Uncovering Developmental Lineages from Single-cell Data with Contrastive Poincaré Maps

Embeddings play a central role in single-cell RNA sequencing (scRNA-seq) data analysis by transforming complex gene expression profiles into interpretable, low-dimensional representations. While Euclidean embeddings distort hierarchical relationships in low dimensions, hyperbolic geometry can represent hierarchies accurately in low dimensions. However, existing hyperbolic methods, such as Poincaré Maps (PM), lose accuracy in deeper hierarchies and require extensive feature engineering and memory. We present Contrastive Poincaré Maps (CPM), a scalable approach that reliably preserves inherent hierarchical structures. On synthetic trees with up to five generations and 34,000 individuals, CPM reduces distortion by 99% (1.9 vs. 126.3) and requires 13-fold less memory than PM. We demonstrate CPM's utility across three case studies: scalable analysis of 116,312 mouse gastrulation cells, accurate reconstruction of hierarchical structure in mouse hematopoiesis, and faithful representation of multi-lineage hierarchies in chicken cardiogenesis. By integrating hyperbolic geometry with contrastive learning, CPM enables scalable, structure-preserving embeddings for developmental scRNA-seq data. Code: https://github.com/NithyaBhasker/ContrastivePoincareMaps