CellEncoding Lifting (Cell to Graph)

[aweers]

Implementation of the Cell to Graph Lifting via Cell Encoding as proposed in Reducing learning on cell complexes to graphs by Jogl, F., Thiessen, M., & Gärtner, T.

Short description:
The lifting takes a cell complex $X$ as source domain and transforms it to a graph $G_X$ as destination domain. Each cell $P_X$ becomes a vertex in $G_X$, such that $V_X=P_X$. Those vertices are connected via two rules:

1. Two cells $\tau, \delta \in P_X$ have a direct boundary relationship.
2. Two cells $\tau, \delta \in P_X$ share a common higher-dimensional cell.

If either rule applies to a pair of cells, their corresponding vertices in $G_X$ get connected with an edge.
Additionally each vertex gets an encoding that corresponds to the one-hot encoded cell dimension.

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[gbg141]

Hello @aweers! 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 guillermo_bernardez@ucsb.edu so I can share access to the voting form. In your email, please include:

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