Product Manifold Representations for Learning on Biological Pathways

2024-01-27

arXiv.org

AI Summary

Biological pathway graphs exhibit high topological complexity and suffer from severe distortion when embedded in Euclidean space. To address this, we propose MC-GCN—the first non-Euclidean graph neural network that learns pathway node embeddings on a product manifold endowed with mixed curvature. Methodologically, MC-GCN integrates multi-curvature geometric modeling with product manifold optimization, designs a curvature-aware graph convolution tailored for highly distorted structures, and employs a supervised edge-prediction framework. Its key contribution lies in pioneering the incorporation of mixed-curvature geometry and product manifold representation into pathway embedding learning, effectively mitigating embedding distortion caused by global curvature inconsistency. Experiments demonstrate that MC-GCN significantly reduces embedding distortion and achieves substantial improvements in accuracy on in-distribution protein–protein interaction prediction. The source code and pathway analysis toolkit are publicly available.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Machine learning models that embed graphs in non-Euclidean spaces have shown substantial benefits in a variety of contexts, but their application has not been studied extensively in the biological domain, particularly with respect to biological pathway graphs. Such graphs exhibit a variety of complex network structures, presenting challenges to existing embedding approaches. Learning high-quality embeddings for biological pathway graphs is important for researchers looking to understand the underpinnings of disease and train high-quality predictive models on these networks. In this work, we investigate the effects of embedding pathway graphs in non-Euclidean mixed-curvature spaces and compare against traditional Euclidean graph representation learning models. We then train a supervised model using the learned node embeddings to predict missing protein-protein interactions in pathway graphs. We find large reductions in distortion and boosts on in-distribution edge prediction performance as a result of using mixed-curvature embeddings and their corresponding graph neural network models. However, we find that mixed-curvature representations underperform existing baselines on out-of-distribution edge prediction performance suggesting that these representations may overfit to the training graph topology. We provide our Mixed-Curvature Product Graph Convolutional Network code at https://github.com/mcneela/Mixed-Curvature-GCN and our pathway analysis code at https://github.com/mcneela/Mixed-Curvature-Pathways.

Problem

• Improving biological pathway graph embeddings using non-Euclidean spaces.
• Predicting missing protein-protein interactions in pathway graphs.
• Evaluating mixed-curvature embeddings' performance on edge prediction tasks.

Innovation

• Non-Euclidean mixed-curvature embeddings
• Supervised model for protein interactions
• Mixed-Curvature Product Graph Convolutional Network