Wasserstein-Based Graph Alignment Article Swipe
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· 2022
· Open Access
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· DOI: https://doi.org/10.1109/tsipn.2022.3169632
We propose a novel method for comparing non-aligned graphs of different\nsizes, based on the Wasserstein distance between graph signal distributions\ninduced by the respective graph Laplacian matrices. Specifically, we cast a new\nformulation for the one-to-many graph alignment problem, which aims at matching\na node in the smaller graph with one or more nodes in the larger graph. By\nintegrating optimal transport in our graph comparison framework, we generate\nboth a structurally-meaningful graph distance, and a signal transportation plan\nthat models the structure of graph data. The resulting alignment problem is\nsolved with stochastic gradient descent, where we use a novel Dykstra operator\nto ensure that the solution is a one-to-many (soft) assignment matrix. We\ndemonstrate the performance of our novel framework on graph alignment and graph\nclassification, and we show that our method leads to significant improvements\nwith respect to the state-of-the-art algorithms for each of these tasks.\n
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/tsipn.2022.3169632
- OA Status
- green
- Cited By
- 14
- References
- 84
- Related Works
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- OpenAlex ID
- https://openalex.org/W3011991560