Product Manifold Representations for Learning on Biological Pathways.

Area of Science:

• Computational Biology
• Graph Representation Learning
• Network Science

Background:

• Machine learning models embedding graphs in non-Euclidean spaces offer advantages but are under-explored in biological pathway analysis.
• Biological pathway graphs possess complex structures challenging existing embedding methods.
• High-quality embeddings are crucial for understanding disease mechanisms and building predictive models.

Purpose of the Study:

• Investigate the impact of embedding biological pathway graphs in non-Euclidean mixed-curvature spaces.
• Compare mixed-curvature embeddings against traditional Euclidean graph representation learning.
• Evaluate the performance of learned embeddings in predicting missing protein-protein interactions.

Main Methods:

• Employed non-Euclidean mixed-curvature spaces for embedding biological pathway graphs.
• Utilized Mixed-Curvature Product Graph Convolutional Networks (GCNs).
• Trained a supervised model on learned node embeddings for edge prediction.

Main Results:

• Achieved significant reductions in distortion using mixed-curvature embeddings.
• Observed improved in-distribution edge prediction performance with mixed-curvature GCNs.
• Noted underperformance on out-of-distribution edge prediction compared to baselines, suggesting potential overfitting.

Conclusions:

• Mixed-curvature embeddings show promise for analyzing biological pathway graphs, particularly for in-distribution tasks.
• The potential for overfitting in mixed-curvature representations requires further investigation for robust biological network analysis.
• Code for the Mixed-Curvature GCN and pathway analysis is publicly available.