Robust Integrative Analysis of Multi-omics Datasets via Nuclear-norm Maximization

Abstract Spatially multimodal omics technologies provide unprecedented opportunities to address cellular heterogeneity within tissue contexts. However, learning robust and informative latent representations from such complex data remains a significant challenge. Existing graph-based methods often rely on static connections or indirect optimization objectives, which can constrain the discriminability and diversity of the learned representations, particularly in the presence of sequencing noise and unknown biological priors. To overcome these limitations, we propose Robust Integrative Analysis of Multi-omics Datasets via Nuclear-norm Maximization (RIA) to adaptively integrate multimodal features and spatial information through a new graph-based architecture. At the core of RIA is the introduction of the batch nuclear norm maximization (bnm) loss, marking the first application of bnm within the multi-omics domain. By maximizing the nuclear norm of the batch assignment matrix derived from the latent space, RIA simultaneously enhances the discriminability and diversity of the learned embeddings. This objective is synergistically combined with a dynamic prototype contrastive learning strategy and a graph stability loss, ensuring comprehensive and robust optimization.Ultimately, RIA produces a structured, information-rich latent space that enables more reliable downstream analyses, including cell type identification, spatial domain discovery, and microenvironment characterization.