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

Single-cell RNA-sequencing (scRNA-seq) enables the study of hierarchical and branching patterns in organismic development at high resolution. Analyzing such data requires visualization and analysis tools that faithfully represent the deep, tree-like structures formed by developmental lineages. Popular Euclidean embedding methods, such as UMAP and t-SNE, as well as domain-specific approaches like PHATE, distort hierarchical relationships in low dimensions, leading to a decrease in performance with growing tree depth. Hyperbolic geometry, which can represent trees with high accuracy in low dimensions, provides a natural remedy. However, existing hyperbolic methods, such as Poincaré Maps (PM), lose accuracy in deeper trees and require extensive feature engineering and memory. We present Contrastive Poincaré Maps (CPM), a self-supervised hyperbolic encoder that leverages contrastive learning in hyperbolic space to efficiently learn robust low-dimensional representations from scRNA-seq data. On synthetic trees with up to 5 generations and 34,000 individuals, CPM cuts distortion by > 99% and requires 13-fold less memory relative to PM. We further demonstrate CPM’s utility on three biological case studies. CPM uncovers accurate hierarchies across 9 developmental stages in the mouse gastrulation dataset comprising 116,312 cells, disentangles global multi-lineage hierarchies in the chicken cardiogenesis dataset while preserving intra-lineage developmental trends, and enables sampling-densityinvariant hierarchical analysis in the mouse hematopoiesis dataset. By leveraging hyperbolic geometry in combination with contrastive learning, CPM delivers a scalable framework that preserves hierarchical dependencies in developmental lineages, accelerates exploratory data analysis and opens new avenues for biological insights into developmental processes using scRNA-seq data.

A preliminary version of a part of this work was presented at the ICLR Workshop on Machine Learning for Genomics Explorations (Bhasker et al., 2024).