InfoGlobe: Local-and-Global Information-Preserving Statistical Manifold Learning for Single-Cell Transcriptomics

Geometry-preserving dimension reduction is critical for single-cell transcriptomics, where low-dimensional distances should reflect biological divergence between cell types along the transcriptomic manifold. Due to inadequate metrics, the global structure is not sufficiently preserved in the low-dimensional manifold in standard dimension reduction regimes. We model RNA counts as Multinomial samples, leveraging their hierarchical closure property: gene-level counts refine functional gene-group counts via nested Multinomial distributions. Extending Chentsov's Theorem, we show that the Fisher-Rao metric on coarse (gene-group) and fine (gene) statistical manifolds is isometric. Following this isometry property, we propose InfoGlobe, an information-preserving statistical manifold learning framework that projects cells from high-dimensional hyperspheres (full transcriptome) to low-dimensional hyperspheres (functional groups) while preserving information geometry. Embeddings on the low-dimensional sphere explicitly represent Multinomial distributions by functional gene groups. Benchmarks demonstrate superior preservation of local-and-global cell-type geodesic distances, automatic and robust gene-group discovery, nuanced cell subtype resolution without manual feature engineering and natural batch effect mitigation without explicit alignments.

Single-cell sequencing allows researchers to measure gene activity in individual cells, but the resulting data are noisy, high-dimensional, and difficult to interpret. In this work, we introduce InfoGlobe, a method for learning compact and meaningful representations of single-cell data. The key idea is to treat sequencing counts as the outcome of a sampling process and to compare cells using a geometry that better matches this type of data. InfoGlobe preserves both local cell neighborhoods and global relationships between cells, while also identifying interpretable factors that correspond to biological programs. Across multiple single-cell and spatial transcriptomics tasks, InfoGlobe improves visualization, clustering, trajectory analysis, batch-effect mitigation, and spatial domain detection. These results suggest that geometry-aware representation learning can help researchers better understand complex cellular populations and biological processes.