Optimal Transport-Based Network Alignment: Graph Classification of Small Molecule Structure-Activity Relationships in Biology

This paper tackles the challenge of aligning graph representations of small biological molecules, crucial for understanding structure-function relationships in biological research. We focus on matching undirected and attributed graphs, addressing the limitations of current methodologies that overlook functional insights provided by node embeddings. Our approach considers graphs as probability distributions in a metric space, introducing a novel embedding scheme that accounts for immediate and secondary neighbors of nodes with continuous attributes. We formulated the graph matching problem as an optimal transport and we present an innovative graph kernel that is based on optimal transport to overcome limitations in traditional kernels, specifically addressing naive aggregation. Experimental results show that our approach outperforms state-of-the-art techniques in five of six common datasets, promising advancements in graph alignment methodologies for molecular analysis and computational biology.Clinical relevance— The porposed method advances drug discovery and development by employing a graph-based framework rooted in optimal transport theory. This approach facilitates enhanced classification of small molecules, notably proteins and enzymes, potentially revolutionizing therapeutic advancements for targeted treatments and drug design precision.