Applicability of non-Euclidean embedding models to biological pathway graphs

Determine the extent to which non-Euclidean graph embedding models—including mixed-curvature product-space embeddings composed of hyperbolic, spherical, and Euclidean components—work effectively for biological pathway graphs, which differ topologically from standard benchmark graphs, in order to assess their suitability for pathway representation learning.

Background

Non-Euclidean graph embedding methods, including hyperbolic and mixed-curvature product spaces, have shown advantages in preserving graph structure and improving downstream tasks on general benchmarking datasets. However, these evaluations largely focus on standard graph types and domains.

Biological pathway graphs have distinct properties and complex topologies compared to typical benchmark graphs. Prior work on pathways has predominantly used Euclidean embedding methods, leaving uncertainty around whether non-Euclidean and mixed-curvature approaches are suitable for such biological data.

References

Only Euclidean embedding methods have been applied to pathway graphs (M A Basher & Hallam, 2020; Pershad et al., 2020), and because pathway graphs differ from standard graphs used to benchmark non-Euclidean embedding models, it is unknown to what extent these models would work for pathway graphs.

— Product Manifold Representations for Learning on Biological Pathways (2401.15478 - McNeela et al., 27 Jan 2024) in Section 2.2 (Pathway Graphs and Embeddings)