Cy2C lifting (Graph to Simplicial)

[dkssudgktpdydn]

Add a lifting from graph to simplicial based on Clique to Cycle (Cy2C) (Choi et al. (2022)).

Overcome the theoretical limitations by enriching the topological properties of the input data admitted by GNNs with clique adjacency matrices.

Clique Adjacency Matrix:
Let $G := (V, E)$ be an undirected graph. Fix the cycle basis $B_G$ of $G$, the set of cyclic subgraphs of $G$ which forms the basis of the cycle space (or the first homology group) of $G$. The clique adjacency matrix of $G$, denoted as $A_C$, is the adjacency matrix of the union of $B_G$ complete subgraphs, each obtained from adding all possible edges among the set of nodes of each basis element $B \in B_G$.

References
Cycle to Clique (Cy2C) Graph Neural Network: A Sight to See beyond Neighborhood Aggregation (Choi et al. ICLR 2022)
Topology-Informed Graph Transformer (Choi et al., ICML GRaM 2024)

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[gbg141]

Hello @dkssudgktpdydn ! Thank you for your submission. As we near the end of the challenge, I am collecting participant info for the purpose of selecting and announcing winners. Please email me (or have one member of your team email me) at [email protected] so I can share access to the voting form. In your email, please include:

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Before July 12, make sure that your submission respects all Submission Requirements laid out on the challenge page. Any submission that fails to meet this criteria will be automatically disqualified.

[dkssudgktpdydn]

Dear Guillermo Bernárdez, I hope this email finds you well. As requested, I am providing the necessary information for my team's participation in the challenge: 1. Team Members: - Yun Young Choi, Ph.D., VOLTWIN INC., ***@***.*** - Minho Lee, Researcher, VOLTWIN INC., ***@***.*** 2. Method Implemented: - Title: Cy2C lifting : lifting from graph to simplicial based on 'Cycle to Clique (Cy2C) Graph Neural Network (Choi et al. (ICLR, 2022))'. - Input Domain: Graph - Output Domain: Simplicial 3. Pull Request Number: - #27 Please let me know if you need any additional information. Thank you for your time and consideration. Best regards, Yun Young Choi 2024년 7월 9일 (화) 오전 2:17, Guillermo Bernárdez ***@***.***>님이 작성:

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