Spatially Aware Nonlinear Dimension Reduction Improves the Efficiency of Spatial Domain Detection in Spatial Multi-Omics Studies

Spatial multi-omics technologies enable the joint characterization of multiple molecular modalities while preserving spatial context, but integrating heterogeneous nonlinear measurements with complex spatial dependencies remains challenging. Here, we introduce SpaLVM, a Bayesian latent variable model that jointly captures cross-modality variation and spatial dependencies through Gaussian process priors, enabling nonlinear dimensionality reduction of spatial multi-omics data. We further develop a sparse, structured variational inference scheme with inducing points for efficient and scalable computation, achieving an approximately 10-fold speedup over the original SpaLVM implementation. Across simulated and real datasets spanning diverse technologies and tissue structures, SpaLVM consistently outperforms existing spatial single-modal, spatial multimodal, non-spatial single-modal, and non-spatial multimodal methods in dimensionality reduction and spatial domain detection. SpaLVM provides a flexible and scalable framework for nonlinear integration and spatial domain detection in spatial multi-omics data.