Structural Liftings

In the context of TDL, liftings facilitate the mapping of data from one topological representation to another. This mapping comprises two key aspects: structural lifting and feature lifting.

• The structural lifting is responsible for the transformation of the underlying relationships or elements of the data. For instance, it might determine how nodes and edges in a graph are mapped into triangles and tetrahedra in a simplicial complex. This structural transformation can be further categorized into connectivity-based, where the mapping relies solely on the existing connections within the data, and feature-based, where the data's inherent properties or features guide the new structure.
• The feature lifting, conversely, addresses the transfer of data attributes or features during mapping, ensuring that the properties associated with the data elements are consistently preserved in the new representation.

This wiki describes in detail the structural liftings implemented in TopoBenchmark --taxonomized by source and destination topological domains. Most of them are submissions of the ICML TDL Challenge 2024 (paper | repo):

• Graph to Simplicial Complex
  • DnD Lifting
  • Random Latent Clique Lifting
  • Line Lifting
  • Neighbourhood Complex Lifting
• Graph to Cell Complex
  • Discrete Configuration Complex
  • Graph Induced Lifting
• Graph to Hypergraph
  • Expander Hypergraph Lifting
  • Kernel Lifting
  • Mapper Lifting
  • Forman‐Ricci Curvature Coarse Geometry Lifting
  • KNN Lifting
• Graph to Combinatorial
  • Matroid lifting
  • Molecule Ring & Close Atoms Lifting
  • Simplicial Paths Lifting
• Pointcloud to Simplicial
  • Delaunay Lifting
  • Random Flag Complex
• Pointcloud to Hypergraph
  • Mixture of Gaussians MST lifting
  • PointNet Lifting
  • Voronoi Lifting
• Hypergraph to Simplicial
  • Hypergraph Heat Kernel Lifting
• Hypergraph to Combinatorial
  • Universal Strict Lifting