Research map / Graph learning / Graph algorithms and clustering
Spectral Graph Matching and Regularized Quadratic Relaxations: Algorithm and Theory
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add all-pairs eigenvector combination with Cauchy spectral weights (GRAMPA) instead of only paired eigenvectors | spectral graph matching · Erdős-Rényi graphs n=100, density 0.5 | fraction of correctly matched vertices | Helped |
| Use Cauchy kernel weights instead of degree-product weights w(λ,µ)=λµ | spectral similarity matrix · theory / heuristic | matching success | Helped |
| Use GRAMPA on correlated Erdős-Rényi graphs in place of Degree Profile | correlated Erdős-Rényi matching · Erdős-Rényi n=500, density 0.5 | fraction of correctly matched vertices | Helped |
| Use GRAMPA instead of DegreeProfile on autonomous systems network | time-evolving AS network matching · Autonomous Systems n=10000 | fraction of correctly matched vertices | Helped |
| Use GRAMPA (with iterative clean-up) instead of existing shape matching methods (EM, GE, RF) | SHREC'16 deformable shape matching · SHREC'16 kid shapes | normalized geodesic error CDF | Helped |
| Add ridge (Cauchy) regularization with bandwidth η instead of η→0 | spectral similarity matrix · theory | variance / stability of similarity matrix | Helped |
| Tune bandwidth η within practical range (performance insensitive except extreme values) (ablation) | GRAMPA · synthetic experiments | matching accuracy | No clear effect |
| Add iterative clean-up procedure after GRAMPA initialization | GRAMPA on SHREC'16 · SHREC'16 kid shapes | normalized geodesic error | Helped |
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