computational physics yield fast learning. • Model parameters useful for downstream machine learning tasks.