Multi-Manifolds fusing hyperbolic graph network balanced by pareto optimization for identifying spatial domains of spatial transcriptomics

Abstract Identifying spatial domains for spatial transcriptomics is crucial for achieving comprehensive insights into the pathogenesis of gene expression. Increasingly, computational methods based on graph neural networks are being developed for spatial transcriptomics. However, previous methods have solely focused on the Euclidean manifold. To effectively exploit and explore the informative and deeper topological structures of inherent manifolds, we presented a Multi-Manifolds fusing hyperbolic graph network, balanced by Pareto optimization, for identifying spatial domains in Spatial Transcriptomics (MManiST). First, we developed multi-manifolds encoders for distinct manifolds using the hyperbolic neural network. Features from different manifolds were then combined using an attention mechanism, with multiple reconstruction losses balanced by Pareto optimization. Extensive experiments on commonly used benchmark datasets show that our method consistently outperforms seven state-of-the-art methods. Additionally, we investigated the validity of each component and the impact of fusion methods in ablation experiments.