AI Insight
Researchers developed a new method called hyperbolic higher-order (HHO) embedding that represents complex biological networks where multiple entities interact simultaneously as groups, not just in pairs. Unlike existing approaches that only capture pairwise connections, HHO embeds simplicial complexes (mathematical structures representing group interactions) into hyperbolic space, preserving information about genuine multi-way interactions such as protein complexes. Tests on synthetic data and real networks, including scientific co-authorship and E. coli protein interactions, demonstrate that HHO more compactly represents actual group interactions and recovers community structure more accurately than pairwise methods.
Why it matters
This advancement could improve our understanding of biological systems where multiple components work together simultaneously, such as protein complexes and metabolic pathways. The method provides a low-dimensional, interpretable representation of complex group interactions that maintains geometric properties useful for analysis while being more faithful to the actual structure of multi-way biological relationships.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: Many biological interactions involve groups rather than pairs, as when several proteins assemble into a multi-protein complex. Simplicial complexes naturally capture these collective interactions. Existing hyperbolic embeddings represent network hierarchy and similarity through a few interpretable coordinates, but rely only on pairwise links: they cannot distinguish three units engaged in a common interaction from three units connected only in pairs. We introduce here the hyperbolic higher-order (HHO) embedding, which embeds a simplicial complex into the Poincar’e disk, while incorporating its group interactions. The hyperbolic area of the triangle spanned by three interacting nodes then measures how compactly their interaction is represented. Testson synthetic and real-world networks, including a co-authorship network and the protein interaction network of textit{Escherichia coli}, show that HHO reduces the hyperbolic area of triangles representing simplices relative to those obtained from pairwise network embeddings. HHO also recovers node groups more accurately than pairwise embeddings and a weighted-clique alternative, with performance competitive with Euclidean embeddings, while providing a low-dimensional representation that can be analyzed with the tools of network geometry.
Source: Hyperbolic embedding of higher-order simplicial networks