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Hyperbolic Graph Representation Learning for Differential Diagnosis on Biomedical Knowledge Graphs
Pietro Miotto, Lucia Mellini, Tommaso Marzi, Cesare Alippi, Elena Casiraghi, Alberto Paccanaro, Giorgio Valentini, Mauricio Soto-Gomez
TL;DR
Biomedical knowledge graphs combine hierarchical ontologies with transversal links, leaving open whether hyperbolic representations remain useful for heterogeneous patient-level diagnosis. The study evaluates hyperbolic models on ontology subgraphs and patient-integrated disease ranking, finding strong low-dimensional hierarchical performance and promising diagnostic ranking results.
Problem
Method
The study integrates disease and phenotype ontologies with patient profiles and evaluates hyperbolic graph representation models through ontology link prediction and patient–disease link ranking.
Source: §1 · p. 2, §2 · pp. 3–4Results
HGCN outperformed Euclidean GNNs on isolated hierarchical subgraphs with substantially lower-dimensional embeddings, while AttH showed promising ranking performance on the rare-disease diagnosis task.
Source: §4 · p. 10Takeaways & Limitations
The results suggest hyperbolic embeddings can exploit biomedical hierarchy while remaining useful in heterogeneous patient-integrated graphs.
Source: §4 · p. 10Future work will investigate hybrid Euclidean–hyperbolic models, including score-level fusion to capture both transversal and hierarchical relations.
Source: §4 · p. 10
Abstract
from arXiv · showhide
Biomedical knowledge graphs combine ontology-derived hierarchies with transversal associations among heterogeneous entities such as phenotypes, diseases, genes, proteins, and patients. This hybrid structure raises the question of whether hyperbolic embeddings, which naturally capture tree-like organization, remain useful beyond purely hierarchical graphs. We present a preliminary study of hyperbolic graph representation learning for Mendelian-disease differential diagnosis on a patient-integrated biomedical graph. Experiments on isolated ontology subgraphs show that hyperbolic models achieve strong performance in substantially lower dimensions than Euclidean baselines. We then evaluate the models on a link-prediction task that ranks candidate diseases for each patient. Results suggest that hyperbolic embeddings can exploit biomedical hierarchical structure while supporting diagnostic reasoning over heterogeneous patient-level graphs.
1 Introduction
Biomedical knowledge graphs combine hierarchy-rich ontologies with non-hierarchical links, creating uncertainty about whether hyperbolic embeddings remain useful in heterogeneous biomedical settings. This study compares Euclidean and hyperbolic representations on ontology subgraphs and patient-level Mendelian-disease ranking.
1 Introduction
- Biomedical KGs preserve hierarchical ontology structure while adding transversal associations across domains, so their topology is not purely tree-like.Examples include phenotype–disease associations, gene–disease links, protein interactions, and patient similarities.Source: §1 · p. 2
- Hyperbolic spaces’ exponentially growing volume can represent hierarchical structures with lower distortion than flat Euclidean spaces, often at low dimensions.The introduction contrasts exponential node growth with hierarchy depth against polynomial Euclidean volume growth.Source: §1 · p. 2
- The study asks whether hyperbolic models retain an advantage on ontology subgraphs and whether their geometric biases support patient-level Mendelian-disease ranking.The authors note that hyperbolic benefits may diminish when hierarchical DAGs are interconnected by non-hierarchical relationships.Source: §1 · p. 2
- The study integrates disease and phenotype ontologies with Mendelian-disease patient profiles to construct a biomedical graph.Differential diagnosis is formulated as link prediction between patient nodes and disease nodes.Source: §1 · pp. 2–3
- Patient–disease ranking is presented as a clinically relevant test bed because rare-disease diagnosis remains challenging despite the diseases’ substantial collective burden.The passage reports that more than 10,000 rare diseases affect about 5% of the global population.Source: §1 · p. 3
2 Background and Methods
The background frames graph representation learning by embedding geometry and encoder type, then contrasts Euclidean and hyperbolic approaches for structured biomedical graphs. The methods describe shallow and message-passing models, including AttH’s relation-aware transformations, and motivate patient-integrated diagnosis as an underexplored setting.
2 Background and Methods
- Graph representation learning maps graph entities and relations into continuous latent spaces, with methods distinguished by embedding geometry and by shallow versus non-shallow encoding.Shallow models optimize entity and relation lookup-table vectors, whereas non-shallow models learn functions from features and neighborhood structure.Source: §2 · pp. 3–4
- Hyperbolic space’s exponentially expanding volume accommodates tree-like structure with low distortion, while tangent-space operations and Möbius addition support computation on the manifold.Logarithmic and exponential maps connect the curved manifold with its local Euclidean approximation.Source: §2 · p. 4
- AttH enriches shallow hyperbolic translation with relation-specific rotation and reflection, attention over the transformed views, and relation-specific curvature.The transformed head representation is mapped to the manifold, translated by a relation embedding, and scored by negative squared Poincaré distance to the tail.Source: §2 · pp. 4–5
- AttH’s training uses cross-entropy with uniformly sampled corrupted tails, while AttE removes curvature and replaces hyperbolic distance and Möbius addition with Euclidean counterparts.The objective pulls translated heads toward true tails and pushes them away from corrupted tails.Source: §2 · p. 5
- Hyperbolic message-passing models extend graph neural networks to manifolds, and HGCN adds feature mapping, target-centered attention aggregation, and trainable layer-wise curvature.The background characterizes HGCN as an inductive architecture suited to hierarchical and scale-free graphs.Source: §2 · p. 6
- Patient-level phenotypic reasoning with non-Euclidean geometry remains underexplored, motivating tests of whether hyperbolic representations can capture biomedical hierarchy alongside transversal relations.Prior biomedical hyperbolic work largely focused on molecular-scale tasks, while patient-augmented diagnostic work included Euclidean GNNs such as SHEPHERD.Source: §2 · p. 6
3 Experimental Results
The patient-integrated graph combines ontology hierarchies with patient–phenotype and patient–disease associations. AttH leads disease-only ranking across most embedding dimensions, while HGCN outperforms Euclidean GNNs on isolated hierarchies, including at low dimensions.
3 Experimental Results
- The patient-integrated graph contains 28,811 nodes and 178,320 edges spanning Person, Phenotype, and Disease nodes and heterogeneous relations.Disease nodes were restricted to those associated with the patient cohort and their ancestors, while Phenotype nodes were retained to preserve patient descriptions and phenotype hierarchy.Source: §3 · p. 7
3.1 Binary Link Prediction on Isolated Hierarchies
- Isolated ontology evaluation uses transitive-closure SubclassOf hierarchies split 80%–10%–10%, with one uniformly sampled negative edge per positive edge.The task predicts link existence against negative samples.Source: §3.1 · pp. 7–8
- HGCN achieves ROC-AUC > 0.90 with low-dimensional embeddings on both Disease and HPO hierarchies, while Euclidean models reach at most 0.8 only at relatively high dimensions on Disease.Euclidean loss remains higher, particularly on the Phenotype ontology; the authors interpret lower hyperbolic loss as indicating more consistent confidence in predicted hierarchy links.Source: Figure 2 · p. 8, §3.1 · p. 8
3.2 Rank-Based Evaluation for Differential Diagnosis Simulation
- Differential diagnosis is evaluated as ranking candidate Disease tails for each Person using AttH, AttE, and HGCN on a shared split.The test set holds out 10% of existing HasDisease edges, approximately 1% of all targeted-graph edges; all candidate diseases are scored for each test query.Source: §3.2 · pp. 8–9
- HGCN is weakest across the three models and metrics, although its H@10 at d = 10 (0.459) nearly matches AttE (0.464).Source: §3.2 · p. 9
- AttH outperforms AttE and HGCN across embedding dimensions on MRR, MR, and H@10, with its best results at d = 26.At the smallest dimensions, AttH has no consistent advantage over AttE for MRR and H@10 at d = 2 and for MR at d ∈{2, 4}.Source: §3.2 · p. 9, Figure 3 · p. 10
4 Conclusion
This preliminary study finds hyperbolic representation learning promising for biomedical graphs combining ontology hierarchies and transversal associations. HGCN performs strongly on isolated hierarchical subgraphs at substantially lower dimensions, while AttH shows promising rare-disease ranking performance.
4 Conclusion
- HGCN outperforms Euclidean GNNs on isolated hierarchical subgraphs using substantially lower-dimensional embeddings.Source: §4 · p. 10
- AttH shows promising ranking performance in the rare-disease differential diagnosis task.Source: §4 · p. 10
- The study suggests hyperbolic embeddings can exploit biomedical hierarchical structure while remaining useful in heterogeneous patient-integrated graphs.Source: §4 · p. 10
- Future work will investigate hybrid Euclidean–hyperbolic models, including score-level fusion to learn the contributions of both geometries.The proposed aim is to better capture both transversal and hierarchical relations.Source: §4 · p. 10