• Corpus ID: 243938560

Graph Matching via Optimal Transport

@article{SaadEldin2021GraphMV,
  title={Graph Matching via Optimal Transport},
  author={Ali Saad-Eldin and Benjamin D. Pedigo and Carey E. Priebe and Joshua T. Vogelstein},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.05366}
}
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it’s applications in operations research, computer vision, neuroscience, and more. However, current stateof-the-art algorithms are inefficient in matching very large graphs, though they produce good accuracy. The main computational bottleneck of these algorithms is the linear assignment problem… 

Figures from this paper

Bisected graph matching improves automated pairing of bilaterally homologous neurons from connectomes

This work presents a modification to a state-of-the-art graph matching algorithm which allows it to solve what they call the bisected graph matching problem and shows that when edge correlation is present between the contralateral (between hemisphere) subgraphs, this approach improves matching accuracy.

Multiscale Graph Comparison via the Embedded Laplacian Distance

This work proposes the Embedded Laplacian Distance (ELD), a simple and fast method for comparing graphs of different sizes that is a pseudometric and is invariant under graph isomorphism and provides intuitive interpretations of the ELD using tools from spectral graph theory.

Bilingual Lexicon Induction for Low-Resource Languages using Graph Matching via Optimal Transport

This work improves bilingual lexicon induction performance across 32 diverse language pairs with a graph-matching method based on opti- mal transport that is especially strong with very low amounts of supervision.

References

SHOWING 1-10 OF 37 REFERENCES

Seeded graph matching

Fast Approximate Quadratic Programming for Graph Matching

This work presents its graph matching algorithm, the Fast Approximate Quadratic assignment algorithm, and empirically demonstrates that the algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art.

A Path Following Algorithm for the Graph Matching Problem

This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching and is compared with some of the best performing graph matching methods on four data sets.

An Eigendecomposition Approach to Weighted Graph Matching Problems

  • S. Umeyama
  • Mathematics
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1988
An approximate solution to the weighted-graph-matching problem is discussed for both undirected and directed graphs and an analytic approach is used instead of a combinatorial or iterative approach to the optimum matching problem.

Vertex nomination via seeded graph matching

This work presents a principled methodology appropriate for situations in which the networks are too large/noisy for brute‐force graph matching, and identifies Vertices in a local neighborhood of the VOIs in the first network that have verifiable corresponding vertices in the second network.

Efficient Matching and Indexing of Graph Models in Content-Based Retrieval

Analytic comparison and experimental results show that the proposed lookahead improves the state-of-the-art in state-space search methods and that the combined use of the proposed matching and indexing scheme permits for the management of the complexity of a typical application of retrieval by spatial arrangement.

Spectral clustering for divide-and-conquer graph matching

Pairwise Global Alignment of Protein Interaction Networks by Matching Neighborhood Topology

An algorithm for global alignment of two protein-protein interaction (PPI) networks is described, guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched, and the results of global alignment are interpreted to identify functional orthologs between yeast and fly.

Sinkhorn Distances: Lightspeed Computation of Optimal Transport

This work smooths the classic optimal transport problem with an entropic regularization term, and shows that the resulting optimum is also a distance which can be computed through Sinkhorn's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transport solvers.

Computational Optimal Transport: With Applications to Data Science

Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes.